scholarly journals On relativistic multipole moments of stationary space–times

2018 ◽  
Vol 5 (7) ◽  
pp. 180640 ◽  
Author(s):  
Francisco Frutos-Alfaro ◽  
Michael Soffel
Keyword(s):  
Gravitational Field ◽  
Exact Solutions ◽  
Vacuum Field ◽  
Multipole Moments ◽  
Field Equations ◽  
Exterior Field ◽  
Static Vacuum ◽  
Vacuum Solutions

Among the known exact solutions of Einstein's vacuum field equations the Manko–Novikov and the Quevedo–Mashhoon metrics might be suitable ones for the description of the exterior gravitational field of some real non-collapsed body. A new proposal to represent such exterior field is the stationary q -metric. In this contribution, we computed by means of the Fodor–Hoenselaers–Perjés formalism the lowest 10 relativistic multipole moments of these metrics. Corresponding moments were derived for the static vacuum solutions of Gutsunayev–Manko and Hernández–Martín. A direct comparison between the multipole moments of these non-isometric space–times is given.

scholarly journals A class of axially symmetric stationary exact solutions of Einstein's vacuum field equations

1978 ◽  
Vol 20 (3) ◽  
pp. 344-351
Author(s):  
M. D. Patel
Keyword(s):  
Gravitational Field ◽  
Exact Solutions ◽  
Coordinate System ◽  
Stationary Distribution ◽  
Vacuum Field ◽  
Axially Symmetric ◽  
Field Equations ◽  
System A ◽  
Oblate Spheroidal

AbstractEinstein's vacuum field equations of an axially symmetric stationary rotating source are studied. Using the oblate spheroidal coordinate system, a class of asymptotically fiat solutions representing the exterior gravitational field of a stationary rotating oblate spheroidal source is obtained. Also it is proved that an analytic axisymmetric and stationary distribution of dust cannot be the source for the gravitational field described by the axisymmetric stationary metric.

A spatially homogeneous gravitational field

1966 ◽  
Vol 62 (1) ◽  
pp. 87-89 ◽  
Author(s):  
V. Joseph
Keyword(s):  
Gravitational Field ◽  
Canonical Form ◽  
Riemann Tensor ◽  
Vacuum Field ◽  
Type I ◽  
Field Equations ◽  
Parameter Group ◽  
Spatially Homogeneous ◽  
Homogeneous Gravitational Field ◽  
Type V

AbstractA solution of Einstein's vacuum field equations, apparently new, is exhibited. The metric, which is homogeneous (that is, admits a three-parameter group of motions transitive on space-like hypersurfaces), belongs to Taub Type V. The canonical form of the Riemann tensor, which is of Petrov Type I, is determined.

Exact solutions of the field equations: twist-free pure radiation fields

1962 ◽  
Vol 270 (1342) ◽  
pp. 328-334 ◽  
Keyword(s):  
General Relativity ◽  
Exact Solutions ◽  
Radiation Field ◽  
Relativity Theory ◽  
Vacuum Field ◽  
Field Equations ◽  
General Relativity Theory ◽  
Pure Radiation ◽  
Radiation Fields ◽  
Null Congruence

This note is intended to give a rough survey of the results obtained in the study of twist-free pure radiation fields in general relativity theory. Here we are using the following Definition. A space-time ( V 4 of signature +2) is called a pure radiation field if it contains a distortion-free geodetic null congruence (a so-called ray congruence ), and if it satisfies certain field equations which we will specify below (e.g. Einstein’s vacuum-field equations). A (null) congruence is called twist-free if it is hypersurface-orthogonal (or ‘normal’). The results listed below were obtained by introducing special (‘canonical’) co-ordinates adapted to the ray congruence. Detailed proofs were given by Robinson & Trautman (1962) and by Jordan, Kundt & Ehlers (1961) (see also Kundt 1961). For the sake of completeness we include in our survey the subclass of expanding fields, and make use of some formulae first obtained by Robinson & Trautman.

scholarly journals Exact Solutions in Poincaré Gauge Gravity Theory

Universe ◽  
2019 ◽  
Vol 5 (5) ◽  
pp. 127 ◽  
Author(s):  
Yuri N. Obukhov
Keyword(s):  
Gravitational Field ◽  
Gravity Models ◽  
Field Potentials ◽  
De Sitter ◽  
Field Equations ◽  
Yang Mills ◽  
Gravitational Field Equations ◽  
Poincaré Symmetry ◽  
Gauge Gravity ◽  
Vacuum Solutions

In the framework of the gauge theory based on the Poincaré symmetry group, the gravitational field is described in terms of the coframe and the local Lorentz connection. Considered as gauge field potentials, they give rise to the corresponding field strength which are naturally identified with the torsion and the curvature on the Riemann–Cartan spacetime. We study the class of quadratic Poincaré gauge gravity models with the most general Yang–Mills type Lagrangian which contains all possible parity-even and parity-odd invariants built from the torsion and the curvature. Exact vacuum solutions of the gravitational field equations are constructed as a certain deformation of de Sitter geometry. They are black holes with nontrivial torsion.

scholarly journals PARAMETRIC NONHOLONOMIC FRAME TRANSFORMS AND EXACT SOLUTIONS IN GRAVITY

2007 ◽  
Vol 04 (08) ◽  
pp. 1285-1334 ◽  
Author(s):  
SERGIU I. VACARU
Keyword(s):  
Gravitational Field ◽  
Exact Solutions ◽  
General Scheme ◽  
Nonlinear Partial Differential Equations ◽  
Killing Vector ◽  
Field Equations ◽  
Finsler Spaces ◽  
Gravitational Field Equations ◽  
Pp Wave ◽  
Physical Consequences

A generalized geometric method is developed for constructing exact solutions of gravitational field equations in Einstein theory and generalizations. First, we apply the formalism of nonholonomic frame deformations (formally considered for nonholonomic manifolds and Finsler spaces) when the gravitational field equations transform into systems of nonlinear partial differential equations which can be integrated in general form. The new classes of solutions are defined by generic off-diagonal metrics depending on integration functions on one, two and three (or three and four) variables if we consider four (or five) dimensional spacetimes. Second, we use a general scheme when one (two) parameter families of exact solutions are defined by any source-free solutions of Einstein's equations with one (two) Killing vector field(s). A successive iteration procedure results in new classes of solutions characterized by an infinite number of parameters for a non-Abelian group involving arbitrary functions on one variable. Five classes of exact off-diagonal solutions are constructed in vacuum Einstein and in string gravity describing solitonic pp-wave interactions. We explore possible physical consequences of such solutions derived from primary Schwarzschild or pp-wave metrics.

The First Solutions and the Challenge of Their Interpretation

2017 ◽  
Author(s):  
Hanoch Gutfreund ◽  
Jürgen Renn
Keyword(s):  
Exact Solution ◽  
Approximate Solution ◽  
Gravitational Field ◽  
Exact Solutions ◽  
De Sitter ◽  
Field Equations ◽  
Gravitational Field Equations ◽  
Nonlinear Character ◽  
Georges Lemaître

This chapter discusses the first wave of the exploration of exact solutions to Einstein's gravitational field equations. When Einstein published the final form of the field equations in 1915, only an approximate solution was known. Given the complicated nonlinear character of the field equations, he did not expect that exact solutions could easily be found. He was all the more surprised when the astronomer Karl Schwarzschild presented him with just such an exact solution. Thus, this chapter presents a series of these solutions, beginning with the work of Karl Schwarzschild, Johannes Droste, Willem de Sitter, Alexander Friedmann, Hans Reissner, Gunnar Nordström, and finally, Georges Lemaître.

PHYSICAL PROPERTIES OF THE THIN ACCRETION DISK OF THE TAUB-NUT BLACK HOLE

2021 ◽  
Vol 0 (1) ◽  
pp. 87-91
Author(s):  
R.M. YUSUPOVA ◽  
◽  
R.N. ZMAILOV ◽  
Keyword(s):  
Black Hole ◽  
Angular Momentum ◽  
Gravitational Field ◽  
Physical Properties ◽  
Accretion Disk ◽  
Energy Flow ◽  
Field Equations ◽  
Effective Potential Energy ◽  
Gravitational Field Equations ◽  
Vacuum Solutions

The Taub-NUT space-time metric is one of the vacuum solutions to Einstein's gravitational field equations. In this metric, the Newman-Unti-Tamburino parameter (NUT) and its effect on the physical properties of a thin accretion disk are of particular interest. In this paper, calculations are performed to determine the physical properties of a thin accretion disk around the Taub-NUT black hole based on the Page-Thorne model. The influence of the NUT parameter on the angular velocity, binding energy, angular momentum of particles, effective potential, energy flow, and temperature of the accretion disk is revealed. According to the data obtained, the temperature of the accretion disk of the Taub-NUT black hole decreases as the value of the NUT parameter increases.

Static axisymmetric discs and gravitational collapse

1987 ◽  
Vol 413 (1844) ◽  
pp. 251-262 ◽  
Keyword(s):  
Gravitational Collapse ◽  
Energy Condition ◽  
Naked Singularity ◽  
Cosmic Censorship ◽  
Field Equations ◽  
Exterior Field ◽  
Thin Disc ◽  
Cosmic Censorship Hypothesis ◽  
Hoop Conjecture ◽  
Vacuum Solutions

Regular static axisymmetric vacuum solutions of Einstein’s field equations representing the exterior field of a finite thin disc are found. These are used to describe the slow collapse of a disc-like object. If no conditions are placed on the matter, a naked singularity is formed and the cosmic censorship hypothesis would be violated. Imposition of the weak energy condition, however, prevents slow collapse to a singularity and preserves the validity of this hypothesis. The validity of the hoop conjecture is also discussed.

Sign in / Sign up

Export Citation Format

Share Document