Geometric properties of a 2-D space-time arising in 4-D black hole physics
| Autor: | Casals, Marc, Nolan, Brien C. |
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| Rok vydání: | 2015 |
| Předmět: | |
| Zdroj: | Phys. Rev. D 92, 104030 (2015) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevD.92.104030 |
| Popis: | 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. Comment: 19 pages, 6 figures |
| Databáze: | arXiv |
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