Related papers: Maximum Mass-Radius Ratio for Compact General Rela…
Motivated by recent achievements of a full general relativistic method in estimating the mass-to-distance ratio of supermassive black holes hosted at the core of active galactic nuclei, we introduce the new concept redshift rapidity in…
One of the stiffest equations of state for matter in a compact star is constant energy density and this generates the interior Schwarzschild radius to mass relation and the Misner maximum mass for relativistic compact stars. If dark matter…
The maximum size of a cosmic structure is given by the maximum turnaround radius -- the scale where the attraction due to its mass is balanced by the repulsion due to dark energy. We derive generic formulae for the estimation of the maximum…
We show that for realistic equations of state of dense matter, the universal proportionality factor relating the maximum rotation rate of neutron stars due to mass-shedding limit to the mass and radius of maximum allowable mass…
The central (surface) energy-density, $E_0 (E_R)$, which appears in the expression of total static and spherical mass, $M$ (corresponding to the total radius $R$) is defined as the density measured only by one observer located at the centre…
By considering a deformation of the Schwarzschild metric in the presence of a minimal measurable length which still respects the equivalence principle, we study corrections to the standard general relativistic predictions for some…
We present a model of relativistic elastic stars featuring scale invariance. This implies a linear mass-radius relation and the absence of a maximum mass. The most compact spherically symmetric configuration that is radially stable and…
Three theoretical criteria for gravitational theories beyond general relativity are considered: obtaining the cosmological constant as an integration constant, deriving the energy conservation law as a consequence of the field equations,…
Spherically symmetric anisotropic static compact solutions to the Einstein equations in dimension $d\geq4$ are considered. Various matter models are examined and upper bounds on the ratio of the gravitational mass to the radius in these…
The mass-radius relation of white dwarfs is largely determined by the equation of state of degenerate electrons, which causes the stellar radius to decrease as mass increases. Here we observationally measure this relation using the…
The problem of deriving a shock-wave geometry with cosmological constant by boosting a Schwarzschild-de Sitter (or anti-de Sitter) black hole is re-examined. Unlike previous work in the literature, we deal with the exact Schwarzschild-de…
We produce the simple formula for the radius R of a cold body of mass M, (4 pi rho/3)^{1/3} R = I.M^{1/3} / [1+ (M/Mp)^{2/3}], where I is one for white dwarfs with non-relativistic electrons, but depends on the ratio of the total mass to…
This is the second of two works, in which we discuss the definition of an appropriate notion of mass for static metrics, in the case where the cosmological constant is positive and the model solutions are compact. In the first part, we have…
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…
Modern instrumentation makes it possible to measure the mass to radius ratio for main sequence stars in open clusters from gravitational redshifts. For stars where independent information is available for either the mass or the radius, this…
We calculate the total gravitational energy and the gravitational energy density of the de Sitter space using the definition of localized energy that arises in the framework of the teleparallel equivalent of general relativity. We find that…
We determine the angle of deflection of light by the gravitational field inside and outside a spherical body with a homogeneous mass density. We show that the largest deflections, which can be measured by weak gravitational lensing, are in…
The Schwarzschild interior solution, when combined with the assumption of a finite central pressure, leads to the well-known Buchdahl bound. This bound establishes an upper limit on the mass-to-radius ratio of an object, which is equivalent…
We derive upper and lower limits for the mass-radius ratio of spin-fluid spheres in Einstein-Cartan theory, with matter satisfying a linear barotropic equation of state, and in the presence of a cosmological constant. Adopting a spherically…
Since the Schwarzschild-de Sitter spacetime is static inside the cosmological event horizon, if the dark energy state parameter is sufficiently close to $-1$, apparently one could still expect an effectively static geometry, in the…