Related papers: Lane-Emden stars, selfgravitating disks and the So…
We investigate how an equation of state for matter is affected when a gravity is present. For this purpose, we consider a box of ideal gas in the presence of Newtonian gravity. In addition to the ordinary thermodynamic quantities, a…
Spherically symmetric relativistic stars with the polytropic equation of state, which possess the local pressure anisotropy, are considered in the context of general relativity. The modified Lane-Emden equations are derived for the special…
Working within the deep-MOND limit (DML), I describe spherical, self-gravitating systems governed by a polytropic equation of state, $P=\mathcal{K}\rho^\gamma$. As self-consistent structures, such systems can serve as heuristic models for…
The modified Lane-Emden equation for stellar hydrostatic equilibrium in f(R)-gravity is numerically solved by using an iterative procedure. Such an integro-differential equation can be obtained in the weak field limit approximation of…
By comparing the observed orbital decay of the binary pulsars PSRB1913+16 and PSRB1534+12 to that predicted by general relativity due to gravitational-wave emission, we are able to bound the mass of the graviton to be less than…
In this paper we establish some explicit and sharp estimates of the spectral gap and the log-Sobolev constant for mean field particles system, uniform in the number of particles, when the confinement potential have many local minimums. Our…
We obtain bounds on the stability of various self-gravitating astrophysical objects using a new measure of shape complexity known as configurational entropy. We apply the method to Newtonian polytropes, neutron stars with an…
We introduce a self-similar mass model for early-type galaxies, and constrain it using the aperture mass-radius relations determined from the geometries of 22 gravitational lenses. The model consists of two components: a concentrated…
From the masses of planets orbiting our Sun, and relative elemental abundances, it is estimated that at birth our Solar System required a minimum disk mass of ~0.01 solar masses within ~100 AU of the star. The main constituent, gaseous…
In the present work we address the issue concerning the relation mass versus radius for bosonic stars, all this in the context of the theory of ultra-cold gases in the dilute regime and within the realm of Newtonian gravity. It will be…
Recent analytic results concerning stationary, self-gravitating fluids in Newtonian theory are discussed. We give a theorem that forbids infinitely extended fluids, depending on the assumed equation of state and the rotation law. This part…
We introduce a rigorous and general framework to study systematically self-gravitating elastic materials within general relativity, and apply it to investigate the existence and viability, including radial stability, of spherically…
Two important avenues into understanding the formation and evolution of galaxies are the Kennicutt-Schmidt (KS) and Elmegreen-Silk (ES) laws. These relations connect the surface densities of gas and star formation (\sigmagas\ and…
The virial, projected and spherical Jeans equation galaxy mass estimators are compared. High-resolution models of elliptical galaxies from N-body simulations are used to compare predicted mass profiles. Averages over eight models and…
Stars are essentially gravitationally stabilised thermonuclear reactors in hydrostatic equilibrium. The fundamental differential equation for all Newtonian gaseous stars in equilibrium is \begin{align}…
Morrey--Sobolev inequalities are established for functions in weighted Sobolev spaces on the $n$-dimensional half-space, where the weight is a power of the distance to the boundary, as well as for Sobolev spaces on the $n$-dimensional…
We analyze stationary self-gravitating disks around spinning black holes that satisfy the recently found general-relativistic Keplerian rotation law. There is a numerical evidence that the angular velocity, circumferential radius and…
This paper is concerned with the three dimensional compressible Euler--Poisson equations with moving physical vacuum boundary condition. This fluid system is usually used to describe the motion of a self-gravitating inviscid gaseous star.…
The stability question of the Lane-Emden stationary gaseous star configurations is an interesting problem arising in astrophysics. We establish both linear and nonlinear dynamical instability results for the Lane-Emden solutions in the…
The existence of both a minimum mass and a minimum density in nature, in the presence of a positive cosmological constant, is one of the most intriguing results in classical general relativity. These results follow rigorously from the…