Related papers: On the concept of mass point in general relativity
Schwarzschild's solution of Einstein's field equations in vacuum can be written in many different forms. Unfortunately Schwarzschild's own original form is less nice looking and simple than that latter derived by Droste and Hilbert. We…
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…
Short note by Marcel Brillouin on the representation of the mass point in general relativity.
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.…
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…
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…
An original way of presentation of the Schwarzschild black hole in the form of a point-like mass with making the use of the Dirac $\delta$-function, including a description of a continuous collapse to such a point mass, is given. A…
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…
Schwarzschild's solution to the Einstein Field Equations was one of the first and most important solutions that lead to the understanding and important experimental tests of Einstein's theory of General Relativity. However, Schwarzschild's…
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…
An outstanding problem posed by Einstein's general theory of relativity to the quantum theory of point particle fields is the fate of a massive point particle; for, in the classical solutions of Einstein's theory, such a system should be a…
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…
Einstein's general relativity is the best available theory of gravity. In recent years, spectacular proofs of Einstein's theory have been conducted, which have aroused interest that goes far beyond the narrow circle of specialists. The aim…
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…
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…
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 demonstrate that the Evans-Rosenquist formulation of the optical mechanical analogy, so successful in the application to classical problems, also describes the motion of massless particles in the Schwarzschild field of general…
Einstein established the theory of general relativity and the corresponding field equation in 1915 and its vacuum solutions were obtained by Schwarzschild and Kerr for, respectively, static and rotating black holes, in 1916 and 1963,…
The exact solution for a static spherically symmetric field outside a charged point particle is found in a non-linear $U(1)$ gauge theory with a logarithmic Lagrangian. The electromagnetic self-mass is finite, and for a particular relation…
The concept of mass is central to any theory of gravity. Nevertheless, defining mass in general relativity is a difficult task, and even when it can be accomplished, we still need to investigate whether the typical properties of mass in…