Homogeneous black strings in Einstein–Gauss–Bonnet with Horndeski hair and beyond

Abstract

In this paper we construct new exact solutions in Einstein-Gauss-Bonnet and Lovelock gravity, describing asymptotically flat black strings. The solutions exist also under the inclusion of a cosmological term in the action, and are supported by scalar fields with finite energy density, which are linear along the extended direction and have kinetic terms constructed out from Lovelock tensors. The divergenceless nature of the Lovelock tensors in the kinetic terms ensures that the whole theory is second order. For spherically, hyperbolic and planar symmetric spacetimes on the string, we obtain an effective Wheeler's polynomial which determines the lapse function up to an algebraic equation. For the sake of concreteness, we explicitly show the existence of a family of asymptotically flat black strings in six dimensions, as well as asymptotically AdS 5 × R black string solutions and compute the temperature, mass density and entropy density. We compute the latter by Wald's formula and show that it receives a contribution from the non-minimal kinetic coupling of the matter part, shifting the one-quarter factor coming from the Einstein term, on top of the usual non areal contribution arising from the quadratic Gauss-Bonnet term. Finally, for a special value of the couplings of the theory in six dimensions, we construct strings that contain asymptotically AdS wormholes as well as rotating solutions on the transverse section. By including more scalars the strings can be extended to p-branes, in arbitrary dimensions.

A new exact solution of black-strings-like with a dS core

“…The warp factor depends only on the extra coordinate W (z) and modifies the four dimensional geometry ds 2 4D , see equation (3). On the other hand, we have imposed the form of the energy momentum tensor (8), such that the warp factor also modifies the information of the four dimensional energy momentum tensor (9) through the function (21).…”

“…The line element (1) corresponds to the Kaluza-Klein black string [2]. So, the last equation corresponds to a solution of the Einstein field equations G M N = 0 and it was obtained by the oxidation of the Schwarzschild solution [3]. This solution has S 2 × R horizon topology for z non compact, i.e has a cylindrical event horizon [2].…”

Lovelock black p -branes with fluxes

“…AB;p are the Lovelock tensor and the energy-momentum tensor of the fundamental ðp − 1Þ-form, respectively, defined as 2 For the p ¼ 1 case, this accommodates the axionic black strings constructed in Ref. [15].…”

Phase transitions of black strings in dynamical Chern-Simons modified gravity

“…Generically, black strings are higher-dimensional asymptotically flat vacuum solutions with extended topology of their horizon that represent interesting counterexamples to topological censorship [38] and to uniqueness theorems in higher-dimensional GR [39][40][41]. They are also known in the presence of nonlinear matter content and in theories beyond GR (for an incomplete list of developments see [28,[42][43][44][45][46][47][48][49][50][51][52][53]). Nevertheless, it is well-known that these solutions usually suffer from the Gregory-Laflamme instability: a long-wavelength linear instability driven by an unstable mode traveling along the extended direction [33,54,55].…”

“…On the other hand, constructing homogeneous black strings in GR with a nonvanishing cosmological constant is a nontrivial task, due to the dynamics. However, this issue can be circumvented by introducing scalar fields with an axionic profile, i.e., with a linear dependence on the extended flat coordinates [28,30,45]. Interestingly enough, this approach allows one to find black strings in four dimensions, despite the fact that these solutions were first believed to be strictly higherdimensional objects.…”