scholarly journals Hyperboloidal initial data for the vacuum Einstein equations with cosmological constant

1996 ◽  
Vol 13 (11) ◽  
pp. 3075-3084 ◽  
Author(s):  
János Kánnár
Keyword(s):  
Initial Data ◽  
Cosmological Constant ◽  
Einstein Equations ◽  
Vacuum Einstein Equations

scholarly journals The universality of vacuum Einstein equations with cosmological constant

1994 ◽  
Vol 11 (6) ◽  
pp. 1505-1517 ◽  
Author(s):  
Marco Ferraris ◽  
Mauro Francaviglia ◽  
Igor Volovich
Keyword(s):  
Cosmological Constant ◽  
Einstein Equations ◽  
Vacuum Einstein Equations

TIME-DEPENDENT SOLUTIONS OF 5D VACUUM EINSTEIN EQUATIONS WITH COSMOLOGICAL CONSTANT

2011 ◽  
Vol 26 (22) ◽  
pp. 1673-1679 ◽  
Author(s):  
TAE HOON LEE
Keyword(s):  
Cosmological Constant ◽  
Time Dependence ◽  
Scale Factor ◽  
Einstein Equations ◽  
Time Dependent ◽  
Vacuum Field ◽  
Field Equations ◽  
Vacuum Einstein Equations ◽  
Dimensional Gravity

We solve vacuum field equations in five-dimensional gravity with cosmological constant to determine the time-dependence of the Robertson–Walker scale factor. We discuss its cosmological implications.

Nonlinear solutions for initial data in the vacuum Einstein equations in plane symmetry

1989 ◽  
Vol 39 (8) ◽  
pp. 2155-2171 ◽  
Author(s):  
Peter Anninos ◽  
Joan Centrella ◽  
Richard Matzner
Keyword(s):  
Initial Data ◽  
Einstein Equations ◽  
Plane Symmetry ◽  
Vacuum Einstein Equations ◽  
Nonlinear Solutions

scholarly journals THE EXISTENCE THEOREM FOR THE GENERAL RELATIVISTIC CAUCHY PROBLEM ON THE LIGHT-CONE

2014 ◽  
Vol 2 ◽  
Author(s):  
PIOTR T. CHRUŚCIEL
Keyword(s):  
Cauchy Problem ◽  
Initial Data ◽  
Existence Theorem ◽  
Light Cone ◽  
Existence Of Solutions ◽  
Einstein Equations ◽  
Vacuum Einstein Equations ◽  
General Relativistic

AbstractWe prove existence of solutions of the vacuum Einstein equations with initial data induced by a smooth metric on a light-cone.

scholarly journals POLYHOMOGENEOUS SOLUTIONS OF NONLINEAR WAVE EQUATIONS WITHOUT CORNER CONDITIONS

2006 ◽  
Vol 03 (01) ◽  
pp. 81-141 ◽  
Author(s):  
PIOTR T. CHRUŚCIEL ◽  
SZYMON ŁȨSKI
Keyword(s):  
Initial Data ◽  
Wave Equations ◽  
Space Time ◽  
Einstein Equations ◽  
Nonlinear Wave Equations ◽  
Linear Wave ◽  
Cauchy Problems ◽  
Time Dimension ◽  
Wave Maps ◽  
Corner Conditions

The study of Einstein equations leads naturally to Cauchy problems with initial data on hypersurfaces which closely resemble hyperboloids in Minkowski space-time, and with initial data with polyhomogeneous asymptotics, that is, with asymptotic expansions in terms of powers of ln r and inverse powers of r. Such expansions also arise in the conformal method for analysing wave equations in odd space-time dimension. In recent work it has been shown that for non-linear wave equations, or for wave maps, polyhomogeneous initial data lead to solutions which are also polyhomogeneous provided that an infinite hierarchy of corner conditions holds. In this paper we show that the result is true regardless of corner conditions.

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
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