Invariant Solutions of Einstein’s Field Equations for Conformally Flat Fluid Spheres of Embedding Class One

2013 ◽  
Vol 52 (11) ◽  
pp. 3960-3964 ◽  
Author(s):  
Smitha Thakadiyil ◽  
M. K. Jasim
Keyword(s):  
Invariant Solutions ◽  
Conformally Flat ◽  
Einstein’S Field Equations ◽  
Field Equations ◽  
Embedding Class One ◽  
Einstein's Field Equations ◽  
Fluid Spheres

INVARIANT SOLUTIONS OF EINSTEIN FIELD EQUATION FOR NONCONFORMALLY FLAT FLUID SPHERES OF EMBEDDING CLASS ONE

2010 ◽  
Vol 25 (20) ◽  
pp. 3993-4000 ◽  
Author(s):  
SACHIN KUMAR ◽  
PRATIBHA ◽  
Y. K. GUPTA
Keyword(s):  
Field Equation ◽  
Einstein Field Equation ◽  
Invariant Solutions ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Free Interface ◽  
Lie Group Of Transformations ◽  
Embedding Class One ◽  
Perfect Fluids ◽  
Fluid Spheres

In the present paper, nonconformal spherical symmetric perfect fluid solutions to Einstein field equations are obtained by using the invariance of the equations under the Lie group of transformations and some new solutions of this category are obtained satisfying the reality conditions like ρ ≥ p ≥ 0, ρr < 0, pr < 0 (p and ρ being pressure and energy-density respectively) in the region 0 < r < a. Such fluids do not represent isolated fluid spheres as pressure free interface is not possible for nonconformally perfect fluids of class one.

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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