English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

It is a well-known fact that the Schwarzschild spacetime admits a maximalspacetime extension in null coordinates which extends the exteriorSchwarzschild region past the Killing horizon, called the Kruskal-Szekeresextension. This method of extending the Schwarzschild spacetime was latergeneralized by Brill-Hayward to a class of spacetimes of "profile $h$" acrossnon-degenerate Killing horizons. Circumventing analytical subtleties in theirapproach, we reconfirm this fact by reformulating the problem as an ODE, andshowing that the ODE admits a solution if and only if the naturally arisingKilling horizon is non-degenerate. Notably, this approach lends itself todiscussing regularity across the horizon for non-smooth metrics.  We will discuss applications to the study of photon surfaces, extendingresults by Cederbaum-Galloway and Cederbaum-Jahns-Vi\v{c}\'{a}nek-Mart\'{i}nezbeyond the Killing horizon. In particular, our analysis asserts that photonsurfaces approaching the Killing horizon must necessarily cross it.

Some new perspectives on the Kruskal--Szekeres extension with applications to photon surfaces