An overview of field theories of gravity

Abstract

In the general relativity theory the basic ingredient to describe gravity is the geometry, which interacts with all forms of matter and energy, and as such, the metric could be interpreted as a true physical quantity. However the metric is not matter nor energy, but instead it is a new dynamical variable that Einstein introduced to describe gravity. In order to conciliate this approach to the more traditional ones, physicists have tried to describe the main ideas of GR in terms of standard conceptions of field theory. In this sense, curved metrics are seen as a dynamical variable emerging from a more fundamental field which lies upon a flat Minkowski spacetime. This was made by the hypothesis that the metric tensor may be written as $g_{μν} = η_{μν} + h_{μν}$ where the tensor $ h_{μν}$ was interpreted either in terms of a spin-2 or constructed in terms of other fields. We review some proposals that were suggested in the treatment of gravity in terms of scalar, spinor and tensor fields configurations.