Related papers: The Schwarzschild Mass in General Relativity
We study the Mass Discrepancy-Acceleration Relation (MDAR) of 57 elliptical galaxies by their Einstein rings from the Sloan Lens ACS Survey (SLACS). The mass discrepancy between the lensing mass and the baryonic mass derived from population…
As is well known, some aspects of General Relativity and Cosmology can be reproduced without even using Einstein's equation. As an illustration, the 0 - 0 component of the Schwarzschild space can be obtained by the requirement that the…
Diffusion-a measure of dynamics, and entropy-a measure of disorder in the system, are found to be intimately correlated in many systems, and the correlation is often strongly non-linear. We explore the origin of this complex dependence by…
We obtain an approximate global stationary and axisymmetric solution of Einstein's equations which can be considered as a simple star model: a self-gravitating perfect fluid ball with constant mass density rotating in rigid motion. Using…
While it is known that any spherical fluid distribution may only source the spherically symmetric Schwarzschild space-time, the inverse is not true. Thus, in this manuscript, we find exact axially symmetric and static fluid (interior)…
In this work we propose a universal basic mass density and a universal basic metric inside dark matter halos in the framework of Einstein equations providing an analytical ground for learning about dark matter. In a previous work the…
These notions in the title are of fundamental importance in any branch of physics. However, there have been great difficulties in finding physically acceptable definitions of them in general relativity since Einstein's time. I shall explain…
We find that if we live at the center of an inhomogeneity with total density contrast of roughly 0.1, dark energy is not a cosmological constant at 95% confidence level. Observational constraints on the equation of state of dark energy, w,…
It is well known that the Schwarzschild solution describes the gravitational field outside compact spherically symmetric mass distribution in General Relativity. In particular, it describes the gravitational field outside a point particle.…
The Lagrangian density of standard relativistic mean-field (RMF) models with density-dependent meson-nucleon coupling vertices is modified by introducing couplings of the meson fields to derivative nucleon densities. As a consequence, the…
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…
Bearing the thermodynamic arguments together with the two definitions of mass in mind, we try to find metrics with spherical symmetry. We consider the adiabatic condition along with the Gong-Wang mass, and evaluate the $g_{rr}$ element…
We present solutions of the Einstein equations that extend the static Schwarzschild solution in empty space into regions of non-zero energy density $\rho$ and radial pressure $p= w \rho$, where $w$ is a constant equation of state parameter.…
The paper considers a set of equations describing the static isotropic gravity field of a macroscopic body within the framework of the theory of gravity with a constraint. A general approximate solution of these equations is obtained. The…
An extension of the generalized relativistic mean-field (gRMF) model with density dependent couplings is introduced in order to describe thermodynamical properties and the composition of dense nuclear matter for astrophysical applications.…
We calculate the equation of state (EoS) of dense matter, using a relativistic mean field (RMF) model with a density dependent coupling that is a slightly modified form of the original NL3 interaction. For nonuniform nuclear matter we…
Early-type galaxies -- slow and fast rotating ellipticals (E-SRs and E-FRs) and S0s/lenticulars -- define a Fundamental Plane (FP) in the space of half-light radius $R_e$, enclosed surface brightness $I_e$ and velocity dispersion…
I define the fields that describe electrical macrostructure, and their rates of change, in terms of the microscopic charge density, electric field, electric potential, and their rates of change. To deduce these definitions, I lay some new…
Through the consideration of spherically symmetric gravitating systems consisting of perfect fluids with linear equation of state constrained to be in a finite volume, an account is given of the properties of entropy at conditions in which…
In recent works, a framework has been developed to describe (quantum) deformed, spherically symmetric and static black holes in four dimensions. The key idea of this so-called Effective Metric Description (EMD) is to parametrise…