General theory of Relativity

5

Einstein’s Field Equations for Non-Empty Space

5.1 INTRODUCTION

After having discussed the case of Einstein’s equations in empty space, we discuss how these equations are formulated in the presence of matter. Further we assume that the system is spherically symmetric and isotropic about a point in space. While treating the case of static line-element with spherical symmetry, both outside as well as inside the sphere of matter, we will derive the Schwarzschild’s exterior and interior solutions. Lastly, we discuss the conservation laws in general relativity.

5.2 STATIC LINE-ELEMENT WITH SPHERICAL SYMMETRY

Let us consider a static distribution of matter, which exhibits spherical symmetry. The line-element with spherical symmetry is expressed in ...