'Time'-covariant Schr\'odinger equation and the canonical quantization of the Reissner-Nordstr\'om black hole
| Autor: | T. Pailas |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Physics and Astronomy (miscellaneous)
Reissner–Nordström black hole Canonical quantization Schrödinger equation horizons 01 natural sciences General Relativity and Quantum Cosmology problem of time symbols.namesake canonical quantization Singularity Minisuperspace 0103 physical sciences minisuperspace quantization 010306 general physics Wave function Mathematical physics Physics 010308 nuclear & particles physics Wheeler-DeWitt equation Astronomy and Astrophysics Statistical and Nonlinear Physics 16. Peace & justice singularity Atomic and Molecular Physics and Optics quantum gravity Problem of time 83C45 (Primary) 83C22 (Secondary) symbols Wheeler–DeWitt equation Gravitational singularity |
| Zdroj: | Quantum Reports Volume 2 Issue 3 Pages 29-441 |
| Popis: | A &ldquo time&rdquo covariant Schrö dinger equation is defined for the minisuperspace model of the Reissner&ndash Nordströ m (RN) black hole, as a &ldquo hybrid&rdquo between the &ldquo intrinsic time&rdquo Schrö dinger and Wheeler&ndash DeWitt (WDW) equations. To do so, a reduced, regular, and &ldquo time(r)&rdquo dependent Hamiltonian density was constructed, without &ldquo breaking&rdquo the re-parametrization covariance r&rarr f(r&tilde ). As a result, the evolution of states with respect to the parameter r and the probabilistic interpretation of the resulting quantum description is possible, while quantum schemes for different gauge choices are equivalent by construction. The solutions are found for Dirac&rsquo s delta and Gaussian initial states. A geometrical interpretation of the wavefunctions is presented via Bohm analysis. Alongside this, a criterion is presented to adjudicate which, between two singular spacetimes, is &ldquo more&rdquo or &ldquo less&rdquo singular. Two ways to adjudicate the existence of singularities are compared (vanishing of the probability density at the classical singularity and semi-classical spacetime singularity). Finally, an equivalence of the reduced equations with those of a 3D electromagnetic pp-wave spacetime is revealed. |
| Databáze: | OpenAIRE |
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