Conformally flat anisotropic spheres in general relativity

2001 ◽  
Vol 42 (5) ◽  
pp. 2129 ◽  
Author(s):  
L. Herrera ◽  
A. Di Prisco ◽  
J. Ospino ◽  
E. Fuenmayor
Keyword(s):  
General Relativity ◽  
Conformally Flat ◽  
Anisotropic Spheres

scholarly journals Nonlocal gravity: Conformally flat spacetimes

2016 ◽  
Vol 13 (06) ◽  
pp. 1650081 ◽  
Author(s):  
Donato Bini ◽  
Bahram Mashhoon
Keyword(s):  
General Relativity ◽  
Killing Vector ◽  
Conformally Flat ◽  
Einstein’S Field Equations ◽  
Field Equations ◽  
Nonlocal Field ◽  
Theory Of Gravitation ◽  
Flat Spacetimes ◽  
Conformally Flat Spacetimes ◽  
Insight Into

The field equations of the recent nonlocal generalization of Einstein’s theory of gravitation are presented in a form that is reminiscent of general relativity. The implications of the nonlocal field equations are studied in the case of conformally flat spacetimes. Even in this simple case, the field equations are intractable. Therefore, to gain insight into the nature of these equations, we investigate the structure of nonlocal gravity (NLG) in 2D spacetimes. While any smooth 2D spacetime is conformally flat and satisfies Einstein’s field equations, only a subset containing either a Killing vector or a homothetic Killing vector can satisfy the field equations of NLG.

scholarly journals Mirror symmetry and conformal flatness in general Relativity

2004 ◽  
Vol 2004 (41) ◽  
pp. 2205-2208
Author(s):  
P. Gravel ◽  
C. Gauthier
Keyword(s):  
General Relativity ◽  
Mirror Symmetry ◽  
Ricci Tensor ◽  
Conformally Flat ◽  
Conformal Flatness

Using symmetry arguments only, we show that every spacetime with mirror-symmetric spatial sections is necessarily conformally flat. The general form of the Ricci tensor of such spacetimes is also determined.

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