Stability of disformally coupled accretion disks

TL;DR

This paper investigates the stability of accretion disks around black holes in scalar-tensor theories with disformal couplings, revealing conditions that can either enhance or suppress scalarisation instabilities relevant for gravitational wave observations.

Contribution

It extends the analysis of spontaneous scalarisation to disformal couplings, showing how these couplings influence black hole stability in scalar-tensor theories.

Findings

Disformal couplings can enhance scalarisation instabilities.

Strong disformal coupling tends to stabilize the system.

Gradients in matter distribution affect the stability outcomes.

Abstract

The no-hair theorem postulates that the only externally observable properties of a black hole are its mass, its electric charge, and its angular momentum. In scalar-tensor theories of gravity, a matter distribution around a black hole can lead to the so called "spontaneous scalarisation" instability that triggers the development of scalar hair. In the Brans-Dicke type theories, this effect can be understood as a result of tachyonic effective mass of the scalar field. Here we consider the instability in the generalised class of scalar-theories that feature non-conformal, i.e. "disformal", couplings to matter. Such theories have gained considerable interest in the recent years and have been studied in a wide variety of systems, both cosmological and astrophysical. In view of the prospects of gravitational wave astronomy, it is relevant to explore the implications of the theories in the strong-gravity regime. In this article, we concentrate on the spontaneous scalarisation of matter configurations around Schwarzschild and Kerr black holes. We find that in the more generic scalar-tensor theories, the instability of the Brans-Dicke theory can be enhanced, suggesting violations of the no-hair theorem. On the other hand, we find that, especially if the coupling is very strong, or if the gradients in the matter distribution are negligible, the disformal coupling tends to stabilise the system.