Black hole spontaneous scalarisation with a positive cosmological constant

TL;DR

This paper investigates how a positive cosmological constant affects the formation and properties of scalarised black holes, revealing new solutions and asymptotic behaviors in de Sitter spacetimes.

Contribution

It demonstrates the existence of new scalarised black hole solutions in de Sitter space, extending previous flat spacetime results, and analyzes their asymptotic properties in different scalar-tensor models.

Findings

No scalarised BH solutions exist if the scalar field is confined between horizons.

Scalarised BHs can extend beyond the cosmological horizon, with mild differences from flat cases.

In extended models, solutions exhibit non-standard asymptotics dominated by tachyonic instability.

Abstract

A scalar field non-minimally coupled to certain geometric [or matter] invariants which are sourced by [electro]vacuum black holes (BHs) may spontaneously grow around the latter, due to a tachyonic instability. This process is expected to lead to a new, dynamically preferred, equilibrium state: a scalarised BH. The most studied geometric [matter] source term for such spontaneous BH scalarisation is the Gauss-Bonnet quadratic curvature [Maxwell invariant]. This phenomenon has been mostly analysed for asymptotically flat spacetimes. Here we consider the impact of a positive cosmological constant, which introduces a cosmological horizon. The cosmological constant does not change the local conditions on the scalar coupling for a tachyonic instability of the scalar-free BHs to emerge. But it leaves a significant imprint on the possible new scalarised BHs. It is shown that no scalarised BH solutions exist, under a smoothness assumption, if the scalar field is confined between the BH and cosmological horizons. Admitting the scalar field can extend beyond the cosmological horizon, we construct new scalarised BHs. These are asymptotically de Sitter in the (matter) Einstein-Maxwell-scalar model, with only mild difference with respect to their asymptotically flat counterparts. But in the (geometric) extended-scalar-tensor-Gauss-Bonnet-scalar model, they have necessarily non-standard asymptotics, as the tachyonic instability dominates in the far field. This interpretation is supported by the analysis of a test tachyon on a de Sitter background.