General theory of Relativity

4

Einstein’s Law of Gravitation in Empty Space—Schwarzschild Solution

4.1 INTRODUCTION

In this chapter, we will be seeking the solution of Einstein’s law of gravitation for empty space surrounding an isolated and stable gravitating mass, by obtaining a line element of such a space. Einstein had solved this problem by the method of successive approximations but the rigorous solution of this problem was provided by Karl Schwarzschild¹ in 1916. The importance of this solution emanates from the fact that it is specially suited for studying the gravitational field of sun and in addition, in discussing the three crucial tests predicted by the general theory of relativity vis-a-vis the predictions of Newton’s theory of gravitation. To make a mention ...