Black holes and stars in Horndeski theory

Abstract

We review black hole and star solutions for Horndeski theory. For non-shift symmetric theories, black holes involve a Kaluza-Klein reduction of higher dimensional Lovelock solutions. On the other hand, for shift symmetric theories of Horndeski and beyond Horndeski, black holes involve two classes of solutions: those that include, at the level of the action, a linear coupling to the Gauss-Bonnet term and those that involve time dependence in the galileon field. We analyze the latter class in detail for a specific subclass of Horndeski theory, discussing the general solution of a static and spherically symmetric spacetime. We then discuss stability issues, slowly rotating solutions as well as black holes coupled to matter. The latter case involves a conformally coupled scalar field as well as an electromagnetic field and the (primary) hair black holes thus obtained. We review and discuss the recent results on neutron stars in Horndeski theories. arXiv:1604.06402v2 [gr-qc] 29 Jul 2016 ‡ Different subsets of Horndeski theory exhibit similar self-tuning properties towards a de Sitter attractor rather than a Minkowski one, see [18].

Cosmological self-tuning and local solutions in generalized Horndeski theories

“…[20] concluded that an arbitrary s 4 (X) gives a similar solution, while the authors of Ref. [33] considered the Horndeski combination of L (4,0) and L (4,1) , i.e., with s ′ 4 = 1 4 f 4 (see the recent review [51]). …”

Circular orbits and accretion process in a class of Horndeski/Galileon black holes

“…[25], Takahashi and Suyama [37], and Tretyakova and Takahashi [39]). We note that recently it has been pointed out by Babichev et al [5,6] that the conclusion of Ogawa et al [33] and Takahashi and Suyama [37] is incorrect. Now from the recent relations, various solutions for different values of C 0 and q can be obtained.…”

“…We study static and spherically symmetric limit of black hole solutions in a subclass of general Horndeski/Galileon theories (see Maselli [29] for the case of slowly rotating black holes in Horndeski theory and also Babichev et al [4] for black hole and star solutions for Horndeski theory). The general form of the line-element for such systems with the metric signature (+, −, −, −) is described by…”

“…2, a huge variety of solutions can be obtained from Eqs. (4)- (6). Here we present a solution of this subclass of the Horndeski/Galileon setup that are characterized by the parameters A, B, C and γ (see for instance Tretyakova [38]).…”

“…Scalar-tensor theories are a prototype alternative and also they are most probably the simplest, consistent and nontrivial modification of the General Relativity [4]. Gregory Horndeski [15] proposed the most general action of the scalar-tensor gravity.…”