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 How Extra Symmetries Affect Solutions in General Relativity

Universe ◽  
2020 ◽  
Vol 6 (10) ◽  
pp. 170
Author(s):  
Aroonkumar Beesham ◽  
Fisokuhle Makhanya
Keyword(s):  
General Relativity ◽  
Exact Solutions ◽  
Einstein’S Field Equations ◽  
Field Equations ◽  
Einstein's Field Equations

To get exact solutions to Einstein’s field equations in general relativity, one has to impose some symmetry requirements. Otherwise, the equations are too difficult to solve. However, sometimes, the imposition of too much extra symmetry can cause the problem to become somewhat trivial. As a typical example to illustrate this, the effects of conharmonic flatness are studied and applied to Friedmann–Lemaitre–Robertson–Walker spacetime. Hence, we need to impose some symmetry to make the problem tractable, but not too much so as to make it too simple.

Exact Solutions of Einstein's Field Equations

2003 ◽  
Author(s):  
Hans Stephani ◽  
Dietrich Kramer ◽  
Malcolm MacCallum ◽  
Cornelius Hoenselaers ◽  
Eduard Herlt
Keyword(s):  
Exact Solutions ◽  
Einstein’S Field Equations ◽  
Field Equations ◽  
Einstein's Field Equations
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