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Effective Stringy Description of Schwarzschild Black Holes

2004
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Advances in Theoretical and Mathematical Physics
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We start by pointing out that certain Riemann surfaces appear rather naturally in the context of wave equations in the black hole background. For a given black hole there are two closely related surfaces. One is the Riemann surface of complexified "tortoise" coordinate. The other Riemann surface appears when the radial wave equation is interpreted as the Fuchsian differential equation. We study these surfaces in detail for the BTZ and Schwarzschild black holes in four and higher dimensions.

doi:10.4310/atmp.2004.v8.n3.a2
fatcat:dzfbd4mh2bfrdaerm4ygd2oyva