Projective equivalence of Einstein spaces in general relativity

2009 ◽  
Vol 26 (12) ◽  
pp. 125009 ◽  
Author(s):  
G S Hall ◽  
D P Lonie
Keyword(s):  
General Relativity ◽  
Projective Equivalence ◽  
Einstein Spaces

scholarly journals f-SYMBOLS, KILLING TENSORS AND CONSERVED BEL-TYPE CURRENTS

2011 ◽  
Vol 26 (05) ◽  
pp. 337-349
Author(s):  
OVIDIU TINTAREANU-MIRCEA
Keyword(s):  
General Relativity ◽  
Vector Fields ◽  
Killing Vector ◽  
Killing Vector Fields ◽  
Killing Tensors ◽  
Einstein Spaces ◽  
Conserved Currents

In the framework of the General Relativity we show that from three generalizations of Killing vector fields, namely f-symbols, symmetric Stäckel–Killing and antisymmetric Killing–Yano tensors, some conserved currents can be obtained through adequate contractions of the above-mentioned objects with rank-four tensors having the properties of Bel or Bel–Robinson tensors in Einstein spaces.

scholarly journals Generic off-diagonal solutions and solitonic hierarchies in (modified) gravity

2015 ◽  
Vol 30 (19) ◽  
pp. 1550090 ◽  
Author(s):  
Sergiu I. Vacaru
Keyword(s):  
General Relativity ◽  
Exact Solutions ◽  
Modified Gravity ◽  
Field Equations ◽  
Physical Data ◽  
Modified Gravity Theories ◽  
De Vries ◽  
Einstein Spaces ◽  
Curve Flows ◽  
Gravity Theories

We have summarized our recent results on encoding exact solutions of field equations in Einstein and modified gravity theories into solitonic hierarchies derived for nonholonomic curve flows with associated bi-Hamilton structure. We argue that there is a canonical distinguished connection for which the fundamental geometric/physical equations decouple in general form. This allows us to construct very general classes of generic off-diagonal solutions determined by corresponding types of generating and integration functions depending on all (spacetime) coordinates. If the integral varieties are constrained to zero torsion configurations, we can extract solutions for the general relativity (GR) theory. We conclude that the geometric and physical data for various classes of effective/modified Einstein spaces can be encoded into multi-component versions of the sine-Gordon, or modified Korteweg–de Vries equations.

General Relativity

2006 ◽  
Author(s):  
M. P. Hobson ◽  
G. P. Efstathiou ◽  
A. N. Lasenby
Keyword(s):  
General Relativity
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