The Problem of Time in the Quantum Theory of Black Holes

We discuss the problem of time in spherically symmetric pure Einstein gravity with the cosmological term by using an exact solution to the Wheeler-DeWitt equation. A positive definite inner product is defined, based on the momentum constraint rather than the hamiltonian constraint. A natural notion...

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Bibliographic Details
Published inarXiv.org
Main Author Hori, Takayuki
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 15.06.1998
Subjects
Black holes
Quantum theory
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Summary:We discuss the problem of time in spherically symmetric pure Einstein gravity with the cosmological term by using an exact solution to the Wheeler-DeWitt equation. A positive definite inner product is defined, based on the momentum constraint rather than the hamiltonian constraint. A natural notion of time is introduced via the Heisenberg equation. This notion enables one to reproduce the time-time component of the classical metric. Non-Hermiticity of the hamiltonian is essential in the definition of time.
ISSN:2331-8422
DOI:10.48550/arxiv.9806111