Gravitational phase transition of fermionic matter in a general-relativistic framework

Bilić, Neven; Viollier, Raoul D.

doi:10.1007/s100529900176

Cited by 41 publications

(71 citation statements)

References 30 publications

(46 reference statements)

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“…20 Equation (105) is valid at equilibrium (for a steady state). Therefore, the expressions (122) and (123) of S and N are justified only at equilibrium. However, it is shown in [51] that Eq.…”

Section: Local Thermodynamic Equilibriummentioning

confidence: 99%

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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: Local Thermodynamic Equilibriummentioning

confidence: 99%

“…(205) and (206) with Eq. (203) [2,123]. Remark: For the general relativistic Fermi gas at T = 0, the free energy F reduces to the binding energy E = (M − N m)c 2 .…”

Section: The Completely Degenerate Fermi Gas (Ground State)mentioning

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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“…is the natural length scale for fermion stars (Bilić & Viollier 1999b). We also take the same value D ol for lensing by a black hole.…”

Section: Lensing By a Schwarzschild Black Hole A Boson Star And A Fmentioning

confidence: 99%

“…Of course, the massive neutrino could be replaced by any weakly interacting fermion of the same mass. Such fermion stars could have been formed in the early Universe during a first-order gravitational phase transition (Bilić & Viollier 1997, Bilić & Viollier 1999a, Bilić & Viollier 1999b). It has recently been shown that the dark-matter concentration observed through stellar 1 Rudjer Bošković Institute, 10000 Zagreb, Croatia 2 Institute of Theoretical Physics and Astrophysics, Department of Physics, University of Cape Town, Rondebosch 7701, South Africa motion at the Galactic center , Genzel et al 1996 is consistent with a supermassive object of 2.5 × 10 6 solar masses made of self-gravitating, degenerate heavy neutrino matter (Tsiklauri & Viollier 1998a).…”

Section: Introductionmentioning

confidence: 99%