Here we have developed the general parametrization for spherically symmetric and asymptotically flat black-hole spacetimes in an arbitrary metric theory of gravity. The parametrization is similar in spirit to the parametrized post-Newtonian (PPN) approximation, but valid in the whole space outside the event horizon, including the near horizon region. This generalizes the continued-fraction expansion method in terms of a compact radial coordinate suggested by Rezzolla and Zhidenko [Phys.Rev.D 90 8, 084009 (2014)] for the four-dimensional case. As the first application of our higher-dimensional parametrization we have approximated black-hole solutions of the Einstein-Lovelock theory in various dimensions. This allows one to write down the black-hole solution which depends on many parameters (coupling constants in front of higher curvature terms) in a very compact analytic form, which depends only upon a few parameters of the parametrization. The approximate metric deviates from the exact (but extremely cumbersome) expressions by fractions of one percent even at the first order of the continued-fraction expansion, which is confirmed here by computation of observable quantities, such as quasinormal modes of the black hole.
Lovelock gravity is a class of higher-derivative gravitational theories whose linearized equations of motion have no more than two time derivatives. Here, it is shown that any Lovelock theory can be effectively described as Einstein gravity coupled to a p-form gauge field. This extends the known example of an f(R) theory of gravity, which can be described as Einstein gravity coupled to a scalar field.
Static, spherically symmetric solutions of the field equations for a particular dimensional continuation of general relativity with negative cosmological constant are found. In even dimensions the solution has many similarities with the \Sch\ metric. In odd dimensions, the equations of motion are explicitly anti de-Sitter invariant, and the solution is alike in many ways to the 2+1 black hole.
The Einstein-Lovelock theory contains an infinite series of corrections to the Einstein term with an increasing power of the curvature. It is well-known that for large black holes the lowest (Gauss-Bonnet) term is the dominant one, while for smaller black holes higher curvature corrections become important. We will show that if one is limited by positive values of the coupling constants, then the dynamical instability of black holes serves as an effective cut-off of influence of higher curvature corrections in the 4D Einstein-Lovelock approach: the higher is the order of the Lovelock term, the…
The regularization procedure for getting the four-dimensional nontrivial Einstein-Gauss-Bonnet effective description of gravity and its Lovelock generalization has been recently developed. Here we propose the regularization for the three-dimensional gravity, which is based on the rescaling of the coupling constants and, afterward, taking the limit $D \to 3$. We obtain the generalization of the Bañados-Teitelboim-Zanelli solution in the presence of the higher curvature (Gauss-Bonnet and Lovelock) corrections of any order. The obtained general solution shows a peculiar behavior: The event horizo…
An interpretation to the physics of stable geodesics of massive particles in black hole backgrounds has been recently proposed in the context of the AdS/CFT correspondence. It was argued that the existence of stable orbits indicates that the dual state does not thermalize on a thermal time scale and the bulk excitations can be interpreted as metastable states in the dual field theory. Here we study motion of massive particles in the background of the D-dimensional asymptotically anti-de Sitter (AdS) black holes in the Einstein-Lovelock theory. We show that, unlike the asymptotically flat case,…
In this work, we provide consistent compactifications of Einstein-Maxwell and Einstein-Maxwell-Lovelock theories on direct product spacetimes of the form $\mathcal{M}_D=\mathcal{M}_d\times\mathcal{K}^{p}$, where $\mathcal{K}^p$ is a Euclidean internal manifold of constant curvature. For these compactifications to take place, it is required the distribution of a precise flux of $p$-forms over the internal manifold. The dynamic of the $p$-forms are demanded to be controlled by two types of interaction. First, by specific couplings with the curvature tensor and, second, by a suitable interaction …
We investigate the thermodynamics of Lovelock-Lifshitz black branes. We begin by introducing the finite action of third order Lovelock gravity in the presence of a massive vector field for a flat boundary, and use it to compute the energy density of these black branes. Using the field equations, we find a conserved quantity along the $r$ coordinate that relates the metric parameters at the horizon and at infinity. Remarkably, though the subleading large-$r$ behavior of Lovelock-Lifshitz black branes differs substantively from their Einsteinian Lifshitz counterparts, we find that the relationsh…
A (3+1)-dimensional Einstein-Gauss-Bonnet effective description of gravity has been recently formulated as the $D \to 4$ limit of the higher dimensional field equations after the rescaling of the coupling constant. This approach has been recently extended to the four-dimensional Einstein-Lovelock gravity. Although validity of the regularization procedure has not been shown for the general case, but only for a wide class of metrics, the black-hole solution obtained as a result of such a regularization is also an exact solution in the well defined 4D Einstein-Gauss-Bonnet theory suggested by Aok…
In this paper, we introduce the counterterms that remove the non-logarithmic divergences of the action in third order Lovelock gravity for static spacetimes. We do this by defining the cosmological constant in such a way that the asymptotic form of the metric have the same form in Lovelock and Einstein gravities. Thus, we employ the counterterms of Einstein gravity and show that the power law divergences of the action of Lovelock gravity for static spacetimes can be removed by suitable choice of coefficients. We find that the dependence of these coefficients on the dimension in Lovelock gravit…
We study the problem of finding brane-like solutions to Lovelock gravity, adopting a general approach to establish conditions that a lower dimensional base metric must satisfy in order that a solution to a given Lovelock theory can be constructed in one higher dimension. We find that for Lovelock theories with generic values of the coupling constants, the Lovelock tensors (higher curvature generalizations of the Einstein tensor) of the base metric must all be proportional to the metric. Hence, allowed base metrics form a subclass of Einstein metrics. This subclass includes so-called `universal…
It is well known that, for a wide class of spacetimes with horizons, Einstein equations near the horizon can be written as a thermodynamic identity. It is also known that the Einstein tensor acquires a highly symmetric form near static, as well as stationary, horizons. We show that, for generic static spacetimes, this highly symmetric form of the Einstein tensor leads quite naturally and generically to the interpretation of the near-horizon field equations as a thermodynamic identity. We further extend this result to generic static spacetimes in Lanczos-Lovelock gravity, and show that the near…
Lovelock theory is a natural extension of Einstein theory of gravity to higher dimensions, and it is of great interest in theoretical physics as it describes a wide class of models. In particular, it describes string theory inspired ultraviolet corrections to Einstein-Hilbert action, while admits the Einstein general relativiy and the so called Chern-Simons theories of gravity as particular cases. Recently, five-dimensional Lovelock theory has been considered in the literature as a working example to illustrate the effects of including higher-curvature terms in the context of AdS/CFT correspon…
We study dynamical structure of Pure Lovelock gravity in spacetime dimensions higher than four using the Hamiltonian formalism. The action consists of cosmological constant and a single higher-order polynomial in the Riemann tensor. Similarly to Einstein-Hilbert action, it possesses a unique constant curvature vacuum and charged black hole solutions. We analyze physical degrees of freedom and local symmetries in this theory. In contrast to the Einstein-Hilbert case, a number of degrees of freedom depends on the background and can vary from zero to the maximal value carried by the Lovelock theo…
We obtain rotating black hole metric for higher dimensional Einstein and pure Lovelock gravity by employing two independent and well motivated methods. One is based on the principle of incorporation of Newtonian acceleration for timelike motion while no acceleration for null motion. The other is the well known Newman-Janis alogrithm that converts a static black hole into a rotating one through a complex transformation. It turns out that both the methods give the same metric which for Einst of the eour pure Lovelock metricein black hole is an exact vacuum solution while for pure Lovelock black …
We explicitly confirm the expectation that generic Lovelock gravity in D dimensions has a unitary massless spin-2 excitation around any one of its constant curvature vacua just like the cosmological Einstein gravity. The propagator of the theory reduces to that of Einstein's gravity, but scattering amplitudes must be computed with an effective Newton's constant which we provide. Tree-level unitarity imposes a single constraint on the parameters of the theory yielding a wide range of unitary region. As an example, we explicitly work out the details of the cubic Lovelock theory.
For spherical symmetry, we provide expressions for the radial null-null components of the generalized Einstein tensor $E_{ab}$ for Lovelock models for diagonal $E_{ab}$ in terms of the metric and of the radial null-null components of the Ricci tensor. We show they can be usefully employed for example in obtaining the Birkhoff-like theorem for Lovelock models, as well as in providing a relation between the null energy and null convergence conditions for the same models.
A $(3+1)$-dimensional Einstein-Gauss-Bonnet theory of gravity has been recently formulated in [D. Glavan and C. Lin, Phys. Rev. Lett. {\bf 124}, 081301 (2020)] which is different from the pure Einstein theory, i.e., bypasses the Lovelock's theorem and avoids Ostrogradsky instability. The theory was formulated in $D > 4$ dimensions and its action consists of the Einstein-Hilbert term with a cosmological constant, while the Gauss-Bonnet term multiplied by a factor $1/(D-4)$. Then, the four-dimensional theory is defined as the limit $D \to 4$. Here we generalize this approach to the four-dimensio…
We construct a familly of exact solutions of Lovelock equations describing codimension four branes with discrete symmetry in the transverse space. Unlike what is known from pure Einstein gravity, where such brane solutions of higher codimension are singular, the solutions we find, for the complete Lovelock theory, only present removable singularities. The latter account for a localised tension-like energy-momentum tensor on the brane, in analogy with the case of a codimension two self-gravitating cosmic string in pure Einstein gravity. However, the solutions we discuss present two main distinc…
We show that the splitting feature of the Einstein tensor, as the first term of the Lovelock tensor, into two parts, namely the Ricci tensor and the term proportional to the curvature scalar, with the trace relation between them is a common feature of any other homogeneous terms in the Lovelock tensor. Motivated by the principle of general invariance, we find that this property can be generalized, with the aid of a generalized trace operator which we define, for any inhomogeneous Euler-Lagrange expression that can be spanned linearly in terms of homogeneous tensors. Then, through an applicatio…
This paper studies a class of $D=n+2(\ge 6)$ dimensional solutions to Lovelock gravity that is described by the warped product of a two-dimensional Lorentzian metric and an $n$-dimensional Einstein space. Assuming that the angular part of the stress-energy tensor is proportional to the Einstein metric, it turns out that the Weyl curvature of an Einstein space must obey two kinds of algebraic conditions. We present some exact solutions satisfying these conditions. We further define the quasilocal mass corresponding to the Misner-Sharp mass in general relativity. It is found that the quasilocal …
A theory of gravity in higher dimensions is considered. The usual Einstein-Hilbert action is supplemented with Lovelock terms, of higher order in the curvature tensor. These terms are important for the low energy action of string theories. The intersection of hypersurfaces is studied in the Lovelock theory. The study is restricted to hypersurfaces of co-dimension 1, $(d-1)$-dimensional submanifolds in a $d$-dimensional space-time. It is found that exact thin shells of matter are admissible, with a mild form of curvature singularity: the first derivative of the metric is discontinuous across th…
We study motion around a static Einstein and pure Lovelock black hole in higher dimensions. It is known that in higher dimensions, bound orbits exist only for pure Lovelock black hole in all even dimensions, D=2N+2, where N is degree of Lovelock polynomial action. In particular, we compute periastron shift and light bending and the latter is given by one of transverse spatial components of Riemann curvature tensor. We also consider pseudo-Newtonian potentials and Kruskal coordinates.
We study collapse of inhomogeneous dust and null dust (Vaidya radiation) in pure Lovelock gravity in higher dimensions. Since pure Lovelock gravity is kinematic in odd d=2N+1 dimension, hence pertinent dimension for the study is even d=2N+2, where N is degree of Lovelock polynomial. It turns out that pure Lovelock collapse favors naked singularity as against black hole for the Einstein case in the same dimension while strength of singularity as measured by divergence of Kretshmann scalar is interestingly the same in the two cases; i.e. the corresponding scalars have the same fall off behavior.
In the present paper, a new class of black hole solutions is constructed in even dimensional Lovelock Born-Infeld theory. These solutions are interesting since, in some respects, they are closer to black hole solutions of an odd dimensional Lovelock Chern-Simons theory than to the more usual black hole solutions in even dimensions. This hybrid behavior arises when non-Einstein base manifolds are considered. The entropies of these solutions have been analyzed using Wald formalism. These metrics exhibit a quite non-trivial behavior. Their entropies can change sign and can even be identically zer…
Lanczos-Lovelock models of gravity represent a natural and elegant generalization of Einstein's theory of gravity to higher dimensions. They are characterized by the fact that the field equations only contain up to second derivatives of the metric even though the action functional can be a quadratic or higher degree polynomial in the curvature tensor. Because these models share several key properties of Einstein's theory they serve as a useful set of candidate models for testing the emergent paradigm for gravity. This review highlights several geometrical and thermodynamical aspects of Lanczos…
We consider the Hamiltonian dynamics and thermodynamics of spherically symmetric spacetimes within a one-parameter family of five-dimensional Lovelock theories. We adopt boundary conditions that make every classical solution part of a black hole exterior, with the spacelike hypersurfaces extending from the horizon bifurcation three-sphere to a timelike boundary with fixed intrinsic metric. The constraints are simplified by a Kuchař-type canonical transformation, and the theory is reduced to its true dynamical degrees of freedom. After quantization, the trace of the analytically continued Loren…
In classical general relativity described by Einstein-Hilbert gravity, black holes behave as thermodynamic objects. In particular, the laws of black hole mechanics can be interpreted as laws of thermodynamics. The first law of black hole mechanics extends to higher derivative theories via the Noether charge construction of Wald. One also expects the statement of the second law, which in Einstein-Hilbert theory owes to Hawking's area theorem, to extend to higher derivative theories. To argue for this however one needs a notion of entropy for dynamical black holes, which the Noether charge const…
We give the equations of motion for a self-gravitating Dirac p-brane embedded in an even co-dimension spacetime. The dynamics of the bulk are dictated by Lovelock gravity and permit matching conditions, even when the codimension is strictly greater than 2. We show that the equations of motion involve both induced Lovelock densities on the brane and regular extrinsic curvature terms. The brane dynamics can be derived from an exact (p+1)-dimensional induced action. The Dirac charge is carried by an overall (solid) angle defect which sets the Planck scale on the brane. In particular, if the codim…
In this paper, we investigate the generalized covariant entropy bound in the theory where the Einstein gravity is perturbed by the higher-order Lovelock terms. After replacing the Bekenstein-Hawking entropy with the Jacobson-Myers entropy and introducing two reasonable physical assumptions, we showed that the corresponding generalized covariant entropy bound is satisfied under a higher-order approximation of the perturbation from the higher-order Lovelock terms. Our result implies that the Jacobson-Myers entropy strictly obeys the entropy bound under the perturbation level, and the generalized…
We present a theorem in d-dimensional static, spherically symmetric spacetime in generic Lovelock gravity coupled with a non-linear electrodynamic source to generate solutions. The theorem states that irrespective of the order of the Lovelock gravity and non-linear Maxwell (NLM) Lagrangian, for the pure electric field case the NLM equations are satisfied by virtue of the Einstein-Lovelock equations. Applications of the theorem, specifically to the study of black hole solutions in Chern-Simons (CS) theory is given. Radiating version of the theorem has been considered, which generalizes the Bonn…
We construct an exact anisotropic star model with a linear barotropic equation of state and with Finch-Skea potential within the framework of pure Lovelock gravity. A comparison with the corresponding Einstein model in a suitable limit is easily deduced. Evidently higher curvature effects induced by the Lovelock contributions generate lower densities, pressures, surface tensions and anisotropy factors when compared to its Einstein counterpart. The maximum moment of inertia is attained for the Einstein case and hence it may be inferred that Lovelock effects soften the equation of state. The mod…
Spacetimes with horizons show a resemblance to thermodynamic systems and one can associate the notions of temperature and entropy with them. In the case of Einstein-Hilbert gravity, it is possible to interpret Einstein's equations as the thermodynamic identity TdS = dE + PdV for a spherically symmetric spacetime and thus provide a thermodynamic route to understand the dynamics of gravity. We study this approach further and show that the field equations for Lanczos-Lovelock action in a spherically symmetric spacetime can also be expressed as TdS = dE + PdV with S and E being given by expression…
We show that the asymptotic large $r$ limit of all Lovelock vacuum and electrovac solutions with $Λ$ is always the Einstein solution in $d \geq 2n+1$ dimensions. It is completely free of the order $n$ of the Lovelock polynomial indicating universal asymptotic behaviour.
It is well known that the Reissner-Norstrom solution of Einstein-Maxwell theory cannot be cylindrically extended to higher dimension, as with the black hole solutions in vacuum. In this paper we show that this result is circumvented in Lovelock gravity. We prove that the theory containing only the quadratic Lovelock term, the Gauss-Bonnet term, minimally coupled to a $U(1)$ field, admits homogeneous black string and black brane solutions characterized by the mass, charge and volume of the flat directions. We also show that theories containing a single Lovelock term of order $n$ in the Lagrangi…
This work is mainly devoted to constructing a multisymplectic description of Lovelock's gravity, which is an extension of General Relativity. We establish a Griffiths variational problem for the Lovelock Lagrangian, obtaining the geometric form of the corresponding field equations. We give the unified Lagrangian--Hamiltonian formulation of this model and we study the correspondence between the unified formulations for the Einstein--Hilbert and the Einstein--Palatini models of gravity.
A four-dimensional regularization of Lovelock-Lanczos gravity up to an arbitrary curvature order is considered. We show that Lovelock-Lanczos terms can provide a non-trivial contribution to the Einstein field equations in four dimensions, for spherically symmetric and Friedmann-Lemaître-Robertson-Walker spacetimes, as well as at first order in perturbation theory around (anti) de Sitter vacua. We will discuss the cosmological and black hole solutions arising from these theories, focusing on the presence of attractors and their stability. Although curvature singularities persist for any finite …
We study the stability of static spherically symmetric charged black holes under tensor type perturbations in Lovelock theory which is a natural higher dimensional generalization of Einstein theory. We derive the master equation for tensor type perturbations and present the criterions for the stability. Examining these criterions numerically, we show that a black hole with small charge has the instability if its mass is as small as extreme mass. Combined with our previous result that neutral black hole has no dynamical instability in odd dimensions, this result suggests that charges have fatal…
We obtain the Buchdahl compactness limit for a pure Lovelock static fluid star and verify that the limit following from the uniform density Schwarzschild's interior solution, which is universal irrespective of the gravitational theory (Einstein or Lovelock), is true in general. In terms of surface potential $Φ(r)$, it means at the surface of the star $r=r_{0}$, $Φ(r_{0}) < 2N(d-N-1)/(d-1)^2$ where $d$, $N$ respectively indicate spacetime dimensions and Lovelock order. For a given $N$, $Φ(r_{0})$ is maximum for $d=2N+2$ while it is always $4/9$, Buchdahl's limit, for $d=3N+1$. It is also remark…
A standard candidate for quasilocal energy in general relativity is the Brown-York energy, which is essentially a two dimensional surface integral of the extrinsic curvature on the two-boundary of a spacelike hypersurface referenced to flat spacetime. Several years back one of us had conjectured that the black hole horizon is defined by equipartition of gravitational and non-gravitational energy. By employing the above definition of quasilocal Brown-York energy, we have verified the equipartition conjecture for static charged and charged axi-symmetric blck holes in general relativity. We have …
Lovelock theory is a natural extension of the Einstein theory of general relativity to higher dimensions in which the first and second orders correspond, respectively, to general relativity and Einstein-Gauss-Bonnet gravity. We present exact black hole solutions of $D\geq 4$-dimensional spacetime for first-, second-, and third-order Lovelock gravities in a string cloud background. Further, we compute the mass, temperature, and entropy of black hole solutions for the higher-dimensional general relativity and Einstein-Gauss-Bonnet theories and also perform thermodynamic stability of black holes.…
The objective of the present paper is to analyze the phase transition of asymptotically anti-de Sitter (AdS) black hole solutions in Lovelock gravity in the presence of nonlinear electrodynamics. First, we present the asymptotically AdS black hole solutions for two classes of the Born-Infeld type of nonlinear electrodynamics coupled with Einstein, Gauss-Bonnet and third order Lovelock gravity, separately. Then, in order to discuss the phase transition, we calculate both the heat capacity and the Ricci scalar of the thermodynamical line element. We present a comparison between the singular poin…
We study the stability of static black holes in Lovelock theory which is a natural higher dimensional generalization of Einstein theory. We derive a master equation for tensor perturbations in general Lovelock theory. It turns out that the resultant equation is characterized by one functional which determines the background black hole solutions. Thus, the stability issue of static black holes under tensor perturbations in general dimensions is reduced to an algebraic problem. We show that small Lovelock black holes in even-dimensions are unstable.
We study the stability of static black holes in the third order Lovelock theory. We derive a master equation for tensor perturbations. Using the master equation, we analyze the stability of Lovelock black holes mainly in seven and eight dimensions. We find there are cases where the linear analysis breaks down. If we restrict ourselves to the regime where the linear analysis is legitimate, black holes are always stable in seven dimensions. However, in eight dimensions, there exists a critical mass below which black holes are unstable. Combining our result in the third order Lovelock theory with…
We present the asymptotically AdS solutions of the Einstein gravity with hyperbolic horizons in the presence of $So(n(n-1)/2-1, 1)$ Yang-Mills fields governed by the non-Abelian Born-Infeld lagrangian. We investigate the properties of these solutions as well as their asymptotic behavior in varies dimensions. The properties of these kind of solutions are like the Einstein-Yang-Mills solutions. But the differences seems to appear in the role of the mass, charge and born-Infeld parameter $β$, in the solutions. For example in Einstein-Yang-Mills theory the solutions with non-negative mass cannot p…
We derive the conformal constraints satisfied by classical vertices of a (Einstein) Gauss-Bonnet theory around flat space, in general dimensions and at $d=4$ (4d EGB). In $4d$ EGB they are obtained by a singular limit of the integral of the Euler-Poincarè density. Our analysis exploits the relation between this theory and the conformal anomaly action, which allows to uncover some interesting features of the GB vertex at cubic and quartic level. If we introduce a conformal decomposition of the metric, the resulting theory can be formulated in two different versions, which are regularization dep…
The exact five-dimensional charged black hole solution in Lovelock gravity coupled to Born-Infeld electrodynamics is presented. This solution interpolates between the Hoffmann black hole for the Einstein-Born-Infeld theory and other solutions in the Lovelock theory previously studied in the literature. The conical singularity of the metric around the origin can be removed by a proper choice of the black hole parameters. The thermodynamic properties of the solution are also analyzed and, in particular, it is shown that the behaviour of the specific heat indicates the existence of a stability tr…
We examine the thermodynamics of a new class of asymptotically AdS black holes with non-constant curvature event horizons in Gauss-Bonnet Lovelock gravity, with the cosmological constant acting as thermodynamic pressure. We find that non-trivial curvature on the horizon can significantly affect their thermodynamic behaviour. We observe novel triple points in 6 dimensions between large and small uncharged black holes and thermal AdS. For charged black holes we find a continuous set of triple points whose range depends on the parameters in the horizon geometry. We also find new generalizations o…
We study the stability of static black holes in Lovelock theory which is a natural higher dimensional generalization of Einstein theory. We show that Lovelock black holes are stable under vector perturbations in all dimensions. However, we prove that small Lovelock black holes are unstable under tensor perturbations in even-dimensions and under scalar perturbations in odd-dimensions. Therefore, we can conclude that small Lovelock black holes are unstable in any dimensions. The instability is stronger on small scales and hence catastrophic in the sense that there is no smooth descendant.
In this paper the dynamic compactification in Lovelock gravity with a cubic term is studied. The ansatz will be of space-time where the three dimensional space and the extra dimensions are constant curvature manifolds with independent scale factors. The numerical analysis shows that there exist a phenomenologically realistic compactification regime where the three dimensional hubble parameter and the extra dimensional scale factor tend to a constant. This result comes as surprise as in Einstein-Gauss-Bonnet gravity this regime exists only when the couplings of the theory are such that the theo…
The product spacetimes of constant curvature describe in Einstein gravity, which is linear in Riemann curvature, Nariai metric which is a solution of $Λ$-vacuum when curvatures are equal, $k_1=k_2$, while it is Bertotti-Robinson metric describing uniform electric field when curvatures are equal and opposite, $k_1=-k_2$. We probe pure Lovelock gravity by these simple product spacetimes and prove that the same characterization of these solutions is indeed true in general for pure Lovelock gravitational equation of order $N$ in $d=2N+2$ dimension. We also consider these solutions for the conventi…
We consider two specific approaches to evaluate the black hole entropy which are known to produce correct results in the case of Einstein's theory and generalize them to Lanczos-Lovelock models. In the first approach (which could be called extrinsic) we use a procedure motivated by earlier work by Pretorius, Vollick and Israel, and by Oppenheim, and evaluate the entropy of a configuration of densely packed gravitating shells on the verge of forming a black hole in Lanczos-Lovelock theories of gravity. We find that this matter entropy is not equal to (it is less than) Wald entropy, except in th…
We construct a plethora of new Euclidean AdS-Taub-NUT and bolt solutions of several four- and six-dimensional higher-curvature theories of gravity with various base spaces $\mathcal{B}$. In $D=4$, we consider Einsteinian cubic gravity, for which we construct solutions with $\mathcal{B}=\mathbb{S}^2,\mathbb{T}^2$. These represent the first generalizations of the Einstein gravity Taub-NUT/bolt solutions for any higher-curvature theory in four dimensions. In $D=6$, we show that no new solutions are allowed for any Generalized quasi-topological gravity at cubic order. They exist however when we co…
In this paper we perform stability analysis for exponential solutions in Einstein-Gauss-Bonnet and cubic Lovelock gravity. We report our findings, provide areas on parameters space and discuss familiarities and differences between cases. Analysis suggests that only several cases out of numerous found solutions could be called stable. In particular, cases with three-dimensional isotropic subspace which could give rise to successful compactification are diminished to one general case and one additional partial solution in the cubic Lovelock case.
We consider a model where massive static spherically symmetric black hole, in the presence of power-Yang-Mills source, is surrounded by a dark fluid with non-linear equation of state. In this set up we construct a new class of magnetized Lovelock black hole solutions of the gravitational field equations. In particular, we work out the metric functions in both D-dimensional massive Einstein and massive Gauss-Bonnet gravities. We study thermodynamics of these black holes also and show that the mass and associated thermodynamic quantities like Hawking temperature and heat capacity depend on param…
We study some universal features of gravity in higher dimensions and by universal we mean a feature that remains true in all dimensions $\geq4$. They include: (a) the gravitational dynamics always follows from the Bianchi derivative of a homogeneous polynomial in Riemann curvature and it thereby characterizes the Lovelock polynomial action, (b) all the $Λ$-vacuum solutions of the Einstein-Lovelock as well as pure Lovelock equation have the same asymptotic limit agreeing with the $d$ dimensional Einstein solution and (c) gravity inside a uniform density sphere is independent of the spacetime di…
We derive electrically charged black hole solutions of the Einstein-Gauss-Bonnet equations with a nonlinear electrodynamics source in $n (\ge 5)$ dimensions. The spacetimes are given as a warped product $M^2 \times K^{n-2}$, where $K^{n-2}$ is a $(n-2)$-dimensional constant curvature space. We establish a generalized Birkhoff's theorem by showing that it is the unique electrically charged solution with this isometry and for which the orbit of the warp factor on $K^{n-2}$ is non-null. An extension of the analysis for full Lovelock gravity is also achieved with a particular attention to the Cher…
We look for the existence of asymptotically flat simple compactifications of the form $M_{D-p}\times T^{p}$ in $D$-dimensional gravity theories with higher powers of the curvature. Assuming the manifold $M_{D-p}$ to be spherically symmetric, it is shown that the Einstein-Gauss-Bonnet theory admits this class of solutions only for the pure Einstein-Hilbert or Gauss-Bonnet Lagrangians, but not for an arbitrary linear combination of them. Once these special cases have been selected, the requirement of spherical symmetry is no longer relevant since actually any solution of the pure Einstein or pur…
We consider static spherically symmetric Lovelock black holes and generalize the dimensionally continued black holes in such a way that they asymptotically for large r go over to the d-dimensional Schwarzschild black hole in dS/AdS spacetime. This means that the master algebraic polynomial is not degenerate but instead its derivative is degenerate. This family of solutions contains an interesting class of pure Lovelock black holes which are the Nth order Lovelock Λ-vacuum solu- tions having the remarkable property that their thermodynamical parameters have the universal character in terms of t…
Higher-derivative gravity theories, such as Lovelock theories, generalize Einstein's general relativity (GR). Modifications to GR are expected when curvatures are near Planckian and appear in string theory or supergravity. But can such theories describe gravity on length scales much larger than the Planck cutoff length scale? Here we find causality constraints on Lovelock theories that arise from the requirement that the equations of motion (EOM) of perturbations be hyperbolic. We find a general expression for the "effective metric" in field space when Lovelock theories are perturbed around so…
