相关论文: When is g_{tt} g_{rr} = -1?
In the Bondi-Sachs formulation of General Relativity space-time is foliated via a family of null cones. If these null cones are defined such that their vertices are traced by a regular world-line then the metric tensor has to obey…
We suggest that the vacuum field equation in Finsler spacetime is equivalent to vanishing of Ricci scalar. Schwarzschild metric can be deduced from a solution of our field equation if the spacetime preserve spherical symmetry. Supposing…
The Kerr-Schild gauge is generalized to the case that the vector generating the deformation is not null. Contrary to naive expectations, this vector generates a finite expansion for the curvature tensor. We prove a theorem on the conditions…
We have proposed a model geometry for the interior of a regular black hole mimicker, the frozen star, whose most startling feature is that each spherical shell in its interior is a surface of infinite redshift. The geometry is a solution 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…
A strict derivation of the Schwarzschild metric, based solely on Newton's law of free fall and the equivalence principle, is presented. In the light of it, regarding Schwarzschild's coordinates as representing the point of view of a distant…
This work is devoted to a mathematical analysis of the distributional Schwarzschild geometry. The Schwarzschild solution is extended to include the singularity; the energy momentum tensor becomes a delta-distribution supported at r=0. Using…
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…
The linearized Kerr metric is considered and put in some Gauss coordinates which are further {\em intrinsic} ones. The linear and angular 4-momenta of this metric are calculated in these coordinates and the resulting value is just zero.…
In (3 + 1) spacetime dimensions the Rainich conditions are a set of equations expressed solely in terms of the metric tensor which are equivalent to the Einstein-Maxwell equations for non-null electromagnetic fields. Here we provide the…
We propose an adaptation of the Kerr-Schild method by implementing the correspondence relations (mapping) between Ricci-based Gravity (RBG) and General Relativity (GR). Basically, we generate GR known solutions from a canonical metric with…
It is shown that if an asymptotically flat spacetime is asymptotically stationary, in the sense that $\Lie_{\xi} g_{ab}$ vanishes at the rate $\sim t^{-3}$ for asymptotically timelike vector field $\xi^a$, and the energy-momentum tensor…
Under consideration of coordinate conditions, we get the Schwarzschild-Beltrami-de Sitter (S-BdS) metric solution of the Einstein field equations with a cosmological constant $\Lambda$. A brief review to the de Sitter invariant special…
To define a free string by the Nambu-Goto action, all we need is the notion of area, and mathematically the area can be defined directly in the absence of a metric. Motivated by the possibility that string theory admits backgrounds where…
It is shown that an arbitrary static, spherically symmetric metric can be presented as an exact solution of a scalar-tensor theory (STT) of gravity with certain nonminimal coupling function $f(\phi)$ and potential $U(\phi)$. The scalar…
The Kerr-Schild pencil of metrics $\tilde g_{ab}=g_{ab}+V l_al_b$, with $g_{ab}$ and $\tilde g_{ab}$ satisfying the vacuum Einstein equations, is investigated in the case when the null vector $l$ has vanishing twist. This class of…
A regularization procedure, that allows one to relate singularities of curvature to those of the Einstein tensor without some of the shortcomings of previous approaches, is proposed. This regularization is obtained by requiring that (i) the…
Spherically symmetric static empty space solutions are studied in f(R) theories of gravity. We reduce the set of modified Einstein's equations to a single equation and show how one can construct exact solutions in different f(R) models. In…
It is well known that asymptotically flat Schwarzschild black holes in general relativity in four spacetime dimensions have vanishing induced linear tidal response. We extend this result beyond linear order for the polar sector, by solving…
The complete set of analytic solutions of the geodesic equation in a Schwarzschild--(anti) de Sitter space--time is presented. The solutions are derived from the Jacobi inversion problem restricted to the theta--divisor. In its final form…