Symmetries of stationary axially symmetric vacuum Einstein equations and the new family of exact solutions

1983 ◽  
Vol 24 (3) ◽  
pp. 606-609 ◽  
Author(s):  
Yoshimasa Nakamura
Keyword(s):  
Exact Solutions ◽  
Einstein Equations ◽  
Axially Symmetric ◽  
New Family ◽  
Vacuum Einstein Equations ◽  
Symmetric Vacuum

scholarly journals HORIZONS AND GEODESICS OF BLACK ELLIPSOIDS

2003 ◽  
Vol 12 (03) ◽  
pp. 479-494 ◽  
Author(s):  
SERGIU I. VACARU
Keyword(s):  
Exact Solutions ◽  
Einstein Equations ◽  
Analytic Extension ◽  
Vacuum Einstein Equations ◽  
Geodesic Structure ◽  
Small Deformations

We analyze the horizon and geodesic structure of a class of 4D off–diagonal metrics with deformed spherical symmetries, which are exact solutions of the vacuum Einstein equations with anholonomic variables. The maximal analytic extension of the ellipsoid type metrics are constructed and the Penrose diagrams are analyzed with respect to the adapted frames. We prove that for small deformations (small eccentricities) there are such metrics that the geodesic behaviour is similar to the Schwarzcshild one. We conclude that some vacuum static and stationary ellipsoid configurations1,2 may describe black ellipsoid objects.

The Kerr solution

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Kerr Black Hole ◽  
Geodesic Equation ◽  
Einstein Equations ◽  
Kerr Metric ◽  
Kerr Solution ◽  
Axially Symmetric ◽  
Observable Universe ◽  
Einstein Vacuum Equations ◽  
Einstein Vacuum ◽  
The Many

This chapter covers the Kerr metric, which is an exact solution of the Einstein vacuum equations. The Kerr metric provides a good approximation of the spacetime near each of the many rotating black holes in the observable universe. This chapter shows that the Einstein equations are nonlinear. However, there exists a class of metrics which linearize them. It demonstrates the Kerr–Schild metrics, before arriving at the Kerr solution in the Kerr–Schild metrics. Since the Kerr solution is stationary and axially symmetric, this chapter shows that the geodesic equation possesses two first integrals. Finally, the chapter turns to the Kerr black hole, as well as its curvature singularity, horizons, static limit, and maximal extension.

Numerical methods for solving the planar vacuum Einstein equations

1991 ◽  
Vol 43 (6) ◽  
pp. 1808-1824 ◽  
Author(s):  
Peter Anninos ◽  
Joan Centrella ◽  
Richard A. Matzner
Keyword(s):  
Numerical Methods ◽  
Einstein Equations ◽  
Vacuum Einstein Equations
Sign in / Sign up

Export Citation Format

Share Document