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arXiv · 1810.00020

Near-horizon modes and self-adjoint extensions of the Schroedinger operator

A. P. Balachandran·A. R. de Queiroz·Alberto Saa
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Abstract

We investigate the dynamics of scalar fields in the near-horizon exterior region of a Schwarzschild black hole. We show that low-energy modes are typically long-living and might be considered as being confined near the black hole horizon. Such dynamics are effectively governed by a Schroedinger operator with infinitely many self-adjoint extensions parameterized by $U(1)$, a situation closely resembling the case of an ordinary free particle moving on a semiaxis. Even though these different self-adjoint extensions lead to equivalent scattering and thermal processes, a comparison with a simplified model suggests a physical prescription to chose the pertinent self-adjoint extensions. However, since all extensions are in principle physically equivalent, they might be considered in equal footing for statistical analyses of near-horizon modes around black holes. Analogous results hold for any non-extremal, spherically symmetric, asymptotically flat black hole.

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A. P. Balachandran, A. R. de Queiroz, Alberto Saa. 2018-09-28. Near-horizon modes and self-adjoint extensions of the Schroedinger operator. https://doi.org/10.1007/978-3-030-24748-5_3

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