Solving the Einstein Equation of Gravity

Abstract

In the previous chapter, we showed how mass creates gravity, via the Einstein equation of gravity. In this chapter, we determine the most famous exact solution of the Einstein equation, that is the Schwarzschild solution. This is about how space-time bends around a ball-like heavy mass like a star or planet. In the preceding chapters, we already learned more or less how space-time bends around a ball, letting a small test-mass free-fall towards the ball, starting from a far-away point. Here we determine how fast this test-mass will free-fall. This enables us to summarize how space-time is bending around a ball-like mass, by writing the Schwarzschild metric in plain language. We also will see how the classical Newton law of gravity fits in.