Relativistic star solutions in Mass-varying Massive Gravity with a diagonal metric

TL;DR

This paper explores relativistic star solutions in Mass-Varying Massive Gravity with a diagonal metric, revealing that non-trivial solutions are generally impossible due to complex differential constraints, unlike in non-diagonal metric cases.

Contribution

It demonstrates that diagonal metric solutions in MVMG cannot support non-trivial relativistic stars, highlighting the importance of metric choice in such theories.

Findings

Diagonal metric solutions are limited to trivial cases with constant graviton mass.

Non-trivial relativistic star solutions exist only with non-diagonal metrics.

Differential-algebraic equations impose constraints preventing non-trivial solutions in diagonal cases.

Abstract

We investigate relativistic star solutions in Mass-Varying Massive Gravity (MVMG) with a diagonal metric. Contrary to the intuition that there is no fundamental difference between diagonal metric and non-diagonal metric solutions regarding relativistic stars, we find that with a diagonal metric, well-behaved relativistic star solutions may not exist except for trivial ones in which the graviton mass is a constant, whereas non-trivial relativistic star solutions had been found in MVMG with a non-diagonal metric. The reason is that with a diagonal metric, the field equations constitute a system of differential-algebraic equations of differential index-2 with two extra constraints that have a significant influence on the system, rendering the relativistic star solution with a non-trivial graviton mass configuration impossible in most cases.