Degenerate equilibrium states of collisionless stellar systems

We study a three dimensional continuous model of gravitating matter rotating at constant angular velocity. In the rotating reference frame, by a finite dimensional reduction, we prove the existence of non radial stationary solutions whose supports are made of an arbitrarily large number of disjoint compact sets, in the low angular velocity and large scale limit. At first order, the solutions behave like point particles, thus making the link with the relative equilibria in N -body dynamics.

The Astrophysical Journal, 2003

We examine the thermodynamical properties of a family of partially relaxed, anisotropic stellar systems, derived earlier from the Boltzmann entropy under the assumption that a third quantity Q is conserved in addition to the total energy and the total number of stars. We now show that the family of models conforms to the paradigm of the gravothermal catastrophe, which is expected to occur (in the presence of adequate energy transport mechanisms) when the one-parameter equilibrium sequence attains sufficiently high values of the concentration parameter; these are the values for which the models are well fitted by the R 1/4 law. In the intermediate concentration regime the models belonging to the sequence exhibit significant deviations from the R 1/4 law. Curiously, in the lowconcentration regime, the global thermodynamical temperature associated with the models becomes negative when the models become too anisotropic so that they are unstable against the radial orbit instability; this latter behavior, while offering a new clue to the physical interpretation of the radial orbit instability, is at variance with respect to the low-concentration limit of the classical case of the isotropic, isothermal sphere investigated by and .

Classical and Quantum Gravity, 1995

The hydrostatic equilibrium of a 2+1 dimensional perfect fluid star in asymptotically anti-de Sitter space is discussed. The interior geometry matches the exterior 2 + 1 black-hole solution. An upper mass limit is found, analogous to Buchdahl's theorem in 3+1, and the possibility of collapse is discussed. The case of a uniform matter density is solved exactly and a new interior solution is presented.

2002

Following our recent finding [1] that for the final state of continued spherical gravitational collapse of sufficiently massive bodies, the final gravitational mass of the fluid, M f → 0, we show that for a physical fluid the eventual value of 2M f /R f → 1 rather than 2M f /R f < 1 (the speed of light c = 1 and the gravitational constant G = 1), indicating the approach to a zero-mass black hole. We also point out that as the final state is approached the curvature components tend to blow up, also the proper radial distance l and the proper time (measured along a radial worldline) τ → ∞ indicating that actually the singularity is never attained. We also identify that, the final state may correspond to the local 3-speed attaining either V = 0 or V → c, even though invariant circumference contraction speed U = dR/dτ → 0. Nonetheless, at a finite observation epoch, such Eternally Collapsing Objects (ECOs) may have a local speed of collapse V ≪ c and the labframe speed of collapse may be negligible because of high surface gravitational redshift. However, if quantum back reaction in the strong gravity regime would cause a phase transition of the form, pressure p = −ρ, where ρ is the density of the collapsing fluid, it may be possible to have static Ultra Compact Objects (UCOs) of arbitrary high mass [2]. While supposed Black Holes have no intrinsic magnetic field, ECOs or UCOs are likely to possess strong intrinsic magnetic field and we point out that there are already some tentative evidence for existence of such intrinsic magnetic fields in some Black Hole Candidates [3,4]. For the benefit of the readers who may not have gone through Paper I, we also include here the summary of the same. It clearly shows that the central result of Paper I can be derived even without knowing the meaning of the nomenclature V or without imposing any of property of V such as whether V < 1 or not. In addition we consolidate the same result from other physical considerations too. 1

Zenodo, 2025

This paper proposes that the Solar System is the result of a localized entropic collapse event, effectively a correlated Big Bang, embedded within a larger steady-state universe. By applying the entropy-decay framework previously developed, we analyse the structural formation, gravitational distribution, and material evolution of the Sun and planets. The Sun is modelled as a sustained entropic release point, while planetary characteristics are interpreted through entropy gradients and decay states. Special attention is given to the anomalous status of Earth and Venus, with a clear statement that the emergence of life on Earth remains outside the explanatory power of entropy-decay physics. This model reframes planetary evolution as one of many local collapses that punctuate a broader equilibriumseeking universe.

2001

In this paper, we investigate the nature of the singularity in the spherically symmetrical, shear-free, gravitational collapse of a star with heat flux using a separable metric . For any non-singular, regular, radial density profile for a star described by this metric, eq. (2.1), the singularity of the gravitational collapse is not naked locally. Our results here unequivocally support the Strong Cosmic Censorship Hypothesis. *

Journal of Cosmology and Astroparticle Physics, 2016

In this article we study the hydrostatic equilibrium configuration of neutron stars and strange stars, whose fluid pressure is computed from the equations of state p = ωρ 5/3 and p = 0.28(ρ − 4B), respectively, with ω and B being constants and ρ the energy density of the fluid. We start by deriving the hydrostatic equilibrium equation for the f (R, T) theory of gravity, with R and T standing for the Ricci scalar and trace of the energy-momentum tensor, respectively. Such an equation is a generalization of the one obtained from general relativity, and the latter can be retrieved for a certain limit of the theory. For the f (R, T) = R + 2λT functional form, with λ being a constant, we find that some physical properties of the stars, such as pressure, energy density, mass and radius, are affected when λ is changed. We show that for a fixed central star energy density, the mass of neutron and strange stars can increase with λ. Concerning the star radius, it increases for neutron stars and it decreases for strange stars with the increment of λ. Thus, in f (R, T) theory of gravity we can push the maximum mass above the observational limits. This implies that the equation of state cannot be eliminated if the maximum mass within General Relativity lies below the limit given by observed pulsars.

Monthly Notices of the Royal Astronomical Society, 2001

An analytical model is presented for the postcollapse equilibrium structure of virialized objects which condense out of a low-density cosmological background universe, either matter-dominated or flat with a cosmological constant. This generalizes the model we derived previously for an Einstein-de Sitter (EdS) universe. The model is based upon the assumption that cosmological haloes form from the collapse and virialization of "top-hat" density perturbations and are spherical, isotropic, and isothermal. This leads to the prediction of a unique, nonsingular, truncated isothermal sphere (TIS), a particular solution of the Lane-Emden equation (suitably modified when Λ = 0). The size and virial temperature are unique functions of the mass and redshift of formation of the object for a given background universe. The central density is roughly proportional to the critical density of the universe at the epoch of collapse. This TIS model is in good agreement with observations of the internal structure of dark matter-dominated haloes on scales ranging from dwarf galaxies to X-ray clusters. It also reproduces many of the average properties of haloes in simulations of the Cold Dark Matter (CDM) model to good accuracy, suggesting that it is a useful analytical approximation for haloes which form from realistic initial conditions. Our TIS model matches the density profiles of haloes in CDM N-body simulations outside the innermost region, while avoiding the steep central cusp of the latter which is in apparent conc 0000 RAS 2 I.T. Iliev and P.R. Shapiro flict with observations. The TIS model may also be relevant to nonstandard CDM models, like self-interacting dark matter, recently proposed to resolve this conflict.

Journal of Modern Physics, 2012

Research by one of the authors suggested that the critical mass of constant-density neutron stars will be greater than eight solar masses when the majority of their neutrons group into bosons that form a Bose-Einstein condensate, provided the bosons interact with each other and have scattering lengths on the order of a picometer. That analysis was able to use Newtonian theory for the condensate with scattering lengths on this order, but general relativity provides a more fundamental analysis. In this paper, we determine the equilibrium states of a static, spherically-symmetric variable-density mixture of a degenerate gas of noninteracting neutrons and a Bose-Einstein condensate using general relativity. We use a Klein-Gordan Lagrangian density with a Gross-Pitaevskii term for the condensate and an effective field for the neutrons. We show that a new class of compact stars can exist with masses above the Oppenheimer-Volkoff limit, provided the scattering length of the bosons is large enough. These stars have no internal singularities, obey causality, and demonstrate a quantum mechanism consistent with general relativity that could prevent collapsed stars from becoming black holes.

Classical and Quantum Gravity, 2011

We develop here a new procedure within Einstein's theory of gravity to generate equilibrium configurations that result as the final state of gravitational collapse from regular initial conditions. As a simplification, we assume that the collapsing fluid is supported only by tangential pressure. We show that the equilibrium geometries generated by this method form a subset of static solutions to the Einstein equations, and that they can either be regular or develop a naked singularity at the center. When a singularity is present, there are key differences in the properties of stable circular orbits relative to those around a Schwarzschild black hole with the same mass. Therefore, if an accretion disk is present around such a naked singularity it could be observationally distinguished from a disk around a black hole.