Static, spherically symmetric objects in Type-II minimally modified gravity

TL;DR

This paper shows that in two specific minimally modified gravity theories, static spherically symmetric star solutions are identical to those in General Relativity when appropriate boundary conditions are applied.

Contribution

It demonstrates that VCDM and VCCDM theories produce solutions identical to GR for static stars under certain boundary conditions, with no extra gravitational degrees of freedom.

Findings

Solutions match GR's TOV equation

No additional gravitational degrees of freedom

Solutions depend on boundary conditions

Abstract

Static, spherically symmetric solutions representing stars made of barotropic perfect fluid are studied in the context of two theories of type-II minimally modified gravity, VCDM and VCCDM. Both of these theories share the property that no additional degree of freedom is introduced in the gravity sector, and propagate only two gravitational waves besides matter fields, as in General Relativity (GR). We find that, on imposing physical boundary conditions on the Misner-Sharp mass of the system, the solutions in V(C)CDM exactly coincide with the ones in GR, namely they also satisfy the Tolman-Oppenheimer-Volkoff equation.