A Bi-Metric Theory with Exchange Symmetry

TL;DR

This paper introduces a bi-metric extension of General Relativity with an exchange symmetry, leading to new source terms and modified solutions like Schwarzschild and Friedmann-Robertson-Walker metrics.

Contribution

It presents a novel bi-metric theory with exchange symmetry, generating additional source terms and exploring its implications on classical solutions.

Findings

Additional source terms modify Einstein's equations.

Exchange symmetry constrains the form of the second metric.

Modified solutions include generalized Schwarzschild and FRW metrics.

Abstract

We propose an extension of General Relativity with two different metrics. To each metric we define a Levi-Cevita connection and a curvature tensor. We then consider two types of fields, each of which moves according to one of the metrics and its connection. To obtain the field equations for the second metric we impose an exchange symmetry on the action. As a consequence of this ansatz, additional source terms for Einstein's field equations are generated. We discuss the properties of these additional fields, and consider the examples of the Schwarzschild solution, and the Friedmann-Robertson-Walker metric.