Reply to: "TOV or OV? The Whole Story"

Semiz, İbrahim

doi:10.48550/arxiv.1702.06002

Cited by 1 publication

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“…An effective thermodynamical formalism involving generalized entropic functionals of the form S = − C(f ) drdv was developed by Chavanis [214-221, 223, 224] who gave various interpretations of these functionals. 7 There is debate [233][234][235] on the name that should be given to these equations: OV or TOV? As far as we can judge, Eq.…”

Section: Introductionmentioning

confidence: 99%

Statistical mechanics of self-gravitating systems in general relativity: I. The quantum Fermi gas

Chavanis

2020

Eur. Phys. J. Plus

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We develop a general formalism to determine the statistical equilibrium states of self-gravitating systems in general relativity and complete previous works on the subject. Our results are valid for an arbitrary form of entropy but, for illustration, we explicitly consider the Fermi-Dirac entropy for fermions. The maximization of entropy at fixed mass-energy and particle number determines the distribution function of the system and its equation of state. It also implies the Tolman-Oppenheimer-Volkoff equations of hydrostatic equilibrium and the Tolman-Klein relations. Our paper provides all the necessary equations that are needed to construct the caloric curves of selfgravitating fermions in general relativity as done in recent works. We consider the nonrelativistic limit c → +∞ and recover the equations obtained within the framework of Newtonian gravity. We also discuss the inequivalence of statistical ensembles as well as the relation between the dynamical and thermodynamical stability of self-gravitating systems in Newtonian gravity and general relativity.PACS numbers: 04.40. Dg, 05.70.Fh, 95.30.Sf, 95.35.+d I. INTRODUCTIONSelf-gravitating fermions play an important role in different areas of astrophysics. They appeared in the context of white dwarfs, neutron stars and dark matter halos where the fermions are electrons, neutrons and massive neutrinos respectively. We start by a brief history of the subject giving an exhaustive list of references. 1 Soon after the discovery of the quantum statistics by Fermi [3,4] and Dirac [5] in 1926, Fowler [6] used this "new thermodynamics" to solve the puzzle of the extreme high density of white dwarfs, which could not be explained by classical physics [7]. He understood that white dwarfs owe their stability to the quantum pressure of the degenerate electron gas resulting from the Pauli exclusion principle [8]. He considered a completely degenerate electron gas at T = 0 based on the fact that the temperature in white dwarfs is much smaller than the Fermi temperature (T ≪ T F ). He also used Newtonian gravity which is a very good approximation to describe white dwarfs in general. The first models [9-11] of white dwarfs were based on the nonrelativistic equation of state of a Fermi gas and provided the corresponding mass-radius relation. Stoner [9] developed an analytical approach based on a uniform density approximation for the star. Chandrasekhar [11] derived the exact mass-radius relation of nonrelativistic white dwarfs by applying the theory of polytropes of index n = 3/2 [12]. It was then realized that special relativity must be taken into account at high densities. When the relativistic equation of state is employed it was found that white dwarfs can exist only below a maximum mass M max = 1.42 M ⊙ [13-25], now known as the Chandrasekhar limiting mass. Frenkel [13] was the first to mention that relativistic effects become important when the mass of white dwarfs becomes larger than the solar mass but he did not envision the existence of an upper mass limit. The maxi...

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Section: Introductionmentioning

confidence: 99%

Statistical mechanics of self-gravitating systems in general relativity: I. The quantum Fermi gas

Chavanis

2020

Eur. Phys. J. Plus

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Reply to: "TOV or OV? The Whole Story"

Cited by 1 publication

References 5 publications

Statistical mechanics of self-gravitating systems in general relativity: I. The quantum Fermi gas

Statistical mechanics of self-gravitating systems in general relativity: I. The quantum Fermi gas

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