On four-dimensional Einsteinian gravity, quasitopological gravity, cosmology and black holes

We show that the combination of cubic invariants defining five-dimensional quasitopological gravity, when written in four dimensions, reduce to the version of four-dimensional Einsteinian gravity recently proposed by Arciniega, Edelstein & Jaime, that produces second order equations of motion in a FLRW ansatz, with a purely geometrical inflationary period. We introduce a quartic version of the four-dimensional Einsteinian theory with similar properties, and study its consequences. In particular we found that there exists a region on the space of parameters which allows for thermodynamically stable black holes, as well as a well-defined cosmology with geometrically driven inflation. We briefly discuss the cosmological inhomogeneities in this setup. We also provide a combination of quintic invariants with those properties.Comment: Minor corrections, 14 pages, 1 figur

Homogeneous Black Strings in Einstein-Gauss-Bonnet with Horndeski hair and beyond

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$_{5}\times R$ 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.Comment: 20 pages, 2 figures. V2: 20 pages, 2 figures. Explicit construction of the asymptotically flat black strings in 6D EGB, included. To appear in EJP

Ehlers Transformations as a Tool for Constructing Accelerating NUT Black Holes

This paper investigates the integrability properties of Einstein's theory of gravity in the context of accelerating NUT spacetimes by utilizing Ernst's description of stationary and axially symmetric electro-vacuum solutions. We employ Ehlers transformations, Lie point symmetries of the Einstein field equations, to efficiently endorse accelerating metrics with a nontrivial NUT charge. Under this context, we begin by re-deriving the known C-metric NUT spacetime described by Chng, Mann, and Stelea in a straightforward manner, and in the new form of the solution introduced by Podolsk\'y and Vr\'atn\'y. Next, we construct for the first time an accelerating NUT black hole dressed with a conformally coupled scalar field. These solutions belong to the general class of type I spacetimes, therefore cannot be obtained from any limit of the Pleban\'ski-Demia\'nski family whatsoever and their integration needs to be carried out independently. Including Maxwell fields is certainly permitted, however, the use of Ehlers transformations is subtle and requires further modifications. Ehlers transformations do not only partially rotate the mass parameter such that its magnetic component appears, but also rotate the corresponding gauge fields. Notwithstanding, the alignment of the electromagnetic potentials can be successfully performed via a duality transformation, hence providing a novel Reissner-Nordstr\"om-C-metric NUT black hole that correctly reproduces the Reissner-Nordstr\"om-C-metric and Reissner-Nordstr\"om-NUT configurations in the corresponding limiting cases. We describe the main geometric features of these solutions and discuss possible embeddings of our geometries in external electromagnetic and rotating backgrounds.Comment: A misleading interpretation of the duality rotation performed in Section V has been deleted. The interpretation of the solution has been corrected and the mathematical result remains unchange