The evolution of the centre-of-mass wave-function for a mesoscopic particle according to the Schrödinger-Newton equation can be approximated by a harmonic potential, if the wave-function is narrow compared to the size of the particle. It was noticed by Colin et al. [Phys. Rev. A, 93, 062102 (2016)] that, in the regime where self-gravitational effects are weak, intermediate and wider wave-functions may be approximated by a harmonic potential as well, but with a width dependent coupling, leading to a time evolution that is determined only by a differential equation for the width of a Gaussian wave-function as a single parameter. Such an approximation results in considerably less computational effort in order to predict the self-gravitational effects on the wave-function dynamics. Here, we provide an alternative approach to this kind of approximation, including a rigorous derivation of the equations of motion for an initially Gaussian wave packet, under the assumption that its shape is conserved. Our result deviates to some degree from the result by Colin et al., specifically in the limit of wide wave-functions.
We study the dynamical stability of self-gravitating systems in presence of anisotropy. In particular, we introduce a stability criterion, in terms of the adiabatic local index, that generalizes the stability condition $<γ> \geq 4/3$ of the isotropic regime. Also, we discuss some applications of the criterion.
We obtain from the first principles a general-relativistic Keplerian rotation law for self-gravitating disks around spinning black holes. This is an extension of a former rotation law that was designed mainly for toroids around spin-less black holes. We integrate numerically axial stationary Einstein equations with self-gravitating disks around spinless or spinning black holes; that includes the first ever integration of the Keplerian selfgravitating tori. This construction can be used for the description of tight black hole-torus systems produced during coalescences of two neutron stars or mo…
In the present paper, we discuss the role of gravitational decoupling to isotropize the anisotropic solution of Einstein's field equations in the context of the complete geometric deformation (CGD) approach and its influence on the complexity factor introduced by L. Herrera (Phys. Rev. D 97, 044010 (2018)) in the static self-gravitating system. Moreover, we also proposed a simple and effective technique to generate new solutions for self-gravitating objects via CGD approach by using two systems with the same complexity factor and vanishing complexity factor proposed by Casadio et al. Eur. Phys…
We prove that in the family of static, asymptotically flat, spherically symmetric scalar hairy black holes with the central electric charge, the set of the charge-to-mass ratios has the exact upper bound $3\sqrt{2}/4\approx1.06$.
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 th…
The post-Newtonian Jeans equation for stationary self-gravitating systems is derived from the post-Newtonian Boltzmann equation in spherical coordinates. The Jeans equation is coupled with the three Poisson equations from the post-Newtonian theory. The Poisson equations are functions of the energy-momentum tensor components which are determined from the post-Newtonian Maxwell--Jüttner distribution function. As an application, the effect of a central massive black hole on the velocity dispersion profile of the host galaxy is investigated and the influence of the post-Newtonian corrections are d…
We determine the mass-radius relation of self-gravitating Bose-Einstein condensates with an attractive $-1/r$ external potential created by a central mass. Following our previous work [P.H. Chavanis, Phys. Rev. D 84, 043531 (2011)], we use an analytical approach based on a Gaussian ansatz. We consider the case of noninteracting bosons as well as the case of self-interacting bosons with a repulsive or an attractive self-interaction. These results may find application in the context of dark matter halos made of self-gravitating Bose-Einstein condensates. In that case, the central mass may mimic …
We review the history of the self-gravitating Fermi gas in Newtonian gravity and general relativity. We mention applications to white dwarfs, neutron stars and dark matter halos. We describe the nature of instabilities and phase transitions in the self-gravitating Fermi gas as energy (microcanonical ensemble) or temperature (canonical ensemble) is reduced. When $N<N_{\rm OV}$, where $N_{\rm OV}$ is the Oppenheimer-Volkoff critical particle number, the self-gravitating Fermi gas experiences a gravothermal catastrophe at $E_c$ stopped by quantum mechanics (Pauli's exclusion principle). The equil…
The entropy principle shows that, for self-gravitating perfect fluid, the Einstein field equations can be derived from the extrema of the total entropy, and the thermodynamical stability criterion are equivalent to the dynamical stability criterion. In this paper, we recast the dynamical criterion for the charged self-gravitating perfect fluid in Einstein-Maxwell theory, and further give the criterion of the star with barotropic condition. In order to obtain the thermodynamical stability criterion, first we get the general formula of the second variation of the total entropy for charged perfec…
Self-gravitating kink solutions of a two-dimensional dilaton gravity are revisited in this work. Analytical kink solutions are derived from a concise superpotential formalism of the dynamical equations. A general analysis on the linear stability is conducted for an arbitrary static solution of the model. After gauge fixing, a Schrödinger-like equation with factorizable Hamiltonian operator is obtained, which ensures the linear stability of the solution.
The coupled system of the spherically symmetric Einstein--Maxwell differential equations is solved under two different source conditions: non-zero electric charge and pressure anisotropy. Expressions for the metric functions, and pressures which extend the Tolman VII exact solution are deduced from the new solutions. By applying boundary conditions to these solutions, all integration constants are computed in terms of parameters that are physically meaningful.
We examine the entropy of self-gravitating anisotropic matter confined to a box in the context of generalrelativity. 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 meth…
We determine the caloric curves of classical self-gravitating systems at statistical equilibrium in general relativity. In the classical limit, the caloric curves of a self-gravitating gas depend on a unique parameter $ν=GNm/Rc^2$, called the compactness parameter, where $N$ is the particle number and $R$ the system's size. Typically, the caloric curves have the form of a double spiral. The "cold spiral", corresponding to weakly relativistic configurations, is a generalization of the caloric curve of nonrelativistic classical self-gravitating systems. The "hot spiral'", corresponding to strong…
The theory presented in this monograph establishes the first mathematically rigorous result on the global nonlinear stability of self-gravitating matter under small perturbations of an asymptotically flat, spacelike hypersurface of Minkowski spacetime. It allows one to exclude the existence of dynamically unstable, self-gravitating massive fields and, therefore, solves a long-standing open problem in General Relativity. By a significant extension of the Hyperboloidal Foliation Method they introduced in 2014, the authors establish global-in-time existence for the Einstein equations expressed as…
We find a crucial miscalculation in [arXiv:1501.00365 [gr-qc]] which leads to the wrong master equation. This follows that there is no wormhole-like solution for hyperbolic scalar potential and the solution at large distances differs from that of [arXiv:1501.00365 [gr-qc]].
Self-gravitating Bose-Einstein condensates (BEC) have been proposed in various astrophysical contexts, including Bose-stars and BEC dark matter halos. These systems are described by a combination of the Gross-Pitaevskii and Poisson equations (the GPP system). In the analysis of these hypothetical objects, the Thomas-Fermi (TF) approximation is widely used. This approximation is based on the assumption that in the presence of a large number of particles, the kinetic term in the Gross-Pitaevskii energy functional can be neglected, yet it is well known that this assumption is violated near the co…
We prove under certain assumptions no-hair theorems for non-canonical self-gravitating static multiple scalar fields in spherically symmetric spacetimes. It is shown that the only static, spherically symmetric and asymptotically flat black hole solutions consist of the Schwarzschild metric and a constant multi-scalar map. We also prove that there are no static, horizonless, asymptotically flat, spherically symmetric solutions with static scalar fields and a regular center. The last theorem shows that the static, asymptotically flat, spherically symmetric reflecting compact objects with Neumann…
