Exact solutions of the Einstein vacuum field equations in Weyl co-ordinates

1969 ◽  
Vol 61 (2) ◽  
pp. 411-424 ◽  
Author(s):  
R. Gautreau ◽  
R. B. Hoffman
Keyword(s):  
Exact Solutions ◽  
Vacuum Field ◽  
Field Equations ◽  
Einstein Vacuum

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 A NEWMAN–PENROSE CALCULATOR FOR INSTANTON METRICS

2008 ◽  
Vol 19 (08) ◽  
pp. 1277-1290 ◽  
Author(s):  
TOLGA BIRKANDAN
Keyword(s):  
Exact Solutions ◽  
Vacuum Field ◽  
Einstein’S Field Equations ◽  
Field Equations ◽  
Gravitational Instantons ◽  
Einstein's Field Equations ◽  
Symbolic Calculator ◽  
Euclidean Signature

We present a Maple11+GRTensorII based symbolic calculator for instanton metrics using Newman–Penrose formalism. Gravitational instantons are exact solutions of Einstein's vacuum field equations with Euclidean signature. The Newman–Penrose formalism, which supplies a toolbox for studying the exact solutions of Einstein's field equations, was adopted to the instanton case and our code translates it for the computational use.

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.

scholarly journals The Axially Symmetric Stationary Vacuum Field Equations in Einstein's Theory of General Relativity

1978 ◽  
Vol 31 (5) ◽  
pp. 427 ◽  
Author(s):  
A Sloane
Keyword(s):  
General Relativity ◽  
Exact Solutions ◽  
Vacuum Field ◽  
Stationary Case ◽  
Axially Symmetric ◽  
Field Equations ◽  
Asymptotically Flat ◽  
Stationary Vacuum ◽  
Flat Metric

All formulations of Einstein's vacuum field equations for which exact solutions have been found in the axially symmetric stationary case are compared, and the inherent restrictions of each are displayed. A measure of their usefulness as theoretical tools is gained by the ease with which they admit Kerr's (1963) solution (it being the simplest asymptotically flat metric of this kind). The solutions found using each formulation are listed and, where possible, suitably classified.

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