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Some new perspectives on the Kruskal–Szekeres extension with applications to photon surfaces
Department of Mathematics, University of Tuebingen, Tübingen, Germany.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.). Department of Mathematics, University of Tuebingen, Tübingen, Germany.
2024 (English)In: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 114, no 2, article id 40Article in journal (Refereed) Published
Abstract [en]

It is a well-known fact that the Schwarzschild spacetime admits a maximal spacetime extension in null coordinates which extends the exterior Schwarzschild region past the Killing horizon, called the Kruskal–Szekeres extension. This method of extending the Schwarzschild spacetime was later generalized by Brill–Hayward to a class of spacetimes of “profile h” across non-degenerate Killing horizons. Circumventing analytical subtleties in their approach, we reconfirm this fact by reformulating the problem as an ODE, and showing that the ODE admits a solution if and only if the naturally arising Killing horizon is non-degenerate. Notably, this approach lends itself to discussing regularity across the horizon for non-smooth metrics. We will discuss applications to the study of photon surfaces, extending results by Cederbaum–Galloway and Cederbaum–Jahns–Vičánek-Martínez beyond the Killing horizon. In particular, our analysis asserts that photon surfaces approaching the Killing horizon must necessarily cross it.

Place, publisher, year, edition, pages
Springer Nature , 2024. Vol. 114, no 2, article id 40
Keywords [en]
53B20, 83C05, 83C75, Double null coordinates, Photon surfaces, Spacetime extensions
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:kth:diva-344603DOI: 10.1007/s11005-024-01779-yISI: 001176972000002Scopus ID: 2-s2.0-85187174334OAI: oai:DiVA.org:kth-344603DiVA, id: diva2:1845991
Note

QC 20240321

Available from: 2024-03-20 Created: 2024-03-20 Last updated: 2024-10-07Bibliographically approved

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Wolff, Markus

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CiteExportLink to record
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