General Relativity

TL;DR

This paper provides an overview of General Relativity, covering its motivation, mathematical framework, Einstein equations, initial value problem, linear approximation, and its implications for non-gravitational physics in curved spacetime.

Contribution

It offers a comprehensive, accessible summary of the foundational concepts and mathematical tools of General Relativity for a broader readership.

Findings

Explanation of Einstein equations and their derivation

Discussion of the initial value problem in General Relativity

Overview of linear approximation and non-gravitational physics in curved spacetime

Abstract

This is an English translation of the Italian version of an encyclopedia chapter that appeared in the Italian Encyclopedia of the Physical Sciences, edited by Bruno Bertotti (1994). Following requests from colleagues we have decided to make it available to a more general readership. We present the motivation for constructing General Relativity, provide a short discussion of tensor algebra, and follow the set up of Einstein equations. We discuss briefly the initial value problem, the linear approximation and how should non gravitational physics be described in curved spacetime.