Related papers: The Schwarzschild Mass in General Relativity
In the first and second post-Newtonian approximation of the Schwarzschild metric, I obtain the energy component of the Einstein and M{\o}ller energy-momentum complex. Both energies involve the rest-mass energy $m$, the energy stored in the…
The equations determining the energy density $\rho$ of a gas of photons in thermodynamic equilibrium with a spherical mass $M$ at a non-zero temperature $T_s>0$ is derived from Einstein's equations. It is found that for large $r$, $\rho…
The relation between microscopic and macroscopic entities in the generally covariant theories is considered, and it is argued that a sensible definition of the macroscopic averages requires a restriction of the allowed transformations of…
We examine various well known exact solutions available in the literature to investigate the recent criterion obtained in ref. [20] which should be fulfilled by any static and spherically symmetric solution in the state of hydrostatic…
The macroscopic model is formulated for a neutron star (NS) as a perfect liquid drop at the equilibrium. We use the leptodermic approximation $a/R\ll 1$, where $a$ is the crust thickness of the effective NS surface (ES), and $R$ is the mean…
Upper limits for the mass-radius ratio are derived for arbitrary general relativistic matter distributions in the presence of a cosmological constant. General restrictions for the red shift and total energy (including the gravitational…
The regularized vacuum energy (or energy density) of a quantum field subjected to static external conditions is shown to satisfy a certain partial differential equation with respect to two variables, the mass and the "time" (ultraviolet…
The Schwarzschild-deSitter metric is the known solution of Einstein field equations with cosmological constant term for vacuum spherically symmetric space around a point mass M. Recently it has been reported that in a $Lamda$-dominant world…
An analysis of insular solutions of Einstein's field equations for static, spherically symmetric, source mass, on the basis of exterior Schwarzschild solution is presented. Following the analysis, we demonstrate that the {\em regular}…
The Schwarzschild metric has a divergent energy density at the horizon, which motivates a new approach to black holes. If matter is spread uniformly throughout the interior of a supermassive black hole, with mass $M\sim M_\star= 2.34…
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…
The problem of constructing a model of an extended charged particle within the context of general relativity has a long and distinguished history. The distinctive feature of these models is that, in some way or another, they require the…
The force density on matter and the kinetic energy-momentum tensor of the electromagnetic field in matter are obtained starting from Maxwell equations and Lorentz force at microscopic level and averaging over a small region of space-time.…
Schwarzschild's 'interior solution' is a space-time metric that satisfies Einstein's gravitational field equations with a source term that Einstein created on the basis of an unjustified identification of the conceptually distinct notions…
A spherically symmetric distribution of classical blackbody radiation is considered, at conditions in which gravitational self-interaction effects become not negligible. Static solutions to Einstein field equations are searched for, for…
Since Schwarzshild discovered the point-mass solution to Einstein's equations that bears his name, many equivalent forms of the metric have been catalogued. Using an elementary coordinate transformation, we derive the most general form for…
The geodesic equations for the general case of diagonal metrics of static, spherically symmetric fields are calculated. The elimination of the proper time variable gives the motion equations for test particles with respect to coordinate…
To make sense of a global space-time model and to give a meaning to the coordinates that we use, a choice of a constant curvature space-metric of reference it is as much necessary as it is a choice of units of mass, length and time. The…
Utilizing various gauges of the radial coordinate we give a description of static spherically symmetric space-times with point singularity at the center and vacuum outside the singularity. We show that in general relativity (GR) there exist…
Following Einstein's definition of Lagrangian density and gravitational field energy density (Einstein, A., Ann. Phys. Lpz., 49, 806 (1916); Einstein, A., Phys. Z., 19, 115 (1918); Pauli, W., {\it Theory of Relativity}, B.I. Publications,…