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

Molaei, MohammadReza

doi:10.1209/0295-5075/ac17a2

Cited by 3 publications

(1 citation statement)

References 21 publications

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“…is the Schwarzschild radius of the massive body with the mass M , and t, r, θ, and ϕ are time coordinate, redial coordinate, polar angle, and azimuthal angle, respectively [13,14].…”

Section: Moreover We Havementioning

confidence: 99%

Hyperbolic cones for casual diffeomorphisms

Rahimi Moghbeli,

Molaei

2023

EPL

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This paper begins with introducing a new class of diﬀeomorphisms on pseudo-Riemannian manifolds which are called casual diﬀeomorphisms. We deduce a new pseudo-Riemannian metric via a casual diﬀeomorphism. We introduce a class of cones for a diﬀeomorphism, and we prove the existence of such cones for each p in a hyperbolic set of a casual diﬀeomorphism. As an example we ﬁnd a hyperbolic casual diﬀeomorphism on Schwarzschild pseudo-Riemannian manifold, and show that the whole manifold is a hyperbolic set for it.

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“…is the Schwarzschild radius of the massive body with the mass M , and t, r, θ, and ϕ are time coordinate, redial coordinate, polar angle, and azimuthal angle, respectively [13,14].…”

Section: Moreover We Havementioning

confidence: 99%

Hyperbolic cones for casual diffeomorphisms

Rahimi Moghbeli,

Molaei

2023

EPL

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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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Singularity formation for the relativistic Euler equations of Chaplygin gases in Schwarzschild spacetime

Hu,

Guo

2024

Stud Appl Math

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We study the formation of singularities of smooth solutions to the relativistic Euler equations of Chaplygin gases in Schwarzschild spacetime. The system is in the spherically symmetric form, and its coefficients and nonhomogeneous terms contain a parameter reflecting the mass of the black hole, which makes it highly nonlinear and complicated. To overcome the influence of the mass parameter of black hole, we introduce a pair of suitable auxiliary variables related to it and derive their characteristic decompositions to establish the estimates of the smooth solution. We show that, for a kind of initial data, the smooth solution develops singularity in finite time and the mass‐energy density itself approaches infinity at the blowup point.

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

Cited by 3 publications

References 21 publications

Hyperbolic cones for casual diffeomorphisms

Hyperbolic cones for casual diffeomorphisms

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

Singularity formation for the relativistic Euler equations of Chaplygin gases in Schwarzschild spacetime

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