Non-Perfect-Fluid Space-Times in Thermodynamic Equilibrium and Generalized Friedmann Equations

We examine the entropy of self-gravitating anisotropic matter confined to a box in the context of general relativity. The configuration of self-gravitating matter is spherically symmetric, but has anisotropic pressure of which angular part is different from the radial part. We deduce the entropy from the relation between the thermodynamical laws and the continuity equation. The variational equation for this entropy is shown to reproduce the gravitational field equation for the anisotropic matter. This result re-assures us the correspondence between gravity and thermodynamics. We apply this method to calculate the entropies of a few objects such as compact star and wormholes. PACS numbers: 95.30.Sf, 04.40.Nr 81.05.Xj, 95.30.Tg, 04.70.Dy, Keywords: entropy, equation of state, general relativity, anisotropic matter, wormholes entropy density is given by s P = 2αwρ 1 1+w . In either cases, the entropy density is proportional to ρ 1 1+w up to a constant.

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“…For w 1 = −1, the Lagrangian exactly corresponds to the one for the entropy density (33) obtained in Sec. III, hence confirms our result.…”

Section: B Anisotropic Matter When W1 = −1mentioning

confidence: 66%

“…[15]. When ρ + p 1 = 0 or w 1 = −1, it is obvious that one cannot use the formula (33) directly. Thankfully, one can use the freedom of choice for the isotropic part to solve this problem.…”

Section: Entropy Density Of Anisotropic Mattermentioning

confidence: 99%

Entropy of self-gravitating anisotropic matter

Kim

Lee

2019

Eur. Phys. J. C

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“…The viscosity of cosmic medium, if it exists, is more important because all GWs would be affected by it. Beside that the viscosity would play very important roles in cosmic evolution Schatz et al (2016); Velten et al (2014), it even may play the role of dark energy, which causes the cosmic acceleration Atreya et al (2019). In above discussion, we regard zv as a constant, but if the damping of GW is caused by cosmic medium, then zv ∝ DL, so zv is function of zc.…”

Section: Damping Of Gw In Viscous Fluidmentioning

confidence: 99%

The effect of redshift degeneracy and the damping effect of viscous medium on the information extracted from gravitational wave signals

Ning

2020

Monthly Notices of the Royal Astronomical Society

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Considering the cosmological redshift zc, the mass of GW source extracted from GW signal is 1 + zc times larger than its intrinsic value, and distance between detector and GW source should be regarded as luminosity distance. However, besides cosmological redshift, there are other kinds of redshifts should be considered, which is actually ignored, in the analysis of GW data, such as Doppler redshift and gravitational redshift, so the parameters extracted from GW may deviate from their intrinsic values. Another factor that may affect GW is the viscous medium in propagation path of GW, which may damp the GW with a damping rate of 16πGη. Some studies indicate dark matter may interact with each other, thus dark matter may be the origin of viscosity of cosmic medium. Then the GW may be rapidly damped by the viscous medium that is made of dark matter, such as dark matter ”mini-spike” around intermediate mass black hole. In this article, we mainly discuss how Doppler and gravitational redshift, together with the damping effect of viscous medium, affect the informations , such as the mass and redshift of GW source, extracted from GW signals.

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Towards a probabilistic foundation of relativistic quantum theory: the one-body Born rule in curved spacetime

Reddiger,

Poirier

2024

Quantum Stud.: Math. Found.

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In this work, we establish a novel approach to the foundations of relativistic quantum theory, which is based on generalizing the quantum-mechanical Born rule for determining particle position probabilities to curved spacetime. A principal motivator for this research has been to overcome internal mathematical problems of relativistic quantum field theory (QFT) such as the ‘problem of infinities’ (renormalization), which axiomatic approaches to QFT have shown to be not only of mathematical but also of conceptual nature. The approach presented here is probabilistic by construction, can accommodate a wide array of dynamical models, does not rely on the symmetries of Minkowski spacetime, and respects the general principle of relativity. In the analytical part of this work, we consider the 1-body case under the assumption of smoothness of the mathematical quantities involved. This is identified as a special case of the theory of the general-relativistic continuity equation. While related approaches to the relativistic generalization of the Born rule assume the hypersurfaces of interest to be spacelike and the spacetime to be globally hyperbolic, we employ prior contributions by C. Eckart and J. Ehlers to show that the former condition is naturally replaced by a transversality condition and that the latter one is obsolete. We discuss two distinct formulations of the 1-body case, which, borrowing terminology from the non-relativistic analog, we term the Lagrangian and Eulerian pictures. We provide a comprehensive treatment of both. The main contribution of this work to the mathematical physics literature is the development of the Lagrangian picture. The Langrangian picture shows how one can address the ‘problem of time’ in this approach and, therefore, serves as a blueprint for the generalization to many bodies and the case that the number of bodies is not conserved. We also provide an example to illustrate how this approach can in principle be employed to model particle creation and annihilation.

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Non-Perfect-Fluid Space-Times in Thermodynamic Equilibrium and Generalized Friedmann Equations

Cited by 3 publications

References 40 publications

Entropy of self-gravitating anisotropic matter

Entropy of self-gravitating anisotropic matter

The effect of redshift degeneracy and the damping effect of viscous medium on the information extracted from gravitational wave signals

Towards a probabilistic foundation of relativistic quantum theory: the one-body Born rule in curved spacetime

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