A characterization for the sensitivity of a metric

Molaei, MohammadReza; Khajoei, Najmeh

doi:10.1140/epjp/i2016-16257-5

Cited by 3 publications

(2 citation statements)

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“…[10][11][12][13] The notion of sensitivity for a non Riemannian metric has been introduced first in 2016. [14] In fact the sensitivity of a metric determines an upper bound for the deviation of it from the Riemannian case. The lower bound of it's deviation from the Riemannian case is called the lower sensitivity of it.…”

Section: Introductionmentioning

confidence: 99%

On the Generalized Lemaitre Tolman Bondi Metric: Classical Sensitivities and Quantum Einstein‐Vaz Shells

Molaei,

Corda

2024

Fortschritte der Physik

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In this paper, in the classical framework, the lower bounds for the sensitivities of the generalized Lemaitre Tolman Bondi metric are evaluated. The calculated lower bounds via the linear dynamical systems , , and are , and respectively. The sensitivities and the lower sensitivities via are zero are also shown. In the quantum framework, the properties of the Einstein‐Vaz shells which are the final result of the quantum gravitational collapse arising from the Lemaitre Tolman Bondi discussed by Vaz in 2014 are analyzed. In fact, Vaz showed that continued collapse to a singularity can only be obtained if one combines two independent and entire solutions of the Wheeler‐DeWitt equation. Forbidding such a combination leads naturally to matter condensing on the Schwarzschild surface during quantum collapse. In that way, an entirely new framework for black holes (BHs) has emerged. The approach of Vaz was also consistent with Einstein's idea in 1939 of the localization of the collapsing particles within a thin spherical shell. Here, following an approach of oned of us (CC), we derive the BH mass and energy spectra via a Schrodinger‐like approach, by further supporting Vaz's conclusions that instead of a spacetime singularity covered by an event horizon, the final result of the gravitational collapse is an essentially quantum object, an extremely compact “dark star”. This “gravitational atom” is held up not by any degeneracy pressure but by quantum gravity in the same way that ordinary atoms are sustained by quantum mechanics. Finally, the time evolution of the Einstein‐Vaz shells is discussed.

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Section: Introductionmentioning

confidence: 99%

On the Generalized Lemaitre Tolman Bondi Metric: Classical Sensitivities and Quantum Einstein‐Vaz Shells

Molaei,

Corda

2024

Fortschritte der Physik

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“…In definition 2.1 if we replace "lim inf" with "lim sup", then the resulted function is denoted by H g ( ∂ ∂x i ), and it is called the sensitivity of g on U in the direction of ∂ ∂x i , and it has been defined by this author in 2016 [16]. The sensitivity functions have been calculated for a class of Bianchi-type cosmological models [17,18] in [16]. Moreover the sensitivity function has been calculated for the reduced Langevin pseudo-metric in [19].…”

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The lower sensitivities and the sensitivities of the Schwarzschild metric near the Schwarzschild black hole

Molaei¹

2021

EPL

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In this paper we define the notion of the lower sensitivity for the pseudo-metrics. We evaluate the lower sensitivities of the Schwarzschild metric when the redial coordinate is near the event horizon. In the black-hole case we find finite lower sensitivity in the direction of time, and infinite lower sensitivities in the other directions. The finiteness of the lower sensitivity of the black hole implies the finiteness of its entropy, which confirms "the recent physical results on black-hole gravitational entropy" mathematically.

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