Schwarzschild mass uncertainty

Davidson, Aharon; Yellin, Ben

doi:10.1007/s10714-013-1662-2

Cited by 7 publications

(8 citation statements)

References 36 publications

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“…An analogy between the Schwarzschild-Reissner-Nordström black holes and hydrogen atoms were drawn in [52,53], where their energy spectrum was obtained based on some constructed Schrödinger type of equation. A study related to a mass operator and the existence of non-zero mass uncertainty can be found in [54,55]. The quantization of an inhomogeneous cosmological model has been performed in [56][57][58][59].…”

Section: Introductionmentioning

confidence: 99%

Time-covariant Schrödinger equation and invariant decay probability: the $$\Lambda $$-Kantowski–Sachs universe

et al. 2021

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The system under study is the $$\Lambda $$ Λ -Kantowski–Sachs universe. Its canonical quantization is provided based on a recently developed method: the singular minisuperspace Lagrangian describing the system, is reduced to a regular (by inserting into the dynamical equations the lapse dictated by the quadratic constraint) possessing an explicit (though arbitrary) time dependence; thus a time-covariant Schrödinger equation arises. Additionally, an invariant (under transformations $$t=f({\tilde{t}})$$ t = f ( t ~ ) ) decay probability is defined and thus “observers” which correspond to different gauge choices obtain, by default, the same results. The time of decay for a Gaussian wave packet localized around the point $$a=0$$ a = 0 (where a the radial scale factor) is calculated to be of the order $$\sim 10^{-42}{-}10^{-41}~\text {s}$$ ∼ 10 - 42 - 10 - 41 s . The acquired value is near the end of the Planck era (when comparing to a FLRW universe), during which the quantum effects are most prominent. Some of the results are compared to those obtained by following the well known canonical quantization of cosmological systems, i.e. the solutions of the Wheeler–DeWitt equation.

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Section: Introductionmentioning

confidence: 99%

Time-covariant Schrödinger equation and invariant decay probability: the $$\Lambda $$-Kantowski–Sachs universe

et al. 2021

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“…An analogy between the Schwarzschild-Reissner-Nordström black holes and hydrogen atoms were drawn in [51,52], where their energy spectrum was obtained based on some constructed Schrödinger type equation. A study related to a mass operator and existence of non-zero mass uncertainty can be found here [53,54]. The quantization of an inhomogeneous cosmological model has been performed in [55][56][57][58].…”

Section: Introductionmentioning

confidence: 99%

Time-covariant Schrödinger equation and invariant decay probability: The $Λ$-Kantowski-Sachs universe

Pailas,

Dimakis,

Terzis

et al. 2021

Preprint

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The system under study is the Λ-Kantowski-Sachs universe. Its canonical quantization is provided based on a recently developed method: the singular minusuperspace Lagrangians describing the system, are reduced to regular (by inserting into the dynamical equations the lapse dictated by the quadratic constraint) plus explicit (though arbitrary) "time" dependence; thus a "time"-covariant Schrödinger equation arises. Additionally, an invariant (under transformations t = f ( t)) Decay Probability is defined and thus "observers" which correspond to different gauge choices will, by default, obtain the same results. The time of decay for a Gaussian wavepacket localized around the point a = 0 (where a the radial scale factor) is calculated to be of the order ∼ 10 −34 . This corresponds to the inflationary epoch, thus hinting to a connection between inflation and quantum gravity effects. Some of the results are compared with those obtained by following the well known quantization of constrained systems (Wheeler-DeWitt equation).

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“…The authors in [50] described a quantum Schwarzschild black hole by a non-singular wave packet composed of plane wave eigenstates of the momentum Dirac-conjugate to the mass operator. Furthermore, in [51], they provided an interpretation to an emergent spacetime as the quantum mechanical Schwarzschild vacuum, which appears to be massless, but exhibits non-zero mass uncertainty. These are only a few examples of the full list of quantum minisuperspace models.…”

Section: Introductionmentioning

confidence: 99%

“Time”-Covariant Schrödinger Equation and the Canonical Quantization of the Reissner–Nordström Black Hole

Pailas

2020

Quantum Reports

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A “time”-covariant Schrödinger equation is defined for the minisuperspace model of the Reissner–Nordström (RN) black hole, as a “hybrid” between the “intrinsic time” Schrödinger and Wheeler–DeWitt (WDW) equations. To do so, a reduced, regular, and “time(r)”-dependent Hamiltonian density was constructed, without “breaking” the re-parametrization covariance r→f(r˜). 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’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 “more” or “less” 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.

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Schwarzschild mass uncertainty

Cited by 7 publications

References 36 publications

Time-covariant Schrödinger equation and invariant decay probability: the $$\Lambda $$-Kantowski–Sachs universe

Time-covariant Schrödinger equation and invariant decay probability: the $$\Lambda $$-Kantowski–Sachs universe

Time-covariant Schrödinger equation and invariant decay probability: The $Λ$-Kantowski-Sachs universe

“Time”-Covariant Schrödinger Equation and the Canonical Quantization of the Reissner–Nordström Black Hole

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