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  • 1.
    Andersson, Lars Erik
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.). Albert Einstein Institute, Germany.
    Bäckdahl, T.
    Blue, P.
    Decay of solutions to the Maxwell equation on the Schwarzschild background2016In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 33, no 8, article id 085010Article in journal (Refereed)
    Abstract [en]

    A new Morawetz or integrated local energy decay estimate for Maxwell test fields on the exterior of a Schwarzschild black hole spacetime is proved. The proof makes use of a new superenergy tensor Hab defined in terms of the Maxwell field and its first derivatives. The superenergy tensor, although not conserved, yields a conserved higher order energy current Hab (∂t)b. The tensor Hab vanishes for the static Coulomb field, and the Morawetz estimate proved here therefore yields integrated decay for the Maxwell field to the Coulomb solution on the Schwarzschild exterior.

  • 2. Babiuc, M. C.
    et al.
    Kreiss, Heinz-Otto
    KTH, School of Computer Science and Communication (CSC).
    Winicour, J.
    Testing the well-posedness of characteristic evolution of scalar waves2014In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 31, no 2, p. 025022-Article in journal (Refereed)
    Abstract [en]

    Recent results have revealed a critical way in which lower order terms affect the well-posedness of the characteristic initial value problem for the scalar wave equation. The proper choice of such terms can make the Cauchy problem for scalar waves well posed even on a background spacetime with closed lightlike curves. These results provide new guidance for developing stable characteristic evolution algorithms. In this regard, we present here the finite difference version of these recent results and implement them in a stable evolution code. We describe test results which validate the code and exhibit some of the interesting features due to the lower order terms.

  • 3.
    Beyer, Florian
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Investigations of solutions of Einstein's field equations close to lambda-Taub-NUT2008In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 25, no 23, p. 235005-Article in journal (Refereed)
    Abstract [en]

    We present investigations of a class of solutions of Einstein's field equations close to the family of lambda-Taub-NUT spacetimes. The studies are done using a numerical code introduced by the author elsewhere. One of the main technical complications is due to the S-3-topology of the Cauchy surfaces. Complementing these numerical results with heuristic arguments, we are able to yield some first insights into the strong cosmic censorship issue and the conjectures by Belinskii, Khalatnikov and Lifschitz in this class of spacetimes. In particular, the current investigations suggest that strong cosmic censorship holds in this class. We further identify open issues in our current approach and point to future research projects.

  • 4. Buchert, T.
    et al.
    Carfora, M.
    Ellis, G. F. R.
    Kolb, E. W.
    MacCallum, M. A. H.
    Ostrowski, J. J.
    Rasanen, S.
    Roukema, B. F.
    Andersson, Lars Erik
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Coley, A. A.
    Wiltshire, D. L.
    Is there proof that backreaction of inhomogeneities is irrelevant in cosmology?2015In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 32, no 21, article id 215021Article in journal (Refereed)
    Abstract [en]

    No. In a number of papers, Green and Wald argue that the standard FLRW model approximates our Universe extremely well on all scales, except close to strong-field astrophysical objects. In particular, they argue that the effect of inhomogeneities on average properties of the Universe (backreaction) is irrelevant. We show that this latter claim is not valid. Specifically, we demonstrate, referring to their recent review paper, that (i) their two-dimensional example used to illustrate the fitting problem differs from the actual problem in important respects, and it assumes what is to be proven; (ii) the proof of the trace-free property of backreaction is unphysical and the theorem about it fails to be a mathematically general statement; (iii) the scheme that underlies the trace-free theorem does not involve averaging and therefore does not capture crucial non-local effects; (iv) their arguments are to a large extent coordinate-dependent, and (v) many of their criticisms of backreaction frameworks do not apply to the published definitions of these frameworks. It is therefore incorrect to infer that Green and Wald have proven a general result that addresses the essential physical questions of backreaction in cosmology.

  • 5. Cabrera Pacheco, A. J.
    et al.
    Cederbaum, C.
    McCormick, Stephen
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.). University of New England, Australia.
    Miao, P.
    Asymptotically flat extensions of CMC Bartnik data2017In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 34, no 10, article id 105001Article in journal (Refereed)
    Abstract [en]

    Let g be a metric on the 2-sphere with positive Gaussian curvature and H be a positive constant. Under suitable conditions on (g, H), we construct smooth, asymptotically flat 3-manifolds M with non-negative scalar curvature, with outer-minimizing boundary isometric to and having mean curvature H, such that near infinity M is isometric to a spatial Schwarzschild manifold whose mass m can be made arbitrarily close to a constant multiple of the Hawking mass of . Moreover, this constant multiplicative factor depends only on (g, H) and tends to 1 as H tends to 0. The result provides a new upper bound of the Bartnik mass associated with such boundary data.

  • 6. Cognola, Guido
    et al.
    Myrzakulov, Ratbay
    Sebastiani, Lorenzo
    Vagnozzi, Sunny
    Zerbini, Sergio
    Covariant Horava-like and mimetic Horndeski gravity: cosmological solutions and perturbations2016In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 33, no 22, article id 225014Article in journal (Refereed)
    Abstract [en]

    We consider a variant of the Nojiri-Odintsov covariant Horava-like gravitational model, where diffeomorphism invariance is broken dynamically via a non-standard coupling to a perfect fluid. The theory allows one to address some of the potential instability problems present in Horava-Lifshitz gravity due to explicit diffeomorphism invariance breaking. The fluid is instead constructed from a scalar field constrained by a Lagrange multiplier. In fact, the Lagrange multiplier construction allows for an extension of the Horavalike model to include the scalar field of mimetic gravity, an extension which we thoroughly explore. By adding a potential for the scalar field, we show how one can reproduce a number of interesting cosmological scenarios. We then turn to the study of perturbations around a flat FLRW background, showing that the fluid in question behaves as an irrotational fluid, with zero sound speed. To address this problem, we consider a modified version of the theory, adding higher derivative terms in a way which brings us beyond the Horndeski framework. We compute the sound speed in this modified higher order mimetic Horava-like model and show that it is non-zero, which means that perturbations therein can be sensibly defined. Caveats to our analysis, as well as comparisons to projectable Horava-Lifshitz gravity, are also discussed. In conclusion, we present a theory of gravity which preserves diffeomorphism invariance at the level of the action but breaks it dynamically in the UV, reduces to General Relativity (GR) in the IR, allows the realization of a number of interesting cosmological scenarios, is well defined when considering perturbations around a flat FLRW background, and features cosmological dark matter emerging as an integration constant.

  • 7. Conroy, Aindriu
    et al.
    Koivisto, Tomi
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Mazumdar, Anupam
    Teimouri, Ali
    Generalized quadratic curvature, non-local infrared modifications of gravity and Newtonian potentials2015In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 32, no 1, p. 015024-Article in journal (Refereed)
    Abstract [en]

    Metric theories of gravity are studied, beginning with a general action that is quadratic in curvature and allows arbitrary inverse powers of the d' Alembertian operator, resulting in infrared non-local extensions of general relativity. The field equations are derived in full generality and their consistency is checked by verifying the Bianchi identities. The weak-field limit is computed and a straightforward algorithm is presented to infer the post-Newtonian corrections directly from the action. This is then applied to various infrared gravity models including non-local Rf (R/square) dark energy and non-local massive gravity models. Generically, the Newtonian potentials are not identical and deviate from the 1/r behaviour at large distances. However, the former does not occur in a specific class of theories that does not introduce additional degrees of freedom in flat spacetime. A new non-local model within this class is proposed, defined by the exponential of the inverse d' Alembertian. This model exhibits novel features, such as the weakening of the gravity in the infrared, suggesting de-gravitation of the cosmological constant.

  • 8.
    Dahl, Mattias
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Gicquaud, Romain
    Humbert, Emmanuel
    A non-existence result for a generalization of the equations of the conformal method in general relativity2013In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 30, no 7, p. 075004-Article in journal (Refereed)
    Abstract [en]

    The constraint equations of general relativity can in many cases be solved by the conformal method. We show that a slight modification of the equations of the conformal method admits no solution for a broad range of parameters. This suggests that the question of existence or non-existence of solutions to the original equations is more subtle than could perhaps be expected.

  • 9. Golovnev, Alexey
    et al.
    Koivisto, Tomi
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Sandstad, Marit
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    On the covariance of teleparallel gravity theories2017In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 34, no 14, article id 145013Article in journal (Refereed)
    Abstract [en]

    The basics of teleparallel gravity and its extensions are reviewed with particular emphasis on the problem of the Lorentz-breaking choice of connection in pure-tetrad versions of the theories. Various possible ways to covariantise such models are discussed. A by-product is a new form of f (T) field equations.

  • 10.
    Guica, Monica
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Uppsala University, Uppsala.
    Ross, Simon F.
    Behind the geon horizon2015In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 32, no 5, article id 055014Article in journal (Refereed)
    Abstract [en]

    We explore the Papadodimas-Raju prescription for reconstructing the region behind the horizon of one-sided black holes in AdS/CFT in the case of the. P2 geon-a simple, analytic example of a single-sided, asymptotically AdS(3) black hole, which corresponds to a pure CFT state that thermalizes at late times. We show that in this specific example, the mirror operators involved in the reconstruction of the interior have a particularly simple form: the mirror of a single trace operator at late times is just the corresponding single trace operator at early times. We use some explicit examples to explore how changes in the state modify the geometry inside the horizon.

  • 11. Heinzle, J. Mark
    et al.
    Ringström, Hans
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Future asymptotics of vacuum Bianchi type VI0 solutions2009In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 26, no 14Article in journal (Refereed)
    Abstract [en]

    In this paper, we present a thorough analysis of the future asymptotic dynamics of spatially homogeneous cosmological models of Bianchi type VI0. Each of these models converges to a flat Kasner solution (Taub solution) for late times; we give detailed asymptotic expansions describing this convergence. In particular, we prove that the future asymptotics of Bianchi type VI0 solutions cannot be approximated in any way by Bianchi type II solutions, which is in contrast to Bianchi type VIII and IX models (in the direction toward the singularity). The paper contains an extensive introduction where we put the results into a broader context. The core of these considerations consists in the fact that there exist regions in the phase space of Bianchi type VIII models where solutions can be approximated, to a high degree of accuracy, by type VI0 solutions. The behavior of solutions in these regions is essential for the question of 'locality', i.e., whether particle horizons form or not. Since Bianchi type VIII models are conjectured to be important role models for generic cosmological singularities, our understanding of Bianchi type VI0 dynamics might thus be crucial to help to shed some light on the important question of whether to expect generic singularities to be local or not.

  • 12.
    Heisenberg, Lavinia
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Quantum corrections in massive bigravity and new effective composite metrics2015In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 32, no 10, article id 105011Article in journal (Refereed)
    Abstract [en]

    We compute the one-loop quantum corrections to the interactions between the two metrics of the ghost-free massive bigravity. When considering gravitons running in the loops, we show how the structure of the interactions gets destabilized at the quantum level, exactly in the same way as in its massive gravity limit. A priori one might have expected a better quantum behavior, however, the broken diffeomorphism invariance out of the two initial diffeomorphisms in bigravity has similar consequences at the quantum level as the broken diffeomorphism in massive gravity. From lessons of the generated quantum corrections through matter loops we propose yet other types of effective composite metrics to which the matter fields can couple. Among these new effective metrics there might be one or more that could provide interesting phenomenology and important cosmological implications.

  • 13.
    Hossenfelder, Sabine
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm Univ, Sweden.
    A no-go theorem for Poincare-invariant networks2015In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 32, no 20, article id 207001Article in journal (Refereed)
    Abstract [en]

    I explain why there are no Poincare-invariant networks with a locally finite distribution of nodes and links in Minkowski-spacetime of any dimension.

  • 14. Hossenfelder, Sabine
    et al.
    Zingg, Tobias
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Analogue gravity models from conformal rescaling2017In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 34, no 16, article id 165004Article in journal (Refereed)
    Abstract [en]

    Analogue gravity is based on a mathematical identity between quantum field theory in curved space-time and the propagation of perturbations in certain condensed matter systems. But not every curved space-time can be simulated in such a way. For analogue gravity to work, one needs not only a condensed matter system that generates the desired metric tensor, but this system then also has to obey its own equations of motion. However, the relation to the metric tensor usually overdetermines the equations of the underlying condensed matter system, such that they in general cannot be fulfilled. In this case the desired metric does not have an analogue. Here, we show that the class of metrics that have an analogue is larger than previously thought. The reason is that the analogue metric is only defined up to a choice of parametrization of the perturbation in the underlying condensed matter system. In this way, the class of analogue gravity models can be vastly expanded.

  • 15. Jiménez, Jose Beltran
    et al.
    Koivisto, Tomi S.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Extended Gauss-Bonnet gravities in Weyl geometry2014In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 31, no 13, p. 135002-Article in journal (Refereed)
    Abstract [en]

    In this paper we consider an extended Gauss-Bonnet gravity theory in arbitrary dimensions and in a space provided with a Weyl connection, which is torsion-free but non-metric-compatible, the non-metricity tensor being determined by a vector field. The action considered consists of the usual Einstein-Hilbert action plus all the terms quadratic in the curvature that reduce to the usual Gauss-Bonnet term for vanishing Weyl connection, i.e., when only the Levi-Civita part of the connection is present. We expand the action in terms of Riemannian quantities and obtain vector-tensor theories. We find that all the free parameters only appear in the kinetic term of the vector field, so two branches are possible: one with a propagating vector field and another one where the vector field does not propagate. We focus on the propagating case. We find that in four dimensions, the theory is equivalent to Einstein's gravity plus a Proca field. This field is naturally decoupled from matter, so it represents a natural dark matter candidate. Also for d = 4, we discuss a non-trivial cubic term in the curvature that can be constructed without spoiling the second-order nature of the field equations, because it leads to the vector-tensor Horndeski interaction. In arbitrary dimensions, the theory becomes more involved. We show that, even though the vector field presents kinetic interactions which do not have U(1) symmetry, there are no additional propagating degrees of freedom with respect to the usual massive case. We show that, interestingly, this relies on the fact that the corresponding Stuckelberg field belongs to a specific class within the general Horndeski theories. Finally, since Weyl geometries provide the natural ground on which to build scale invariant theories, we apply the usual Weyl gauging in order to make the Horndeski action locally scale invariant, and discuss new terms that can be added.

  • 16.
    Keränen, Ville
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Thorlacius, Larus
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Thermal correlators in holographic models with Lifshitz scaling2012In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 29, no 19, p. 194009-Article in journal (Refereed)
    Abstract [en]

    We study finite temperature effects in two distinct holographic models that exhibit Lifshitz scaling, looking to identify model independent features in the dual strong coupling physics. We consider the thermodynamics of black branes and find different low-temperature behavior of the specific heat. Deformation away from criticality leads to non-trivial temperature dependence of correlation functions and we study how the characteristic length scale in the two point function of scalar operators varies as a function of temperature and deformation parameters.

  • 17. Khoo, Fech Scen
    et al.
    Ong, Yen Chin
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Lux in obscuro: photon orbits of extremal black holes revisited2016In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 33, no 23, article id 235002Article in journal (Refereed)
    Abstract [en]

    It has been shown in the literature that the event horizon of an asymptotically flat extremal Reissner-Nordstrom black hole is also a stable photon sphere. We further clarify this statement and give a general proof that this holds for a large class of static spherically symmetric black hole spacetimes with an extremal horizon. In contrast, in the Doran frame, an asymptotically flat extremal Kerr black hole has an unstable photon orbit on the equatorial plane of its horizon. In addition, we show that an asymptotically flat extremal Kerr-Newman black hole exhibits two equatorial photon orbits if a < M/2, one of which is on the extremal horizon in the Doran frame and is stable, whereas the second one outside the horizon is unstable. For a > M/2, there is only one equatorial photon orbit, located on the extremal horizon, and it is unstable. There can be no photon orbit on the horizon of a non-extremal Kerr-Newman black hole.

  • 18. Kozameh, Carlos
    et al.
    Kreiss, Heinz-Otto
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis and Computer Science, NADA.
    Reula, Oscar
    On the well posedness of Robinson-Trautman-Maxwell solutions2008In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 25, no 2, p. 025004-Article in journal (Refereed)
    Abstract [en]

    We show that the so-called Robinson - Trautman - Maxwell equations do not constitute a well-posed initial-value problem. That is, the dependence of the solution on the initial data is not continuous in any norm built out from the initial data and a finite number of its derivatives. Thus, they cannot be used to solve for solutions outside the analytic domain.

  • 19.
    Kreiss, Heinz-Otto
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis and Computer Science, NADA.
    Reula, O.
    Sarbach, O.
    Winicour, J.
    Well-posed initial-boundary value problem for the harmonic Einstein equations using energy estimates2007In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 24, no 23, p. 5973-5984Article in journal (Refereed)
    Abstract [en]

    In recent work, we used pseudo-differential theory to establish conditions that the initial-boundary value problem for second-order systems of wave equations be strongly well-posed in a generalized sense. The applications included the harmonic version of the Einstein equations. Here we show that these results can also be obtained via standard energy estimates, thus establishing strong well-posedness of the harmonic Einstein problem in the classical sense.

  • 20.
    Kreiss, Heinz-Otto
    et al.
    KTH, School of Computer Science and Communication (CSC).
    Winicour, J.
    Geometric boundary data for the gravitational field2014In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 31, no 6, p. 065004-Article in journal (Refereed)
    Abstract [en]

    An outstanding issue in the treatment of boundaries in general relativity is the lack of a local geometric interpretation of the necessary boundary data. For the Cauchy problem, the initial data is supplied by the 3-metric and extrinsic curvature of the initialCauchy hypersurface, subject to constraints. This Cauchy data determine a solution to Einstein's equations which is unique up to a diffeomorphism. Here, we show how three pieces of unconstrained boundary data, which are associated locally with the geometry of the boundary, likewise determine a solution of the initial-boundary value problem which is unique, up to a diffeomorphism. Two pieces of this data constitute a conformal class of rank-2 metrics, which represent the two gravitational degrees of freedom. The third piece, constructed from the extrinsic curvature of the boundary, determines the dynamical evolution of the boundary.

  • 21.
    Kreiss, Heinz-Otto
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis and Computer Science, NADA.
    Winicour, J.
    Problems which are well posed in a generalized sense with applications to the Einstein equations2006In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 23, no 16, p. S405-S420Article in journal (Refereed)
    Abstract [en]

    In the harmonic description of general relativity, the principal part of the Einstein equations reduces to a constrained system of ten curved space wave equations for the components of the spacetime metric. We use the pseudo-differential theory of systems which are strongly well posed in the generalized sense to establish the well posedness of constraint-preserving boundary conditions for this system when treated in a second-order differential form. The boundary conditions are of a generalized Sommerfeld type that is benevolent for numerical calculation.

  • 22.
    Kreiss, Heinz-Otto
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis and Computer Science, NADA.
    Winicour, J.
    The well-posedness of the null-timelike boundary problem for quasilinear waves2011In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 28, no 14, p. 145020-Article in journal (Refereed)
    Abstract [en]

    The null-timelike initial-boundary value problem for a hyperbolic system of equations consists of the evolution of data given on an initial characteristic surface and on a timelike worldtube to produce a solution in the exterior of the worldtube. We establish the well-posedness of this problem for the evolution of a quasilinear scalar wave by means of energy estimates. The treatment is given in characteristic coordinates and thus provides a guide for developing stable finite difference algorithms. A new technique underlying the approach has potential application to other characteristic initial-boundary value problems.

  • 23.
    McInnes, Brett
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Shearing black holes and scans of the quark matter phase diagram2014In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 31, no 2, p. 025009-Article in journal (Refereed)
    Abstract [en]

    Future facilities such as FAIR and NICA are expected to produce collisions of heavy ions generating quark-gluon plasmas (QGPs) with large values of the quark chemical potential; peripheral collisions in such experiments will also lead to large values of the angular momentum density, associated with the internal shearing motion of the plasma. It is well known that shearing motions in fluids can lead to instabilities which cause a transition from laminar to turbulent flow, and such instabilities in the QGP have recently attracted some attention. We set up a holographic model of this situation by constructing a gravitational dual system exhibiting an instability which is indeed triggered by shearing angular momentum in the bulk. We show that holography indicates that the transition to an unstable fluid happens more quickly as one scans across the quark matter phase diagram towards large values of the chemical potential. This may have negative consequences for the observability of quark polarization effects.

  • 24. Myrzakulov, Ratbay
    et al.
    Sebastiani, Lorenzo
    Vagnozzi, Sunny
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm University, Sweden.
    Zerbini, Sergio
    Static spherically symmetric solutions in mimetic gravity: rotation curves and wormholes2016In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 33, no 12, article id 125005Article in journal (Refereed)
    Abstract [en]

    In this work, we analyse static spherically symmetric solutions in the framework of mimetic gravity, an extension of general relativity where the con-formal degree of freedom of gravity is isolated in a covariant fashion. Here we extend previous works by considering, in addition, a potential for the mimetic field. An appropriate choice of such a potential allows for the reconstruction of a number of interesting cosmological and astrophysical scenarios. We explicitly show how to reconstruct such a potential for a general static spherically symmetric space-time. A number of applications and scenarios are then explored, among which are traversable wormholes. Finally, we analytically reconstruct potentials, which leads to solutions to the equations of motion featuring polynomial corrections to the Schwarzschild space-time. Accurate choices for such corrections could provide an explanation for the inferred flat rotation curves of spiral galaxies within the mimetic gravity framework, without the need for particle dark matter.

  • 25.
    Nungesser, Ernesto
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Lim, Woei Chet
    The electromagnetic spike solutions2013In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 30, no 23, p. 235020-Article in journal (Refereed)
    Abstract [en]

    The aim of this paper is to use the existing relation between polarized electromagnetic Gowdy spacetimes and vacuum Gowdy spacetimes to find explicit solutions for electromagnetic spikes by a procedure which has been developed by one of the authors for gravitational spikes. We present new inhomogeneous solutions which we call the EME and MEM electromagnetic spike solutions.

  • 26. Ringström, Hans
    Asymptotic expansions close to the singularity in Gowdy spacetimes2004In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 21, no 3, p. S305-S322Article in journal (Refereed)
    Abstract [en]

    We consider Gowdy spacetimes under the assumption that the spatial hypersurfaces are diffeomorphic to the torus. The relevant equations are then wave map equations with the hyperbolic space as a target. In a paper by Grubisic and Moncrief, a formal expansion of solutions in the direction towards the singularity was proposed. Later, Kichenassamy and Rendall constructed a family of real analytic solutions with the maximum number of free functions and the desired asymptotics at the singularity. The condition of real analyticity was subsequently removed by Rendall. In a previous paper, we proved that one can put a condition on initial data that leads to asymptotic expansions. However, control of up to and including three derivatives in L-2 was necessary, and the condition was rather technical. The main point of the present paper is to demonstrate the existence of certain monotone quantities and to illustrate how these can be used to weaken the assumptions to one derivative in the sup norm. Furthermore, we demonstrate that the false spikes do not appear in the disc model. Finally, we show that knowledge concerning the behaviour of the solution (as time tends to the singularity) for one fixed spatial point in some situations can be used to conclude that there are smooth expansions in the neighbourhood of that spatial point.

  • 27.
    Ringström, Hans
    KTH, Superseded Departments, Mathematics.
    Curvature blow up in Bianchi VIII and IX vacuum spacetimes2000In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 17, no 4, p. 713-731Article in journal (Refereed)
    Abstract [en]

    The maximal globally hyperbolic development of non-Taub-NUT Bianchi IX vacuum initial data and of non-NUT Bianchi VIII vacuum initial data is C-2-inextendible. Furthermore, a curvature invariant is unbounded in the incomplete directions of inextendible causal geodesics.

  • 28.
    Ringström, Hans
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Data at the moment of infinite expansion for polarized Gowdy2005In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 22, no 9, p. 1647-1653Article in journal (Refereed)
    Abstract [en]

    In a recent paper by Thomas Jurke, it was proved that the asymptotic behaviour of a solution to the polarized Gowdy equation in the expanding direction is of the form alpha ln t + beta + t(-1/2)v + O(t(-3/2)), where alpha and beta are constants and v is a solution to the standard wave equation with zero mean value. Furthermore, it was proved that alpha, beta and v uniquely determine the solution. Here we wish to point out that given alpha, beta and v with the above properties, one can construct a solution to the polarized Gowdy equation with the above asymptotics. In other words, we show that alpha, beta and v constitute data at the moment of infinite expansion. We then use this fact to make the observation that there are polarized Gowdy spacetimes such that in the areal time coordinate, the quotient of the maximum and the minimum of the mean curvature on a constant time hypersurface is unbounded as time tends to infinity.

  • 29. Ringström, Hans
    Future asymptotic expansions of Bianchi VIII vacuum metrics2003In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 20, no 11, p. 1943-1989Article in journal (Refereed)
    Abstract [en]

    Bianchi VIII vacuum solutions to Einstein's equations are causally geodesically complete to the future, given an appropriate time orientation, and the objective of this paper is to analyse the asymptotic behaviour of solutions in this time direction. For the Bianchi class A spacetimes, there is a formulation of the field equations that was presented in a paper by Wainwright and Hsu, and in a previous paper we analysed the asymptotic behaviour of solutions in these variables. One objective of this paper is to give an asymptotic expansion for the metric. Furthermore, we relate this expansion to the topology of the compactified spatial hypersurfaces of homogeneity. The compactified spatial hypersurfaces have the topology of Seifert fibred spaces, and we prove that in the case of NUT Bianchi VIII spacetimes, the length of a circle fibre converges to a positive constant but that in the case of general Bianchi VIII solutions, the length tends to infinity at a rate we determine. Finally, we give asymptotic expansions for general Bianchi VII0 metrics.

  • 30.
    Ringström, Hans
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Origins and development of the Cauchy problem in general relativity2015In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 32, no 12, article id 124003Article in journal (Refereed)
    Abstract [en]

    The seminal work of Yvonne Choquet-Bruhat published in 1952 demonstrates that it is possible to formulate Einstein's equations as an initial value problem. The purpose of this article is to describe the background to and impact of this achievement, as well as the result itself. In some respects, the idea of viewing the field equations of general relativity as a system of evolution equations goes back to Einstein himself; in an argument justifying that gravitational waves propagate at the speed of light, Einstein used a special choice of coordinates to derive a system of wave equations for the linear perturbations on a Minkowski background. Over the following decades, Hilbert, de Donder, Lanczos, Darmois and many others worked to put Einstein's ideas on a more solid footing. In fact, the issue of local uniqueness (giving a rigorous justification for the statement that the speed of propagation of the gravitational field is bounded by that of light) was already settled in the 1930s by the work of Stellmacher. However, the first person to demonstrate both local existence and uniqueness in a setting in which the notion of finite speed of propagation makes sense was Yvonne Choquet-Bruhat. In this sense, her work lays the foundation for the formulation of Einstein's equations as an initial value problem. Following a description of the results of Choquet-Bruhat, we discuss the development of three research topics that have their origin in her work. The first one is local existence. One reason for addressing it is that it is at the heart of the original paper. Moreover, it is still an active and important research field, connected to the problem of characterizing the asymptotic behaviour of solutions that blow up in finite time. As a second topic, we turn to the questions of global uniqueness and strong cosmic censorship. These questions are of fundamental importance to anyone interested in justifying that the Cauchy problem makes sense globally. They are also closely related to the issue of singularities in general relativity. Finally, we discuss the topic of stability of solutions to Einstein's equations. This is not only an important and active area of research, it is also one that only became meaningful thanks to the work of Yvonne Choquet-Bruhat.

  • 31.
    Ringström, Hans
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Strong cosmic censorship in the case of T(3)-Gowdy vacuum spacetimes2008In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 25, no 11, p. 114010-Article in journal (Refereed)
    Abstract [en]

    In 1952, Yvonne Choquet-Bruhat demonstrated that it makes sense to consider Einstein's vacuum equations from an initial value point of view; given initial data, there is a globally hyperbolic development. Since there are many developments, one does, however, not obtain uniqueness. This was remedied in 1969 when Choquet-Bruhat and Robert Geroch demonstrated that there is a unique maximal globally hyperbolic development (MGHD). Unfortunately, there are examples of initial data for which the MGHD is extendible, and, what is worse, extendible in inequivalent ways. Thus it is not possible to predict what spacetime one is in simply by looking at initial data and, in this sense, Einstein's equations are not deterministic. Since the examples exhibiting this behaviour are rather special, it is natural to conjecture that for generic initial data, the MGHD is inextendible. This conjecture is referred to as the strong cosmic censorship conjecture and is of central importance in mathematical relativity. In this paper, we shall describe this conjecture in detail, as well as its resolution in the special case of T(3)-Gowdy spacetimes.

  • 32. Ringström, Hans
    The future asymptotics of Bianchi VIII vacuum solutions2001In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 18, no 18, p. 3791-3823Article in journal (Refereed)
    Abstract [en]

    Bianchi VIII vacuum solutions to Einstein's equations are causally geodesically complete to the future, given an appropriate time orientation, and the objective of this paper is to analyse the asymptotic behaviour of solutions in this time direction. For the Bianchi class A spacetimes, there is a formulation of the field equations that was presented in an article by Wainwright and Hsu, and we will analyse the asymptotic behaviour of solutions in these variables. We also try to give the analytic results a geometric interpretation by analysing how a normalized version of the Riemannian metric on the spatial hypersurfaces of homogeneity evolves.

  • 33.
    Sakovich, Anna
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Constant mean curvature solutions of the Einstein-scalar field constraint equations on asymptotically hyperbolic manifolds2010In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 27, no 24, p. 245019-Article in journal (Refereed)
  • 34.
    Zlosnik, Tom
    et al.
    Czech Acad Sci, Inst Phys, CEICO, Slovance 1999-2, Prague 18221, Czech Republic..
    Urban, Federico
    Czech Acad Sci, Inst Phys, CEICO, Slovance 1999-2, Prague 18221, Czech Republic..
    Marzola, Luca
    NICPB, Ravala Pst 10, EE-10143 Tallinn, Estonia..
    Koivisto, Tomi S.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. NICPB, Ravala Pst 10, EE-10143 Tallinn, Estonia.
    Spacetime and dark matter from spontaneous breaking of Lorentz symmetry2018In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 35, no 23, article id 235003Article in journal (Refereed)
    Abstract [en]

    It is shown that a spontaneously-broken gauge theory of the Lorentz group contains Ashtekar's chiral formulation of general relativity accompanied by dust. From this perspective, gravity is described entirely by a connection omega valued in the Lie algebra of the complexified Lorentz group and a Lorentz-charged scalar field tau. The model is 'pre-geometric' in the sense that the spacetime metric may be constructed only in the symmetry-broken regime. We speculate on the extent to which this dust may account for dark matter and on the behaviour of the theory in regimes where the symmetry is not broken.

1 - 34 of 34
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