Static and spherically symmetric general relativity solutions in Minimal Theory of Bigravity

TL;DR

This paper explores static, spherically symmetric solutions in the Minimal Theory of Bigravity, revealing conditions under which Schwarzschild-de Sitter spacetimes are solutions in different branches and coordinate systems, including matter configurations like neutron stars.

Contribution

It demonstrates the existence of specific Schwarzschild-de Sitter solutions in the self-accelerating branch of MTBG and clarifies their coordinate dependence and matter compatibility.

Findings

Schwarzschild-de Sitter solutions exist in the self-accelerating branch of MTBG.

Different coordinate choices affect solution compatibility with branches.

Matter solutions like neutron stars are compatible in the self-accelerating branch.

Abstract

We investigate static and spherically symmetric solutions in the Minimal Theory of Bigravity (MTBG). First, we show that a pair of Schwarzschild-de Sitter spacetimes with different cosmological constants and black hole masses written in the spatially-flat Gullstrand-Painlev\'e (GP) coordinates is a solution in the self-accelerating branch of MTBG, while it cannot be a solution in the normal branch. We then illustrate how Schwarzschild-de Sitter solutions can become compatible with the normal branch when using different coordinates. We also confirm that the self-accelerating branch of MTBG admits static and spherically symmetric general relativity solutions with matter written in the spatially-flat coordinates, including neutron stars with arbitrary matter equations of state. Finally, we show that in the self-accelerating branch nontrivial solutions are given by the Schwarzschild-de Sitter metrics written in nonstandard coordinates.