The Problem of Time in the Quantum Theory of Black Holes | Zendy

Takayuki Hori | Zendy

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The Problem of Time in the Quantum Theory of Black Holes

Author(s) -

Takayuki Hori

Publication year - 1998

Publication title -

progress of theoretical physics

Language(s) - English

Resource type - Journals

eISSN - 1347-4081

pISSN - 0033-068X

DOI - 10.1143/ptp.100.191

Subject(s) - physics , hamiltonian constraint , hamiltonian (control theory) , mathematical physics , problem of time , constraint (computer aided design) , wheeler–dewitt equation , einstein , classical mechanics , quantum gravity , metric (unit) , theoretical physics , quantum , quantum mechanics , quantum cosmology , loop quantum gravity , mathematical optimization , operations management , mathematics , economics , mechanical engineering , engineering

We discuss the problem of time in spherically symmetric pure Einstein gravitywith the cosmological term by using an exact solution to the Wheeler-DeWittequation. A positive definite inner product is defined, based on the momentumconstraint rather than the hamiltonian constraint. A natural notion of time isintroduced via the Heisenberg equation. This notion enables one to reproducethe time-time component of the classical metric. Non-Hermiticity of thehamiltonian is essential in the definition of time.Comment: 9 pages,LaTeX, no figure

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