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

• URL: http://arxiv.org/abs/2402.15549v1
• Date: Fri, 23 Feb 2024 16:39:59 GMT
• Title: On the Generalized Lemaitre Tolman Bondi Metric: Classical Sensitivities and Quantum Einstein-Vaz Shells
• Authors: Mohammadreza Molaei and Christian Corda
• Abstract summary: We show that the sensitivities and the lower sensitivities via L_fracpartialpartial t are zero. We analyse the properties of the Einstein-Vaz shells which are the final result of the quantum gravitational collapse.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, in the classical framework we evaluate the lower bounds for the sensitivities of the generalized Lemaitre Tolman Bondi metric. The calculated lower bounds via the linear dynamical systems L_{\frac{\partial}{\partial\theta}}, L_{\frac{\partial}{\partial r}}, and L_{\frac{\partial}{\partial\phi}} are -\ln2+\ln|(\dot{R}B)^{2}-(R')^{2}|-2\ln|B|, 2\ln|\dot{B}|-\ln2 and -\ln2-2\ln|B|+\ln|(\dot{R}^{2}B^{2}-R'^{2})\sin^{2}\theta-B^{2}\cos^{2}\theta| respectively. We also show that the sensitivities and the lower sensitivities via L_{\frac{\partial}{\partial t}} are zero. In the quantum framework we analyse 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. 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 combinatin 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 as 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, we discuss the time evolution of the Einstein-Vaz shells

Related papers

• Probing Quantum Entanglement from Quantum Correction to Newtonian Potential Energy [0.0]
  Inspired by string theory ideas, we probe quantum entanglement from the gravitational potential energy. We show that the two masses cannot be separable due to the induced gravitational entanglement. We derive the expression of the resulting extremely weak entanglement force from the corresponding gravitational entanglement energy.
  arXiv  Detail & Related papers  (2024-01-25T17:43:13Z)
• Coherent states of quantum spacetimes for black holes and de Sitter spacetime [0.0]
  We provide a group theory approach to coherent states describing quantum space-time and its properties. This provides a relativistic framework for the metric of a Riemmanian space with bosonic and fermionic coordinates.
  arXiv  Detail & Related papers  (2023-12-07T19:54:15Z)
• Small-time controllability for the nonlinear Schr\"odinger equation on $\mathbb{R}^N$ via bilinear electromagnetic fields [55.2480439325792]
  We address the small-time controllability problem for a nonlinear Schr"odinger equation (NLS) on $mathbbRN$ in the presence of magnetic and electric external fields. In detail, we study when it is possible to control the dynamics of (NLS) as fast as desired via sufficiently large control signals.
  arXiv  Detail & Related papers  (2023-07-28T21:30:44Z)
• Double-scale theory [77.34726150561087]
  We present a new interpretation of quantum mechanics, called the double-scale theory. It is based on the simultaneous existence of two wave functions in the laboratory reference frame. The external wave function corresponds to a field that pilots the center-of-mass of the quantum system. The internal wave function corresponds to the interpretation proposed by Edwin Schr"odinger.
  arXiv  Detail & Related papers  (2023-05-29T14:28:31Z)
• Beyond the Born rule in quantum gravity [0.0]
  We show that there is no Born rule at the fundamental level of quantum gravity with a non-normalisable Wheeler-DeWitt wave functional $Psi$. The universe is in a perpetual state of quantum nonequilibrium with a probability density $Pneqleftvert Psirightvert 2$.
  arXiv  Detail & Related papers  (2022-12-23T07:15:35Z)
• Geometric relative entropies and barycentric Rényi divergences [16.385815610837167]
  monotone quantum relative entropies define monotone R'enyi quantities whenever $P$ is a probability measure. We show that monotone quantum relative entropies define monotone R'enyi quantities whenever $P$ is a probability measure.
  arXiv  Detail & Related papers  (2022-07-28T17:58:59Z)
• Interpolation between modified logarithmic Sobolev and Poincare inequalities for quantum Markovian dynamics [12.151998897427012]
  We show that the quantum Beckner's inequalities interpolate between the Sobolev-type inequalities and the Poincar'e inequality. We introduce a new class of quantum transport distances $W_2,p$ interpolating the quantum 2-Wasserstein distance by Carlen and Maas. We prove that the positive Ricci curvature implies the quantum Beckner's inequality, from which a transport cost and Poincar'e inequalities can follow.
  arXiv  Detail & Related papers  (2022-07-13T18:19:24Z)
• The Franke-Gorini-Kossakowski-Lindblad-Sudarshan (FGKLS) Equation for Two-Dimensional Systems [62.997667081978825]
  Open quantum systems can obey the Franke-Gorini-Kossakowski-Lindblad-Sudarshan (FGKLS) equation. We exhaustively study the case of a Hilbert space dimension of $2$.
  arXiv  Detail & Related papers  (2022-04-16T07:03:54Z)
• Probing low-energy Lorentz violation from high-energy modified dispersion in dipolar Bose-Einstein condensates [9.99039271814434]
  impurity atom in a dipolar Bose-Einstein condensate (BEC) We show that the density fluctuations in the dipolar BEC possess a Lorentz-violating Bogoliubov spectrum. We reproduce the same responds of Unruh-DeWitt detector to Lorentz-violating quantum fields.
  arXiv  Detail & Related papers  (2021-04-22T14:01:37Z)
• Schrodinger theory of black holes [0.0]
  The Schrodinger equation of the Schwarzschild black hole (SBH) is derived via Feynman's path integral approach. The traditional classical singularity in the core of the SBH is replaced by a nonsingular two-particle system.
  arXiv  Detail & Related papers  (2020-12-15T12:09:19Z)
• Quantum and classical approaches in statistical physics: some basic inequalities [0.0]
  We present some basic inequalities between the classical and quantum values of free energy, entropy and mean energy. We derive the semiclassical limits for four cases, that is, for $hbarto0$, $Ttoinfty$, $omegato0$, and $Ntoinfty$.
  arXiv  Detail & Related papers  (2020-06-19T19:06:10Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.