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.
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