Spin-Induced Black Hole Spontaneous Scalarization

Abstract

We study scalar fields in a black hole background and show that, when the scalar is suitably coupled to curvature, rapid rotation can induce a tachyonic instability. This instability, which is the hallmark of spontaneous scalarization in the linearized regime, is expected to be quenched by nonlinearities and endow the black hole with scalar hair. Hence, our results demonstrate the existence of a broad class of theories that share the same stationary black hole solutions with general relativity at low spins, but which exhibit black hole hair at sufficiently high spins (a/M 0.5). This result has clear implications for tests of general relativity and the nature of black holes with gravitational and electromagnetic observations.

Spin-Induced Scalarized Black Holes

“…The prospect of such elusive non-Kerr BHs takes a different guise in gravity theories that allow BH scalarization [13,14]. Theories that fashion a coupling between a scalar and the Gauss-Bonnet invariant can exhibit a tachyonic instability near BHs when the BH spin exceeds a certain threshold [15]. Interestingly, crossing that threshold also allows these models to circumvent a known no-hair theorem [13,15].…”

Embedding Gauss–Bonnet Scalarization Models in Higher Dimensional Topological Theories

“…Equations ( 35) are solved numerically, by using the same approach as in the EGBs case. The numerical results indicate the existence, for any α, of a continuum of solutions in terms of the constants φ H , v 1 which enter the near horizon expansion (36). The asymptotic values of the scalar and vector fields depend of the input parameters φ H , v 1 , r H and α (note that, as expected from the structure of the equations, the vector field vanishes identically, when taking v 1 = 0).…”

“…Further work includes the study of scalarized BHs in various extensions of the initial framework [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] and the investigation of solutions' stability [25][26][27][28]; furthermore, partial analytical results are reported in Refs. [29][30][31][32], while scalarized, rotating BHs are studied in [33][34][35][36][37][38][39].…”

Massive scalar field perturbation on Kerr black holes in dynamical Chern–Simons gravity

“…[33]. This is different from the case in sEGB, where α > 0 and α < 0 yield different pictures of instability and spontaneous scalarization, with the latter resulting the so-called spin-induced spontaneous scalarization [43][44][45][46][47][48][49].…”

“…Actually, this novel phenomenon has long been observed in neutron stars but there the instability is caused by the surrounding matter instead of the curvature [35]. It has also been observed and studied extensively most recently in sEGB theory where a similar coupling is present but between the scalar field and the Gauss-Bonnet invariant [36][37][38][39][40][41][42][43][44][45][46][47][48][49].…”