The Problem of Time in the Quantum Theory of Black Holes

Details The Problem of Time in the Quantum Theory of Black Holes The Problem of Time in the Quantum Theory of Black Holes

1998-06-15

arxiv.org/abs/hep-th/9806111v1

Prog.Theor.Phys.100:191-198,1998

Physics

High Energy Physics

High Energy Physics - Theory

9 pages,LaTeX, no figures

Scientific paper

10.1143/PTP.100.191

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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