Related papers: The Schwarzschild Mass in General Relativity
Understanding the observations of dynamical tracers and the trajectories of lensed photons at galactic scales within the context of General Relativity (GR), requires the introduction of a hypothetical dark matter dominant component. The…
We present a simple derivation of a point-source boundary condition for the Schwarzschild solution that relates the Schwarzschild radius to the mass of its source without appealing to the Newtonian limit. Interpretation of the Schwarzschild…
New exact interior solutions to the Einstein field equations for anisotropic spheres are found. We utilise a procedure that necessitates a choice for the energy density and the radial pressure. This class contains the constant density model…
The present work describes an immersion in 5D of the interior Schwarzschild solution of the general relativity equations. The model theory is defined in the context of a flat 5D space time matter Minkowski model, using a Tolman like…
We study the periapsis shift of a quasi-circular orbit in general static spherically symmetric spacetimes. We derive two formulae in full order with respect to the gravitational field, one in terms of the gravitational mass $m$ and the…
For Schwarzschild space-time, distributional expressions of energy-momentum densities and of scalar concomitants of the curvature tensors are examined for a class of coordinate systems which includes those of the Schwarzschild and of…
Most astrophysical systems in our Universe are characterized by shallow gravitational potentials, with dimensionless compactness $|\Phi| \equiv r_s / R \ll 1$, where $r_{s}$ and $R$ are their Schwarzschild radius and typical size,…
Applying Dirac's procedure to $r$-dependent constrained systems, we derive a reduced total Hamiltonian, resembling an upside down harmonic oscillator, which generates the Schwarzschild solution in the mini super-spacetime. Associated with…
We define compactness of a gravitational lens as the scaled closest distance of approach (i.e., $r_0/M$) of the null geodesic giving rise to an image. We model forty supermassive dark objects as Schwarzschild lenses and compute compactness…
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…
Energy in nuclear matter is, in practice, completely characterized at different densities and asymmetries, when the density dependencies of symmetry energy and of energy of symmetric matter are specified. The density dependence of the…
The Lagrangian density of relativistic mean-field (RMF) theory with non-linear derivative (NLD) interactions is applied to isospin asymmetric nuclear matter. We study the symmetry energy and the density and energy dependences of nucleon…
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 self-force acting on a (scalar or electric) charge held in place outside a massive body contains information about the body's composition, and can therefore be used as a probe of internal structure. We explore this theme by computing…
Relativistic energy density functionals (EDF) have become a standard tool for nuclear structure calculations, providing a complete and accurate, global description of nuclear ground states and collective excitations. Guided by the medium…
We develop a density-dependent quark mean-field (DDQMF) model to study the properties of nuclear matter and neutron stars, where the coupling strength between $\sigma$ meson and nucleon is generated by the degree of freedom of quarks, while…
The density dependence of the symmetry energy, instrumental in understanding the behaviour of the asymmetric nuclear matter, is investigated within the extended relativistic mean field (ERMF) model which includes the contributions from the…
Nullification of the Einstein tensor curvature for the elementary material space with active gravitational field (radial source) and passive field distribution of its inertial particle (radial sink) maintains the conceptual equivalence of…
The description of a point mass in general relativity (GR) is given in the framework of the field formulation of GR where all the dynamical fields, including the gravitational field, are considered in a fixed background spacetime. With the…
In practical implementations of density-functional theory, the only term where an orbital description is needed is the kinetic one. Even this term in principle depends on the density only, but its explicit form is unknown. We provide a…