Stability of black holes with non-minimally coupled scalar hair to the Einstein tensor

Abstract

General relativity admits a plethora of exact compact object solutions. The augmentation of Einstein’s action with non-minimal coupling terms leads to modified theories with rich structure, which, in turn, provide non-trivial solutions with intriguing phenomenology. Thus, assessing their viability under generic fluctuations is of utmost importance for gravity theories. We consider static and spherically-symmetric solutions of a Horndeski subclass which includes a massless scalar field non-minimally coupled to the Einstein tensor. Such theory possesses second-order field equations and admits an exact black hole solution with scalar hair. Here, we study the stability of such solution under axial gravitational perturbations and find that it is linearly stable. The qualitative features of the ringdown waveform depend solely on the ratio of the two available parameters of spacetime, namely the black hole mass m and the non-minimal coupling strength $$\ell _\eta $$ ℓ η . Finally, we demonstrate the gravitational-wave ringdown transitions between three distinct patterns as the ratio $$m/\ell _\eta $$ m / ℓ η increases; a state which is dominated by photon-sphere excitations and maintains a typical quasinormal ringdown, an intermediate long-lived state which exhibits gravitational-wave echoes and, finally, a state where the ringdown and echoes are depleted rapidly to turn to an exponential tail.

On the effective metric of axial black hole perturbations in DHOST gravity

“…In DHOST theories, axial perturbations involve, as in GR, a single degree of freedom, in contrast with polar (or even-parity) perturbations which contain two degrees of freedom, one from the metric and the other from the scalar field. For this reason, axial perturbations are easier to study and they have already been investigated in several works in the context of DHOST theories, or subfamilies: from generic BH backgrounds in [6][7][8][9][10] to "stealth" solutions JCAP08(2022)040…”

Stealth Ellis wormholes in Horndeski theories

“…unstable solutions, since it is probable that the higher order kinetic term contributions are able to rectify the instability pathologies associated with a phantom scalar field [97]. In particular, due to the higher order derivative couplings, it is unclear from the definition of the conjugate momentum of the scalar field whether the matter content is indeed of phantom nature.…”

Axial perturbations of black holes in scalar-tensor gravity: near-horizon behaviour

“…Perturbations of BH in the context of DHOST theories have been explored in several works (see e.g. [11][12][13][14][15][16][17][18][19][20][21][22][23][24]). One can also mention other works based on an EFT approach [25][26][27][28][29].…”