Strong breaking of black-hole uniqueness from coexisting scalarization mechanisms

Abstract

Black-hole uniqueness, i.e., the statement that all stationary vacuum black holes in the universe are described by the Kerr solution, is expected to break in theories beyond General Relativity. This breaking can take a particularly strong form, if several branches of black-hole solutions beyond the Kerr solution coexist. We find an example of a theory that exhibits such strong breaking. In this theory, a cubic coupling of a scalar field to the Gauss-Bonnet invariant triggers black-hole scalarization through a non-linear instability of the Kerr solution. At large spin, curvature-induced and spin-induced scalarization mechanisms compete at fixed sign of the coupling. This results in a rich phase structure of black-hole solutions and continuous as well as discontinuous transitions between the different branches of black holes.

Figures (4)

• Figure 1: We plot the Gauss-Bonnet invariant (in units of the black-hole mass) as a function of $\rho$ and $\cos(\theta)$ for $j=0.95$. For a cubic interaction term and fixed sign of the coupling, e.g., $\alpha>0$, there is an unstable direction for the scalar field in all spacetime regions; those with positive Gauss-Bonnet (yellow tones) and those with negative Gauss-Bonnet (blue-gray tones).
• Figure 2: Domain of existence for curvature-induced solutions. The color bars display the deviations of the scalarized solutions (denoted by the subscript “s”) relative to the Kerr solution (denoted by the subscript “Kerr”). Each point in the domain of existence corresponds to a solution characterized by a dimensionless spin $j$ and a coupling parameter $-\alpha/M^2$. From top left to bottom right, we present the deviations in: the horizon area of the scalarized black hole, $A_s$; its Hawking temperature, $T_s$; its entropy, $S_s$; and the scalar charge of the field, $Q_s$.
• Figure 3: Domain of existence of spin-induced solutions. The color scale shows the deviation of the scalarized black hole (denoted by the subscript “s”) from the Kerr solution (denoted by the subscript “Kerr”). Each point corresponds to a solution specified by a coupling $-\alpha/M^2$ and a dimensionless spin $j$. From top left to bottom right, we display the deviations in: the horizon area of the scalarized black hole, $A_s$; its Hawking temperature, $T_s$; its entropy, $S_s$; and the scalar charge, $Q_s$.
• Figure 4: Phase diagram of the theory. The plot is split in four regions: in region I, Kerr and spin-induced solutions co-exist; in region II Kerr, spin- and curvature-induced solutions co-exist. This is the region where black-hole uniqueness is strongly broken; in region III Kerr and curvature-induced solutions co-exist and in region IV only the Kerr solution is present. The main plot is a zoom-in of the whole phase diagram, presented in the inset. The region of the whole phase diagram we zoom in is highlighted with a blue box in the inset. A continuous line describes a discontinuous phase transition and a dashed line a continuous one.