Determination of the upper and lower bound of the mass limit of degenerate fermionic dark matter objects

Kupi, Gábor

doi:10.1103/physrevd.77.023001

Cited by 3 publications

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References 10 publications

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“…Rhoades and Ruffini [2] used the general restrictions of the equations of state to give a maximum mass of neutron stars. Other effects, such as temperature, interactions of the particles and kinetic constraints, have been considered to obtain stable configurations of various compact stars [3][4][5][6][7][8][9][10][11][12][13][14][15]. However, when we examine the solutions of the general relativistic field equations of neutron stars (Tolman-Oppenheimer-Volkoff equations), we find there are types of solutions missing from the analysis of the solutions in the paper of Oppenheimer and Volkoff [1] and also not considered in other references.…”

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confidence: 94%

Solutions without a maximum mass limit of the general relativistic field equations for neutron stars

2011

Sci. China Phys. Mech. Astron.

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We have investigated the general relativistic field equations for neutron stars. We find that there are solutions for the equilibrium mass distribution without a maximum mass limit. The solutions correspond to stars with a void inside their centers. In these solutions, the mass density and pressure increase first from zero at the inner radius to a peak and then decrease to zero at the outer radius. With the change of the void boundary, the mass and particle number of the star can approach infinity. Neutron stars with large masses can remain stable and do not collapse into black holes. neutron stars, Tolman-Oppenheimer-Volkoff equations, general relativistic field equations PACS: 04.40.Dg, 97.60.Jd, 95.30.Sf IntrodutionThe internal structures and the maximum masses of neutron stars have long attracted attention. Oppenheimer and Volkoff solved the general relativistic field equations for neutron stars and gave a maximum mass of 0.72 solar masses (M ) against gravitational collapse [1]. Rhoades and Ruffini [2] used the general restrictions of the equations of state to give a maximum mass of neutron stars. Other effects, such as temperature, interactions of the particles and kinetic constraints, have been considered to obtain stable configurations of various compact stars [3][4][5][6][7][8][9][10][11][12][13][14][15]. However, when we examine the solutions of the general relativistic field equations of neutron stars (Tolman-Oppenheimer-Volkoff equations), we find there are types of solutions missing from the analysis of the solutions in the paper of Oppenheimer and Volkoff [1] and also not considered in other references. In this work, we show that the general relativistic field equations of neutron stars have types of solutions without a maximum mass limit. In these solutions, the neutron stars have an equilibrium mass distribution with a void in the center and are characterized by two radii: the inner radius r i and outer radius r o . The mass density and pressure increase first from zero at the inner †Recommended by LONG GuiLu (Editorial Board Member) radius r i to a peak and then decrease to zero at the outer radius r o . The mass in the middle region around the peak of the mass density attracts the matter and prevents the collapse to the void. These types of solutions do not exist in the Newtonian gravitational equations and can only be given by the Einstein general relativistic theory. Solutions of the general relativistic field equationsLet us begin with the analysis of the solutions for the TolmanOppenheimer-Volkoff equations [1,16]. Inside neutron stars, the general static metric for stars with spherical symmetry is given by ds 2 = −e λ dr 2 − r 2 dθ 2 − r 2 sin 2 θdφ 2 + e ν dt 2 .(1)With the help of the auxiliary function u = r(1 − e −λ )/2, the field equations become (in c = G = 1 units)dp dr = − p + ρ r(r − 2u) (4πp 2 r 3 + u),where ρ and p are the macroscopic energy density and pressure measured in proper coordinators, respectively. Eqs.

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confidence: 94%

Solutions without a maximum mass limit of the general relativistic field equations for neutron stars

2011

Sci. China Phys. Mech. Astron.

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“…A lower bound on the fermion mass was obtained by Tremaine and Gunn [83] using constraints arising from the Vlasov equation. The first models decribed dark matter halos at T = 0 using the equation of state of a completely degenerate fermion gas either in the nonrelativistic limit [82,[84][85][86][87][88][89][90][91] or in general relativity [80,[92][93][94][95][96][97][98][99][100]. Subsequent models considered dark matter halos at finite temperature showing that they have a "core-halo" structure consisting in a dense core (fermion ball) surrounded by a dilute isothermal atmosphere leading to flat rotation curves.…”

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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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Jeans mass-radius relation of self-gravitating Bose-Einstein condensates and typical parameters of the dark matter particle

Chavanis

2021

Phys. Rev. D

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Determination of the upper and lower bound of the mass limit of degenerate fermionic dark matter objects

Cited by 3 publications

References 10 publications

Solutions without a maximum mass limit of the general relativistic field equations for neutron stars

Solutions without a maximum mass limit of the general relativistic field equations for neutron stars

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

Jeans mass-radius relation of self-gravitating Bose-Einstein condensates and typical parameters of the dark matter particle

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