Black holes in a type-II minimally modified gravity

TL;DR

This paper investigates black hole solutions within a novel type-II minimally modified gravity theory, revealing deviations from classical solutions and conditions under which standard Schwarzschild metrics are recovered.

Contribution

It provides the first analysis of spherically symmetric vacuum solutions in a new gravity theory, highlighting differences from Einstein gravity and conditions for recovering standard black hole metrics.

Findings

Vacuum solutions differ locally from Schwarzschild metrics.

Solutions can violate the null convergence condition.

Standard Schwarzschild solutions are recovered under certain asymptotic conditions.

Abstract

In the context of the recently proposed type-II minimally modified gravity theory, i.e. a metric theory of gravity with two local physical degrees of freedom that does not possess an Einstein frame, we study spherically symmetric vacuum solutions to explore the strong gravity regime. Despite the absence of extra degrees of freedom in the gravity sector, the vacuum solutions are locally different from the Schwarzschild or Schwarzschild-(A)dS metric in general and thus the Birkhoff theorem does not hold. The general solutions are parameterized by several free functions of time and admit regular trapping and event horizons. Depending on the choice of the free functions of time, the null convergence condition may be violated in vacuum. Even in the static limit, while the solutions in this limit reduce to the Schwarzschild or Schwarzschild-(A)dS solutions, the effective cosmological constant deduced from the solutions is in general different from the cosmological value that is determined by the action. Nonetheless, once a set of suitable asymptotic conditions is imposed so that the solutions represent compact objects in the corresponding cosmological setup, the standard Schwarzschild or Schwarzschild-(A)dS metric is recovered and the effective cosmological constant agrees with the value inferred from the action.