Asymptotically flat black holes in Horndeski theory and beyond

Abstract

Abstract. We find spherically symmetric and static black holes in shift-symmetric Horndeski and beyond Horndeski theories. They are asymptotically flat and sourced by a non trivial static scalar field. The first class of solutions is constructed in such a way that the Noether current associated with shift symmetry vanishes, while the scalar field cannot be trivial. This in certain cases leads to hairy black hole solutions (for the quartic Horndeski Lagrangian), and in others to singular solutions (for a Gauss-Bonnet term). Additionally, we find the general spherically symmetric and static solutions for a pure quartic Lagrangian, the metric of which is Schwarzschild. We show that under two requirements on the theory in question, any vacuum GR solution is also solution to the quartic theory. As an example, we show that a Kerr black hole with a non-trivial scalar field is an exact solution to these theories.

Constraints on tidal charge of the supermassive black hole at the Galactic Center with trajectories of bright stars

“…Moreover, a Reissner–Nordström metric could arise in a natural way in alternative theories of gravity like Reissner–Nordström solutions with a tidal charge in Randall–Sundrum model [2] (such an approach is widely discussed in the literature). Recently, it was found that Reissner–Nordström metric is a rather natural solution in Horndeski gravity [71] and in this case parameter reflects an interaction with a scalar field and it could be also negative similarly to a tidal charge. In paper [71] it was expressed an opinion that the hairy black hole solutions look rather realistic and these objects could exist in centers of galaxies and if such objects (hairy black holes in Horndeski gravity) exist in nature, in particular in the Galactic Center, current and future advanced facilities such as GRAVITY [72], E-ELT [73], TMT [74] etc.…”

Black holes in vector-tensor theories

“…Moving inward from infinity, g rr and F vary continuously taking non-zero values, so only the allowed profile consistent with J r = 0 is the no-hair solution satisfying φ ′ = 0. In other words, in order to have a non-trivial hairy BH solution, one has to break at least one of the assumptions made by Hui and Nicolis. If the constancy of F is not imposed in the limit φ ′ → 0, there exist some hairy BH solutions in shift-symmetric Horndeski theories with non-vanishing values of φ ′ [24][25][26][27][28][29]. In the case where the scalar field is linearly coupled to a Gauss-Bonnet term, the function F contains a negative power of φ ′ , which allows the existence of solutions with φ ′ = 0 [27,28].…”

Gravitational lensing by a Horndeski black hole

“…Recently, a new class of scalar-tensor theories that extend Horndeski (dubbed "beyond Horndeski") was introduced, with equations of motion of higher order in the derivatives [52,53], but with the property that the true propagating degrees of freedom obey well-behaved second-order equations, thus being free from Ostrogradski instabilities. The study of black holes in Horndeski and beyond Horndeski theories has received much attention lately [54][55][56][57][58][59][60][61]. Other researchers have explored various related topics in these theories [62,63].…”

“…In this work, we investigate the behavior as gravitational lenses of the spherically symmetric and asymptotically flat black holes in Horndeski gravity introduced in Ref. [61]. In Sect.…”