Related papers: Bounds on 2m/R for static spherical objects
Perturbations of rotating relativistic stars can be classified by their behavior under parity. For axial perturbations (r-modes), initial data with negative canonical energy is found with angular dependence $e^{im\phi}$ for all values of…
We consider perfect fluid bodies (stars) in general relativity, characterized by particle number density and entropy per particle. A star is said to be in dynamic equilibrium if it is a stationary, axisymmetric solution to the…
In this paper, we study the steady solutions of Euler-Poisson equations in bounded domains with prescribed angular velocity. This models a rotating Newtonian star consisting of a compressible perfect fluid with given equation of state…
We consider a self-gravitating body composed of ideal Fermi gas of tachyons at zero temperature. The Oppenheimer-Volkoff equation is solved for various central densities and various tachyon mass parameter $m$. Although a pure tachyon star…
The equation-of-state (EOS) parameter $\phi \equiv P/\varepsilon$, defined as the ratio of pressure to energy density, encapsulates the fundamental response of matter under extreme compression. Its value at the center of the most massive…
We investigate the equilibrium and stability of supermassive stars of mass $M \agt 10^5M_{\odot}$ in binary systems. We find that corotating binaries are secularly unstable for close, circular orbits with $r \alt 4R(M/10^6M_{\odot})^{1/6}$…
The radial motion of a self-graviting charged dust and stability condition of the static charged dust spheres are considered. The stability is possible for the bound states of the weakly charged layer with abnormal charge with respect to…
$H^2$-spatial regularity of stationary and non-stationary problems for Bingham fluids formulated with the pseudo-stress tensor is discussed. The problem is mathematically described by an elliptic or parabolic variational inequality of the…
The time independent spherically symmetric solutions of General Relativity (GR) coupled to a dynamical unit timelike vector are studied. We find there is a three-parameter family of solutions with this symmetry. Imposing asymptotic flatness…
The initial state of the spherical gravitational collapse in general relativity has been studied with different methods, especially by using {\it a priori} given equations of state that describe the matter as a perfect fluid. We propose an…
We discuss the question of how the number of dimensions of space and time can influence the equilibrium configurations of stars. We find that dimensionality does increase the effect of mass but not the contribution of the pressure, which is…
Within the context of Rastall gravity, we investigate the hydrostatic equilibrium and dynamical stability against radial pulsations of compact stars, where a free parameter $\beta$ measures the deviations from General Relativity (GR). We…
This diploma thesis analyses static, spherically symmetric perfect fluid solutions to Einstein's field equations with cosmological constant. Constant density solutions are derived for different values of the cosmological constant. Eleven…
In the paper, we consider the free boundary value problem to 3D spherically symmetric compressible isentropic Navier-Stokes-Poisson equations for self-gravitating gaseous stars with $\gamma$-law pressure density function for $6/5 <\gamma…
Given a manifold with boundary, one can consider the space of subsurfaces of this manifold meeting the boundary in a prescribed fashion. It is known that these spaces of subsurfaces satisfy homological stability if the manifold has at least…
We prove local well-posedness for the Muskat problem on the half-plane, which models motion of an interface between two fluids of distinct densities (e.g., oil and water) in a porous medium (e.g., an aquifer) that sits atop an impermeable…
We complete our previous investigation concerning the structure and the stability of "isothermal" spheres in general relativity. This concerns objects that are described by a linear equation of state $P=q\epsilon$ so that the pressure is…
Recent observations of high-redshift supernovae seem to suggest that the global geometry of the Universe may be affected by a `cosmological constant', which acts to accelerate the expansion rate with time. But these data by themselves still…
We perform a detailed analysis of radial oscillations to discuss dynamical stability in two-fluid neutron stars composed of ordinary nuclear matter and a gravitationally coupled dark matter component. Using a fully relativistic two-fluid…
Neutrons stars lighter than the Sun are basically composed of nuclear matter of density up to around twice normal nuclear density. In our recent analyses, we showed that possible simultaneous observations of masses and radii of such neutron…