相关论文: The space-time line element for static ellipsoidal…
A recent paper proposes a static ellipsoidal space-time metric that reduces to Schwarzschild. After examining the corrected line element using Maple's Differential geometry package, we find that the Einstein tendor and Ricci scalar are…
This work is a purely syntactic geometric exploration of some few elements, which are our axioms, that in last instance it is the set of differential equations whose solutions give the geodesic lines of the Schwarzschild spacetime. We…
In this paper, we address the issue of linear stability of Schwarzschild space- time subject to certain axisymmetric perturbations. In particular, we prove that associ- ated solutions to the linearized vacuum Einstein equations centered at…
The Einstein field equations are derived for a static cylindrically symmetric spacetime with elastic matter. The equations can be reduced to a system of two nonlinear ordinary differential equations and we present analytical and numerical…
This paper presents a new line element based on the assumption of the variable rest mass in gravitational field, and explores some its implications. This line element is not a vacuum solution of Einstein's equations, yet it is sufficiently…
In this paper we study the even part of the linear stability of the Schwarzschild spacetime as a continuation of [22]. By taking the harmonic gauge, we prove that the energy decays at a rate $\tau^{-2+}$ for the solution of the linearized…
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…
In this paper we analyze the spacetime geometry due to a Schwarzschild object having uniform accelerated motion. In the beginning, we investigate the gravitational field due to a uniformly moving Schwarzschild object and obtain 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…
The Schwarzschild solution is a complete solution of Einstein's field equations for a static spherically symmetric field. The Einstein's field equations solutions appear in the literature, but in different ways corresponding to different…
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.…
We determine the exact solution of the Einstein field equations for the case of a spherically symmetric shell of liquid matter, characterized by an energy density which is constant with the Schwarzschild radial coordinate $r$ between two…
The paper deals with a special kind of problems that appear in solutions of Einstein's field equations for extended bodies: many structure-dependent terms appear in intermediate calculations that cancel exactly in virtue of the local…
The known static isotropic metric of Schwarzschild solution of Einstein equation cannot cover with the range of r<2MG, a new isotropic metric of Schwarzschild solution is obtained. The new isotropic metric has the characters: (1) It is…
A one-fold infinity of explicit quasi-stationary regular line elements for the Schwarzschild geometry is obtained directly from the vacuum Einstein equations. The class includes the familiar Eddington-Finkelstein coordinates, and the…
We present a stationary generalization of the static $q-$metric, the simplest generalization of the Schwarzschild solution that contains a quadrupole parameter. It possesses three independent parameters that are related to the mass,…
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 prove that given a solution of the Einstein equations $g_{ab}$ for the matter field $T_{ab}$, an autoparallel null vector field $l^{a}$ and a solution $(l_{a}l_{c}, \mathcal{T}_{ac})$ of the linearized Einstein equation on the given…
The multipole moments method is not only an aid to understand the deformation of the space-time, but also an effective tool to solve the approximate solutions of the Einstein field equation. However, The usual multipole moments are…
The existence of a simple spherically symmetric and static solution of the Einstein equations in the presence of a cosmological constant vanishing outside a definite value of the radial distance is investigated. A particular succession of…