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The Problem of Time in the Quantum Theory of Black Holes

Takayuki Hori
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Abstract

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.

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Takayuki Hori. 1998-06-15. The Problem of Time in the Quantum Theory of Black Holes. https://doi.org/10.1143/ptp.100.191

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