Related papers: What is wrong with Schwarzschild's coordinates?
A careful analysis of the maximally extended metrics of Schwarzschild manifold shows that the original Schwarzschild's solution (1916) and Brillouin's solution (1923) are the only ones that are adequate from the physical standpoint.…
We consider the deformation of the Schwarzschild solution in general relativity due to spherically symmetric quantum fluctuations of the metric and the matter fields. In this case, the 4D theory of gravity with Einstein action reduces to…
A central idea in general relativity is that physics should not depend on the space-time coordinates in use \cite{einstein}. But the qualitative description of various phenomena can appear superficially quite different. Here we consider…
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…
The quantum field theoretic description of general relativity is a modern approach to gravity where gravitational force is carried by spin-2 gravitons. In the classical limit of this theory, general relativity as described by the Einstein…
The definition of well-behaved coordinate charts for black hole spacetimes can be tricky, as they can lead for example to either unphysical coordinate singularities in the metric (e.g. $r=2M$ in the Schwarzschild black hole) or to an…
We consider the perturbation of the Schwarzschild solution by the perimeter action. The asymptotic behaviour of the solution at infinity and at the horizon are calculated and analysed in the first approximation. The perturbation is…
In their original study of conformal gravity, a candidate alternate gravitational theory, Mannheim and Kazanas showed that in any empty vacuum region exterior to a localized static spherically symmetric gravitational source, the geometry…
The so called gamma metric corresponds to a two-parameter family of axially symmetric, static solutions of Einstein's equations found by Bach. It contains the Schwarzschild solution for a particular value of one of the parameters, that…
We show that the Novikov coordinates can be obtained in a direct and physically transparent way from the radial geodesics of massive particles with negative energy in the Schwarzschild spacetime. These geodesics form a complete congruence…
We report a family of self-similar exact solutions in General Relativity. The solutions are found in a Painleve-Gullstrand coordinate system but can also be transformed smoothly into a diagonal form. The solutions represent a gravitational…
We study spherically symmetric static empty space solutions in $R+\varepsilon/R$ model of $f(R)$ gravity. We show that the Schwarzschild metric is an exact solution of the resulted field equations and consequently there are general…
The Painleve-Gullstrand coordinates provide a convenient framework for presenting the Schwarzschild geometry because of their flat constant-time hypersurfaces, and the fact that they are free of coordinate singularities outside r=0.…
The Doppler shift considered in general relativity involves mixed contributions of distinct, gravitational and kinematical origins and for most metrics or trajectories it takes a complex form. The expression for the Doppler shift may…
A general geometrical scheme is presented for the construction of novel classical gravity theories whose solutions obey two-sided bounds on the sectional curvatures along certain subvarieties of the Grassmannian of two-planes. The…
Making use of the classical Binet's equation a general procedure to obtain the gravitational force corresponding to an arbitrary 4-dimensional spacetime is presented. This method provides, for general relativistic scenarios, classics…
The problem of consistent formulation of the correspondence principle in quantum gravity is considered. The usual approach based on the use of the two-particle scattering amplitudes is shown to be in disagreement with the classical result…
Contents: 1) Introduction and a few excursions [A word on the role of explicit solutions in other parts of physics and astrophysics. Einstein's field equations. "Just so" notes on the simplest solutions: The Minkowski, de Sitter and anti-de…
By considering a deformation of the Schwarzschild metric in the presence of a minimal measurable length which still respects the equivalence principle, we study corrections to the standard general relativistic predictions for some…
It is has been long known that the curved space in the presence of gravitation can be described as a non-homogeneous anisotropic medium in flat geometry with different constitutive equations. In this article, we show that the…