Related papers: On the Buchdahl inequality for spherically symmetr…
We consider spherically symmetric space-times in GR under the unconventional assumptions that the spherical radius $r$ is either a constant or has a null gradient in the $(t,x)$ subspace orthogonal to the symmetry spheres (i.e., $(\partial…
The critical buckling characteristics of hydrostatically pressurized complete spherical shells filled with an elastic medium are demonstrated. A model based on small deflection thin shell theory, the equations of which are solved in…
We prove the linear stability of subextremal Reissner-Nordstr\"om spacetimes as solutions to the Einstein-Maxwell equation. We make use of a novel representation of gauge-invariant quantities which satisfy a symmetric system of coupled wave…
The ordinary surface magnetic phase transition is studied for the exactly solvable anisotropic spherical model (ASM), which is the limit D \to \infty of the D-component uniaxially anisotropic classical vector model. The bulk limit of the…
We discuss static spherically symmetric solutions in a recently proposed non-local infrared modification of Einstein equations induced by a term $m^2g_{\mu\nu}\Box^{-1} R$, where $m$ is a mass scale. We find that, contrary to what happens…
We provide all basic equations and concepts required to carry out a general study on axially symmetric static sources. The Einstein equations and the conservation equations are written down for a general anisotropic static fluid endowed…
The thermodynamic equilibrium states of a static thin ring shell in a (2+1)-dimensional spacetime with a negative cosmological constant are analyzed. Inside the ring, the spacetime is pure anti-de Sitter (AdS), whereas outside it is a…
We have investigated the stability of a set of non-rotating anisotropic spherical models with a phase-space distribution function of the Osipkov-Merritt type. The velocity distribution in these models is isotropic near the center and…
We review the General Relativistic model of a (quasi) point-like particle represented by a massive shell of electrically charged matter, which displays an ADM mass M equal to the electric charge |Q| in the small-volume limit. We employ the…
We reduce the equations governing the spherically symmetric perturbations of static spherically symmetric solutions of the Einstein-Vlasov system (with either massive or massless particles) to a single stratified wave equation…
In this paper, we study the Minkowski-type inequality for asymptotically flat static manifolds $(M^{n}, g)$ with boundary and with dimension $ n < 8$ that was establishedby McCormick. First, we show that any asymptotically flat static…
A stability version of the Blaschke-Santal\'o inequality and the affine isoperimetric inequality for convex bodies of dimension n>2 is proved. The first step is the reduction to the case when the convex body is o-symmetric and has axial…
We study the static stellar equilibrium configurations ofuncharged and charged spheres composed by a relativistic polytropic fluid, and compare with those of spheres composed by a non-relativistic polytropic fluid, the later case already…
Requiring that the matter fields are subject to the dominant energy condition, we establish the lower bound $(4\pi)^{-1} \kappa {\cal A}$ for the total mass $M$ of a static, spherically symmetric black hole spacetime. (${\cal A}$ and…
We show that, in a model where a non-relativistic particle is coupled to a quantized relativistic scalar Bose field, the embedded mass shell of the particle dissolves in the continuum when the interaction is turned on, provided the coupling…
Using direct methods of the calculus of variations we establish the existence of an infinite class of spherically-symmetric solutions to the multi-field Schr\"odinger-Poisson system. This is achieved by proving that the energy functional…
We consider the following Scr\"odinger system $$\begin{cases}\displaystyle i\partial_t u + \Delta u +(|u|^2+\beta |v|^2) u= 0, \\ \displaystyle i\partial_t v + \Delta v +(|v|^2+\beta |u|^2) v = 0,\end{cases}$$ with initial data $(u_0,v_0)…
We construct the general spherically symmetric and self-similar solution of the Einstein-Vlasov system (collisionless matter coupled to general relativity) with massless particles, under certain regularity conditions. Such solutions have a…
A new class of complex scalar field objects, which generalize the well known boson stars, was recently found as solutions to the Einstein-Klein-Gordon system. The generalization consists in incorporating some of the effects of angular…
We analyze the isothermal property in static fluid spheres within the framework of the modified $f(R, T)$ theory of gravitation. The equation of pressure isotropy of the standard Einstein theory is preserved however, the energy density and…