Do we really require a curved description of spacetime to explain gravity?

Abstract

The most radical feature of General Relativity was its identification of gravity with spacetime curvature. However, in attempts to find a unified field theory, Einstein himself discovered an alternate way to look at gravity in which spacetime was globally flat, but gravity was mediated by torsion. In this thesis, we will discuss two such theories of gravity which are equivalent to general relativity but build upon globally flat spacetime. The theories which will be discussed are Teleparallel Equivalent of General Relativity (TEGR) and Symmetric Teleparallel Equivalent of General Relativity (STEGR). We will show that the identification of gravity with spacetime curvature is not unique but a mere convention. These theories give two other equivalent but conceptually very different ways to look at gravity. We will show that classically all three theories are indistinguishable and which one represents the reality we do not know.