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arXiv · 1509.03911

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

Marc Casals·Brien C. Nolan
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Abstract

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

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Marc Casals, Brien C. Nolan. 2015-09-13. Geometric properties of a 2-D space-time arising in 4-D black hole physics. https://doi.org/10.1103/physrevd.92.104030

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