A new interior solution of Einstein's field equations for a spherically symmetric perfect fluid in shear-free motion

1983 ◽  
Vol 16 (15) ◽  
pp. 3529-3532 ◽  
Author(s):  
H Stephani
Keyword(s):  
Perfect Fluid ◽  
Free Motion ◽  
Interior Solution ◽  
Spherically Symmetric ◽  
Einstein’S Field Equations ◽  
Field Equations ◽  
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.

scholarly journals THE SCHWARZSCHILD'S BRANEWORLD SOLUTION

2010 ◽  
Vol 25 (39) ◽  
pp. 3323-3334 ◽  
Author(s):  
J. OVALLE
Keyword(s):  
Interior Solution ◽  
Einstein’S Field Equations ◽  
Field Equations ◽  
Einstein's Field Equations ◽  
Geometric Deformation ◽  
Weyl Functions ◽  
Interior Solutions ◽  
Deformation Approach

In the context of the Randall–Sundrum braneworld, the minimal geometric deformation approach, which has been successfully used to generate exact interior solutions to Einstein's field equations for static braneworld stars with local and nonlocal bulk terms, is used to obtain the braneworld version of the Schwarzschild's interior solution. Using this new solution, the behavior of the Weyl functions is elucidated in terms of the compactness for different stellar distributions.

Sign in / Sign up

Export Citation Format

Share Document