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The modern notion of a black hole singularity is considered with reference to the Schwarzschild solution to Einstein's field equations of general relativity. A brief derivation of both the original and the modern line elements is given. The…

Translation by S. Antoci and A. Loinger of the fundamental memoir, that contains the ORIGINAL form of the solution of Schwarzschild's problem. The solution is regular in the whole space-time, with the only exception of the origin of the…

General relativity is a non-linear theory with the distinguishing feature that gravitational field energy also acts as gravitational charge density. In the well-known Schwarzschild solution describing field of an isolated massive body at…

A gravitational theory is formulated by considering the physical processes underlying relativistic dilation of time and contraction of space. It is shown that the point mass solution of general relativity's field equation - the…

In this paper, we solved the Einstein's field equation and obtained a line element for static, ellipsoidal objects characterized by the linear eccentricity ($\eta$) instead of quadrupole parameter ($q$). This line element recovers the…

The Einstein gravitational field of a material point at rest is derived anew - by a suitable limit process - from the field of a sphere of a homogeneous and incompressible fluid. This result supports clearly the thesis according to which…

Einstein's general theory of relativity poses many problems to the quantum theory of point particle fields. Among them is the fate of a massive point particle. Since its rest mass exists entirely within its Schwarzschild radius, in the…

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 stationary line element of general relativity seems to be compatible to essential cosmological facts (though only as far as one can expect solving the nonlinear Einstein equations neglecting local cosmic evolution and all spatial…

The Einstein equations for static gravitational field depend on energy density and pressure. So one may expect that solutions should depend on two parameters: mass and its analogue originated from pressure. Yet the Schwarzschild solution…

Gravitational-wave astronomy has the potential to explore one of the deepest and most puzzling aspects of Einstein's theory: the existence of black holes. A plethora of ultracompact, horizonless objects have been proposed to arise in models…

In this paper a solution for a static spherically symmetric body is thoroughly considered in the framework of the Relativistic Theory of Gravitation. By the comparison of this solution with the Schwarzschild solution in General Relativity…

We derive a particular approximate solution of Einstein equations, describing the gravitational field of a mass distribution that slightly deviates from spherical symmetry. The deviation is described by means of a quadrupole parameter that…

The existence of charged elementary 'point particles' still is a basically unsolved puzzle in theoretical physics. The present work takes a fresh look at the problem by including gravity---without resorting to string theory. Using…

The theoretical description of compact structures that share some key features with mass varying particles allows for a simple analysis of equilibrium and stability for massive stellar bodies. We investigate static, spherically symmetric…

Utilizing various gauges of the radial coordinate, we give a General Relativistic (GR) description of static spherically symmetric spacetimes with a massive point source and vacuum outside this singularity. We show that in GR there exists a…

The energy density of the gravitational field is a full-fledged source of the gravitational field. This principle of Einstein was not implemented by him in the Einstein equation. Not long ago it was possible to find an energy-momentum…

We study a numerical solution to Einstein's equation for a compact object composed of null particles. The solution avoids quantum scale regimes and hence neither relies upon nor ignores the interaction of quantum mechanics and gravitation.…

Motivated by studies on gravitational lenses, we present an exact solution of the field equations of general relativity, which is static and spherically symmetric, has no mass but has a non-vanishing spacelike components of the…

Guided by a Hamiltonian treatment of spherically symmetric geometry, we find a remarkably simple -- stationary, but not static -- form for the line element of Schwarzschild (and Reissner-Nordstrom) geometry. The line element continues…