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

The Schwarzschild exterior space-time is conformally related to a directproduct space-time, $\mathcal{M}_2 \times S_2$, where $\mathcal{M}_2$ is atwo-dimensional space-time. This direct product structure arises naturally whenconsidering the wave equation on the Schwarzschild background. Motivated bythis, we establish some geometrical results relating to $\mathcal{M}_2$ thatare useful for black hole physics. We prove that $\mathcal{M}_2$ has the rareproperty of being a causal domain. Consequently, Synge's world function and theHadamard form for the Green function on this space-time are well-definedglobally. We calculate the world function and the van Vleck determinant on$\mathcal{M}_2$ numerically and point out how these results will be used toestablish global properties of Green functions on the Schwarzschild black holespace-time.

Geometric properties of a 2-D space-time arising in 4-D black hole physics