# Spontaneously scalarised Kerr black holes

## TL;DR

This paper constructs and analyzes spinning scalarised black holes in extended scalar-tensor-Gauss-Bonnet models, revealing their properties, stability, and potential observational signatures, especially in relation to black hole spin and deviations from general relativity.

## Contribution

It introduces a new class of spinning scalarised black holes, explores their domain of existence, stability, and observational differences from Kerr black holes, highlighting the influence of spin on scalarisation effects.

## Key findings

- Scalarised black holes exist in a specific mass and spin range.
- Non-uniqueness with Kerr black holes is observed, with scalarised black holes being entropically favored.
- Observable differences from Kerr black holes decrease with increasing spin, especially for high spin values.

## Abstract

We construct asymptotically flat, spinning, regular on and outside an event horizon, scalarised black holes (SBHs) in extended scalar-tensor-Gauss-Bonnet models. They reduce to Kerr BHs when the scalar field vanishes. For an illustrative choice of non-minimal coupling, we scan the domain of existence. For each value of spin, SBHs exist in an interval between two critical masses, with the lowest one vanishing in the static limit. Non-uniqueness with Kerr BHs of equal global charges is observed; the SBHs are entropically favoured. This suggests SBHs form dynamically from the spontaneous scalarisation of Kerr BHs, which are prone to a scalar-triggered tachyonic instability, below the largest critical mass. Phenomenologically, the introduction of BH spin damps the maximal observable difference between comparable scalarised and vacuum BHs. In the static limit, (perturbatively stable) SBHs can store over 20% of the spacetime energy outside the event horizon; in comparison with Schwarzschild BHs, their geodesic frequency at the ISCO can differ by a factor of 2.5 and deviations in the shadow areal radius may top 40%. As the BH spin grows, low mass SBHs are excluded, and the maximal relative differences decrease, becoming of order $\sim$ few % for dimensionless spin $j\gtrsim 0.5$. This reveals a spin selection effect: non-GR effects are only significant for low spin. We discuss if and how the recently measured shadow size of the M87 supermassive BH, constrains the length scale of the Gauss-Bonnet coupling.