Related papers: When is g_{tt} g_{rr} = -1?
We present a formalism to study the metric perturbations of the Schwarzschild spacetime. The formalism is gauge invariant, and it is also covariant under two-dimensional coordinate transformations that leave the angular coordinates…
It is well known that asymptotically flat black holes in general relativity have vanishing tidal Love numbers. In the case of Schwarzschild and Kerr black holes, this property has been shown to be a consequence of a hidden structure of…
Projective invariance is a symmetry of the Palatini version of General Relativity which is not present in the metric formulation. The fact that the Riemann tensor changes nontrivially under projective transformations implies that, unlike in…
In this note we discuss the hypothesis of a presence of the negative mass in the Schwarzschild's spacetime following to ideas of \cite{Villata,Chardin}. We demonstrate, that the discrete $PT$ transformation of the coordinates and mass…
It was previously proved that the G\"{o}del-type metrics with flat three-dimensional background metric solve exactly the field equations of the Einstein-Aether theory in four dimensions. We generalize this result by showing that 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…
This paper examines the inhomogeneous Einstein equation for a static spherically symmetric metric with a source term corresponding to a perfect fluid with p=-rho. By a careful treatment of the equation near the origin we find an analytic…
We investigate a general metric of the Kundt class of spacetimes in higher dimensions. Geometrically, it admits a non-twisting, non-shearing and non-expanding geodesic null congruence. We calculate all components of the curvature and Ricci…
Space-time is spherically symmetric if it admits the group of SO(3) as a group of isometries,with the group orbits spacelike two-surfaces. These orbits are necessarily two-surface of constant positive curavture. One commonly chooses…
Starting with the curvature 2-form a recursive construction of totally antisymmetrised 2p-forms is introduced, to which we refer as p-Riemann tensors. Contraction of indices permits a corresponding generalisation of the Ricci tensor.…
We discuss the opportunity that the singularity inside a Schwarzschild black hole could be replaced by a regular bounce, described as a regular minimum of the spherical radius (instead of zero) and a regular maximum of the longitudinal…
Starting from a general transformation for spherically symmetric metrics where g\_11=-1/g\_00, we analyze coordinates with the common property of conformal flatness at constant solid angle element. Three general possibilities arise: one…
We briefly revisit the Schwarzschild-de Sitter solution in the context of five-dimensional general relativity. We obtain a class of five-dimensional solutions of Einstein vacuum field equations into which the four-dimensional…
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…
Regularity of the horizon radius $r_g$ of a collapsing body constrains a limiting form of a spherically-symmetric energy-momentum tensor near it. Its non-zero limit belongs to one of four classes that are distinguished only by two signs. As…
A contribution linear in r to the gravitational potential can be created by a suitable conformal duality transformation: the conformal factor is 1/(1+r)^2 and r will be replaced by r/(1+r), where r is the Schwarzschild radial coordinate.…
We analyze the quantum mechanical equivalence of the metrics of a centrally symmetric uncharged gravitational field. We consider the static Schwarzschild metric in spherical and isotropic coordinates, the stationary Eddington-Finkelstein…
In a geometric unified theory there is an energy momentum equation, apart from the field equations and equations of motion. The general relativity Einstein equation with cosmological constant follows from this energy momentum equation for…
The Goldberg-Sachs theorem is generalized for all four-dimensional manifolds endowed with torsion-free connection compatible with the metric, the treatment includes all signatures as well as complex manifolds. It is shown that when the Weyl…
The Schwarzschild and Reissner-Nordstrom solutions to Einstein's equations describe space- times which contain spherically symmetric black holes. We consider solutions to the linear wave equation in the exterior of a fixed black hole space-…