Symmetries of Einstein’s field equations with a perfect fluid source as examples of Lie–Bäcklund symmetries

1988 ◽  
Vol 29 (7) ◽  
pp. 1650-1654 ◽  
Author(s):  
H. Stephani
Keyword(s):  
Perfect Fluid ◽  
Einstein’S Field Equations ◽  
Field Equations ◽  
Fluid Source ◽  
Einstein's Field Equations

Generalized Ricci recurrent spacetimes and GRW spacetimes

2021 ◽  
pp. 2150209
Author(s):  
Sudhakar K. Chaubey ◽  
Young Jin Suh
Keyword(s):  
Vector Field ◽  
Cosmological Constant ◽  
Perfect Fluid ◽  
Ricci Soliton ◽  
Einstein’S Field Equations ◽  
Field Equations ◽  
Einstein's Field Equations ◽  
Almost Ricci Soliton ◽  
Perfect Fluid Spacetime ◽  
Fluid Spacetimes

The main goal of this paper is to study the properties of generalized Ricci recurrent perfect fluid spacetimes and the generalized Ricci recurrent (generalized Robertson–Walker (GRW)) spacetimes. It is proven that if the generalized Ricci recurrent perfect fluid spacetimes satisfy the Einstein’s field equations without cosmological constant, then the isotropic pressure and the energy density of the perfect fluid spacetime are invariant along the velocity vector field of the perfect fluid spacetime. In this series, we show that a generalized Ricci recurrent perfect fluid spacetime satisfying the Einstein’s field equations without cosmological constant is either Ricci recurrent or Ricci symmetric. An [Formula: see text]-dimensional compact generalized Ricci recurrent GRW spacetime with almost Ricci soliton is geodesically complete, provided the soliton vector field of almost Ricci soliton is timelike. Also, we prove that a (GR)n GRW spacetime is Einstein. The properties of (GR)n GRW spacetimes equipped with almost Ricci soliton are studied.

A brief survey of general relativity

2019 ◽  
pp. 25-50
Author(s):  
Nils Andersson
Keyword(s):  
General Relativity ◽  
Geometric Theory ◽  
Einstein’S Field Equations ◽  
Curved Spacetime ◽  
Field Equations ◽  
Einstein's Field Equations ◽  
Theory Of Gravity

This chapter provides an overview of Einstein’s geometric theory of gravity – general relativity. It introduces the mathematics required to model the motion of objects in a curved spacetime and provides an intuitive derivation of Einstein’s field equations.

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