2019•Cambridge University Press eBooksRequires access

Nonperturbative Gravity: The Vacuum Schwarzschild Solution

Horaƫiu Năstase

Abstract

The nonpeturbative Schwarzschild solution of the Einstein's equations in vacuum is found. We start with the Newtonian limit for gravity, and find the metric in terms of the Newton potential. We write an ansatz, and solve the equations of motion to find the solution. The Schwarzschild black hole and its event horizon are defined. Birkhoff's theorem for the uniqueness of the Schwarzschild solution is stated.

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Available abstract

Key concepts: Deriving the Schwarzschild solution, Schwarzschild metric, Schwarzschild geodesics, Schwarzschild radius, Kerr metric, Event horizon, Ansatz, Physics