Black hole scalarisation from the breakdown of scale-invariance

Abstract

Electro-vacuum black holes are scale-invariant; their energy-momentum tensor is traceless. Quantum corrections of various sorts, however, can often produce a trace anomaly and a breakdown of scale-invariance. The (quantum-corrected) black hole solutions of the corresponding gravitational effective field theory (EFT) have a non-vanishing Ricci scalar. Then, the presence of a scalar field with the standard non-minimal coupling $\xi {\varphi }^{2}R$ naturally triggers a spontaneous scalarisation of the corresponding black holes. This scalarisation phenomenon occurs for an (infinite) discrete set of $\xi$. We illustrate the occurrence of this phenomenon for two examples of static, spherically symmetric, asymptotically flat black hole solution of EFTs. In one example the trace anomaly comes from the matter sector -- a novel, closed form, generalisation of the Reissner-Nordström solution with an $F^4$ correction -- whereas in the other example it comes from the geometry sector -- a noncommutative geometry generalization of the Schwarzschild black hole. For comparison, we also consider the scalarisation of a black hole surrounded by (non-conformally invariant) classical matter (Einstein-Maxwell-dilaton black holes). We find that the scalarised solutions are, generically, entropically favoured.

27 pages, 11 figures

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Cited by in corpus (5)

• Black hole spontaneous scalarisation with a positive cosmological constant
• Spontaneous scalarization of charged black holes at the approach to extremality
• On the Existence of Solutions with a Horizon in Pure Scalar-Gauss-Bonnet Theories
• A class of solitons in Maxwell-scalar and Einstein-Maxwell-scalar models
• Scalarization of compact stars in the scalar-Gauss-Bonnet gravity