Charged Gauss-Bonnet black holes supporting non-minimally coupled scalar clouds: Analytic treatment in the near-critical regime

Abstract

Recent numerical studies have revealed the physically intriguing fact that charged black holes whose charge-to-mass ratios are larger than the critical value $(Q/M{)}_{\text{crit}}=\sqrt{2(9+\sqrt{6})}/5$ can support hairy matter configurations which are made of scalar fields with a non-minimal negative coupling to the Gauss-Bonnet invariant of the curved spacetime. Using {\it analytical} techniques, we explore the physical and mathematical properties of the composed charged-black-hole-nonminimally-coupled-linearized-massless-scalar-field configurations in the near-critical $Q/M\gtrsim (Q/M{)}_{\text{crit}}$ regime. In particular, we derive an analytical resonance formula that describes the charge-dependence of the dimensionless coupling parameter ${\bar{\eta }}_{\text{crit}}={\bar{\eta }}_{\text{crit}}(Q/M)$ of the composed Einstein-Maxwell-nonminimally-coupled-scalar-field system along the {\it existence-line} of the theory, a critical border that separates bald Reissner-Nordström black holes from hairy charged-black-hole-scalar-field configurations. In addition, it is explicitly shown that the large-coupling $-{\bar{\eta }}_{\text{crit}}(Q/M)\gg 1$ analytical results derived in the present paper for the composed Einstein-Maxwell-scalar theory agree remarkably well with direct numerical computations of the corresponding black-hole-field resonance spectrum.

8 pages

References in corpus (14)

• Spontaneously scalarised Kerr black holes
• Black holes with scalar hair in light of the Event Horizon Telescope
• Spin-induced scalarized black holes
• Spin-induced black hole scalarization in Einstein-scalar-Gauss-Bonnet theory
• Kerr-Newman black holes with stationary charged scalar clouds
• Black hole scalarization induced by the spin -- 2+1 time evolution
• Gravity and Scalar Fields
• Spontaneous scalarization of Gauss-Bonnet black holes: Analytic treatment in the linearized regime
• No nonminimally coupled massless scalar hair for spherically symmetric neutral black holes
• Reissner-Nordström black holes supporting non-minimally coupled massive scalar field configurations
• No hair for spherically symmetric neutral black holes: nonminimally coupled massive scalar fields
• Gauss-Bonnet black holes supporting massive scalar field configurations: The large-mass regime
• Spin-charge induced scalarization of Kerr-Newman black-hole spacetimes
• Nontrivial spatial behavior of the Gauss-Bonnet curvature invariant of rapidly-rotating Kerr black holes

Cited by in corpus (1)

• Aschenbach effect and circular orbits in static and spherically symmetric black hole backgrounds