Large and ultracompact Gauss-Bonnet black holes with a self-interacting scalar field

Abstract

We consider the Einstein-scalar-Gauss-Bonnet theory, and study the case where a negative cosmological constant is replaced by a more realistic, negative scalar-field potential. We study different forms of the coupling function between the scalar field and the Gauss-Bonnet term as well as of the scalar potential. In all cases, we obtain asymptotically-flat, regular black-hole solutions with a non-trivial scalar field which naturally dies out at large distances. For a quadratic negative potential, two distinct subgroups of solutions emerge: the first comprises light black holes with a large horizon radius, and the second includes massive, ultra-compact black holes. The most ultra-compact solutions, having approximately the 1/20 of the horizon radius of the Schwarzschild solution with the same mass, emerge for the exponential and linear coupling functions. For other polynomial forms of the scalar potential, the subgroup of ultra-compact solutions disappears, and the black holes obtained may have a horizon radius larger or smaller than the Schwarzschild solution depending on the particular value of their mass.

Embedding Gauss–Bonnet Scalarization Models in Higher Dimensional Topological Theories

“…Setting A = 0, the scalar field possess two ground states at φ ≡ φ 0 = ±1. Also, let us remark that the model is invariant under the transformation φ → −φ, α → −α ; (16) we shall restrict our study to the ground state φ 0 = 1, only. An important physical consequence of the symmetry ( 16) is that, in contrast to other models in the literature [4,5], the scalarization of Schwarzschild BH occurs for both signs of the coupling constant α.…”

“…This model has been extensively studied, starting with [4][5][6][7], where the first examples of scalarized BHs resulting from this type of mechanism have been reported. 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].…”

Horizon curvature and spacetime structure influences on black hole scalarization

“…The generalized study of scalarized black hole solutions and compact objects in asymptotical flat spacetime of ESGB theories was discussed in [44][45][46][47][48][49][50][51][52][53][54]. The spontaneous scalarization of asymptotically AdS/dS black holes in ESGB theory with a negative/positive cosmological constant was extended in [55][56][57][58][59]. Especially, the connections of asymptotically AdS black holes scalarization with holographic phase transitions in the dual boundary theory was studied in [60,61].…”

Scalarized black holes

“…By allowing for more general coupling functions of the scalar field a new interesting phenomenon was observed: curvature induced spontaneous scalarization of black holes [1][2][3][6][7][8]13,[16][17][18]22,24,27,29,30,40,52,[55][56][57]66,67]. In that case an appropriate choice of coupling function allows the GR black holes to remain solutions of the EsGB equations, while, at critical values of the coupling, GR black holes develop a tachyonic instability where new branches of spontaneously scalarized black holes arise.…”