scholarly journals Extending Sibgatullin's ansatz for the Ernst potential to generate a richer family of axially symmetric solutions of Einstein's equations

2005 ◽  
Vol 8 ◽  
pp. 23-27 ◽  
Author(s):  
T P Sotiriou ◽  
G Pappas
Keyword(s):  
Axially Symmetric ◽  
Einstein’S Equations ◽  
Einstein's Equations ◽  
Ernst Potential

scholarly journals Some axially symmetric zero mass meson solutions of Einstein's equations

1975 ◽  
Vol 19 (2) ◽  
pp. 140-145 ◽  
Author(s):  
L. K. Patel ◽  
V. M. Trivedi
Keyword(s):  
Exact Solutions ◽  
Electromagnetic Fields ◽  
Axially Symmetric ◽  
Einstein’S Equations ◽  
Field Equations ◽  
Einstein's Equations ◽  
Zero Mass ◽  
Oblate Spheroidal

AbstractAn axially symmetric metric in oblate spheroidal co-ordinates is considered. Two exact solutions of the field equations corresponding to zero mass meson fields are obtained. The details of the solutions are also discussed. These solutions are also generalized to include electromagnetic fields.

COVARIANT CONFORMAL DECOMPOSITION OF EINSTEIN EQUATIONS

2002 ◽  
Vol 17 (20) ◽  
pp. 2762-2762
Author(s):  
E. GOURGOULHON ◽  
J. NOVAK
Keyword(s):  
Numerical Simulations ◽  
Extrinsic Curvature ◽  
Einstein Equations ◽  
Numerical Implementation ◽  
Einstein’S Equations ◽  
Einstein's Equations ◽  
Tensor Density ◽  
Dirac Gauge ◽  
Ill Posed ◽  
Isolated Systems

It has been shown1,2 that the usual 3+1 form of Einstein's equations may be ill-posed. This result has been previously observed in numerical simulations3,4. We present a 3+1 type formalism inspired by these works to decompose Einstein's equations. This decomposition is motivated by the aim of stable numerical implementation and resolution of the equations. We introduce the conformal 3-"metric" (scaled by the determinant of the usual 3-metric) which is a tensor density of weight -2/3. The Einstein equations are then derived in terms of this "metric", of the conformal extrinsic curvature and in terms of the associated derivative. We also introduce a flat 3-metric (the asymptotic metric for isolated systems) and the associated derivative. Finally, the generalized Dirac gauge (introduced by Smarr and York5) is used in this formalism and some examples of formulation of Einstein's equations are shown.

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