In this paper we study the perturbation theory of the recently proposed Regularized Lovelock Gravity, on the curved FLRW space-time. We provide the first order perturbation equations both in the scalar and tensor sector in the presence of an additional minimally coupled scalar field. A general expression for the velocity of gravitational waves at the generic order is inferred. Moreover, we apply the results on the study of slow-roll inflation on flat FLRW background, at second order in the Regularized Lovelock Gravity, i.e. in the presence of the Gauss-Bonnet correction only. We derive the power spectra of scalar and tensor perturbations, and provide the equations for the inflation observable quantities: the spectral indices and the tensor-to-scalar spectra ratio.
We reformulate the recently proposed regularized version of Lovelock gravity in four dimensions as a scalar-tensor theory. By promoting the warp factor of the internal space to a scalar degree of freedom by means of Kaluza-Klein reduction, we show that regularized Lovelock gravity can be described effectively by a certain subclass of the Horndeski theory. Cosmological aspects of this particular scalar-tensor theory are studied. It is found that the background with a scalar charge is generically allowed. The consequences of this scalar charge are briefly discussed.
The recently proposed regularized Lovelock tensors are kinetically coupled to the scalar field. The resulting equation of motion is second order. In particular, it is found that when the $p=3$ regularized Lovelock tensor is kinetically coupled to the scalar field, the scalar field is the potential candidate of cosmic dark energy.
We study some properties of exact cosmological solutions for a flat multidimensional anisotropic Universe in Lovelock gravity. A particular attention is paid to some features of solution in a general Lovelock gravity which have no their counterparts in analogous solution of General Relativity. We consider exponential solutions and so called generalized Milne solution and discuss reasons for these solution to exist in Lovelock gravity and do not exist in General Relativity.
It is found that, when the coupling constants $α_p$ in the theory of regularized Lovelock gravity are properly chosen and the number of Lovelock tensors $p\rightarrow \infty$, there exist a fairly large number of nonsingular (singularity free) black holes and nonsingular universes. Some nonsingular black holes have numerous horizons and numerous energy levels (a bit like atom) inside the outer event horizon. On the other hand, some nonsingular universes start and end in two de Sitter phases. The ratio of energy densities for the two phases are $120$ orders. It is thus helpful to understand the…
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…
Boundary terms for Lovelock gravity are obtained by calculating in arbitrary dimension the index theorem for the de Rham complex of a manifold with nonempty boundary.
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 derive boundary terms appropriate for the general Lanczos-Lovelock action on a null boundary, when Dirichlet boundary conditions are imposed. We believe that these boundary terms have been derived for the first time in the literature. In this derivation, we rely only on the structure of the boundary variation of the action for Lanczos-Lovelock gravity. We also provide the null boundary term for Gauss-Bonnet gravity separately.
In this work a new family of black hole solutions in Lovelock gravity is discussed. These solutions describe anisotropic fluids which extend to the spatial infinity. Though far from the horizon their geometries approach some previously known black holes solutions the location of the horizons differ. Furthemore, although the masses of these solutions match the masses of those previously known black holes, their temperatures and entropies differ.
We show universality of isothermal fluid spheres in pure Lovelock gravity where the equation of motion has only one $N$th order term coming from the corresponding Lovelock polynomial action of degree $N$. Isothermality is characterized by the equation of state, $p = αρ$ and the property, $ρ\sim 1/r^{2N}$. Then the solution describing isothermal spheres, which exist only for the pure Lovelock equation, is of the same form for the general Lovelock degree $N$ in all dimenions $d \geq 2N+2$. We further prove that the necessary and sufficient condition for the isothermal sphere is that its metric i…
We revisit the spherically symmetric third order Lovelock black hole solution in 7-dimensions. We show that the general solution for the metric function does not admit the Gauss-Bonnet (GB) limit. This is not expected due to the linear superposition of the second (GB) and third order Lovelock Lagrangians in the general action. It is found that the two branches of the GB solutions are indeed the limit of the other two complex solutions of the field equations in the third order Lovelock gravity. These two complex solutions could not be accepted as the solutions of the Einstein's field equations …
We consider the Lovelock theory of gravity that assumes a nonlinearity of the field equations in the second-order derivatives of the metric. We prove the opportunity of obtaining cosmological solutions without isotropization in the presence of matter in the form of a perfect fluid, which is necessary for invisibility of extra dimensions that inevitably emerge in the Lovelock theory. In particular, the Jacobs solution has been generalized to an arbitrary order of the theory, and in the third order, an anisotropic exponential solution has been found.
We obtain plane fronted gravitational waves (PFGWs) in arbitrary dimension in Lovelock gravity, to any order in the Riemann tensor. We exhibit pure gravity as well as Lovelock-Yang-Mills PFGWs. Lovelock-Maxwell and $pp$ waves arise as particular cases. The electrovac solutions trivially satisfy the Lovelock-Born-Infeld field equations. The peculiarities that arise in degenerate Lovelock theories are also analyzed.
We provide an algorithm that shows how to decouple gravitational sources in Pure Lovelock gravity. This method allows to obtain several new and known analytic solutions of physical interest in scenarios with extra dimensions and with presence of higher curvature terms. Furthermore, using our method, it is shown that applying the minimal geometric deformation to the Anti de Sitter space time it is possible to obtain regular black hole solutions.
It is generally believed that wormholes are supported by exotic matter violating Null Energy Condition (NEC). However, various studies of wormhole geometries under Lovelock theories of gravity have reported existence of wormhole supported by matter satisfying NEC. Being inspired by these results, we explore the possibility of the existence of wormhole supported by normal quark matter in third order Lovelock gravity theory. Well known MIT Bag Model Equation of state is chosen for describing the quark matter. Taking physically acceptable approximations, we solve the field equations for shape fun…
We present the black hole solutions possessing horizon with nonconstant-curvature and additional scalar restrictions on the base manifold in Lovelock gravity coupled to Born-Infeld (BI) nonlinear electrodynamics. The asymptotic and near origin behavior of the metric is presented and we analyze different behaviors of the singularity. We find that, in contrast to the case of the black hole solutions of BI-Lovelock gravity with constant curvature horizon and Maxwell-Lovelock gravity with nonconstant horizon which has only timelike singularities, spacelike, and timelike singularities may exist for…
We present a general solution of third order Lovelock gravity in the presence of a specific type II perfect fluid. This solution for linear equation of state, $p=w(ρ-4B)$ contains all the known solutions of third order Lovelock gravity in the literature and some new static and radiating solutions for different values of $w$ and $B$. Specially, we consider the properties of static and radiating solutions for $w=0$ and $w=(n-2)^{-1}$ with B=0 and $B\neq0$. These solutions are asymptotically flat for B=0, while they are asymptotically (anti)-de Sitter for $B\neq0$. The new static solutions for th…
In this paper, the BF theory method is applied to the nonrotating isolated horizons in Lovelock theory. The final entropy matches the Wald entropy formula for this theory. We also confirm the conclusion got by Bodendorfer et. al. that the entropy is related to the flux operator rather than the area operator in general diffeomorphic-invariant theory.
A study of Universal thermodynamics is done in Lanczos-Lovelock gravity. The Universe is chosen as FRW model bounded by apparent or event horizon. The unified first law is examined, assuming extended Hawking temperature on the horizon. As a result there is a modification of Bekenstein entropy on the horizons. Further the validity of generalized second law of thermodynamics and thermodynamical equilibrium are also investigated for perfect fluid (with constant equation of state), modified chaplygin gas model and holographic dark energy model.
We derived equations of motion corresponding to Bianchi-I cosmological models in the Lovelock gravity. Equations derived in the general case, without any specific ansatz for any number of spatial dimensions and any order of the Lovelock correction. We also analyzed the equations of motion solely taking into account the highest-order correction and described the drastic difference between the cases with odd and even numbers of spatial dimensions. For power-law ansatz we derived conditions for Kasner and generalized Milne regimes for the model considered. Finally, we discuss the possible influen…
The hierarchies of both Lovelock gravity and power-Yang-Mills field are combined through gravity in a single theory. In static, spherically symmetric ansatz exact particular integrals are obtained in all higher dimensions. The advantage of such hierarchies is the possibility of choosing coefficients, which are arbitrary otherwise, to cast solutions into tractable forms. To our knowledge the solutions constitute the most general spherically symmetric metrics that incorporate complexities both of Lovelock and Yang-Mills hierarchies within the common context. A large portion of our general class …
We present a novel derivation of the boundary term for the action in Lanczos-Lovelock gravity, starting from the boundary contribution in the variation of the Lanczos-Lovelock action. The derivation presented here is straightforward, i.e., one starts from the Lanczos-Lovelock action principle and the action itself dictates the boundary structure and hence the boundary term one needs to add to the action to make it well-posed. It also gives the full structure of the contribution at the boundary of the complete action, enabling us to read off the degrees of freedom to be fixed at the boundary, t…
In this study we present evolving wormhole configurations in third-order {Lovelock} gravity and investigate the possibility that these solutions satisfy the energy conditions. Using a generalized Friedmann-Robertson-Walker spacetime, we derive evolving wormhole geometries by considering a constraint on the Ricci scalar. In standard cosmological models, the Ricci scalar is independent of the radial coordinate $r$ and is only a function of time. We use this property to introduce dynamic wormhole solutions expanding in an inflationary cosmological background and explore the effects of higher-orde…
For the description of the Universe expansion, compatible with observational data, a model of modified gravity - Lovelock gravity with dilaton - is investigated. D-dimensional space with 3- and (D-4)-dimensional maximally symmetric subspaces is considered. Space without matter and space with perfect fluid are under test. In various forms of the theory under way (third order without dilaton and second order - Einstein-Gauss-Bonnet gravity - with dilaton and without it) stationary, power-law, exponential and exponent-of-exponent form cosmological solutions are obtained. Last two forms include so…
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…
We present a Born-Infeld type theory to describe the evolution of p-branes propagating in an N = (p+2)-dimensional Minkowski spacetime. The expansion of the BI-type volume element gives rise to the (p+1) Lovelock brane invariants associated with the worldvolume swept out by the brane. Contrary to the Lovelock theory in gravity, the number of Lovelock brane Lagrangians differs in this case, depending on the dimension of the worldvolume as a consequence that we consider the embedding functions, instead of the metric, as the field variables. This model depends on the intrinsic and the extrinsic g…
We present exact spherically symmetric null dust solutions in the third order Lovelock gravity with a string cloud background in arbitrary $N$ dimensions,. This represents radiating black holes and generalizes the well known Vaidya solution to Lovelock gravity with a string cloud in the background. We also discuss the energy conditions and horizon structures, and explicitly bring out the effect of the string clouds on the horizon structure of black hole solutions for the higher dimensional general relativity and Einstein-Gauss-Bonnet theories. It turns out that the presence of the coupling con…
We construct conserved quantities in pure Lovelock gravity for both static and dynamic Vaydia-type black holes with AdS, dS and flat asymptotics, applying field-theoretical formalism developed earlier. Global energy (where applicable), quasi-local energy together with fluxes of these quantities are presented for both types of black holes, considering asymptotic spacetime as background. The same quantities are constructed for dynamic black holes on the background of the related static black holes. Besides, for the dynamic black holes, energy densities and densities of energy flux are calculated…
In this paper we construct new hairy black holes of Lovelock-Born-Infeld-Scalar gravity in diverse dimensions. We study horizon structures of the black holes and find the black holes may possess three horizons, two horizons or one horizon. We give the thermodynamic quantities and check the first laws. We study the thermal phase transition behaviors of the black holes in $T$-$S$ plane, and find for even-dimensional black holes, in some ranges of the parameters Van der Waals-like phase transitions occur, in some ranges of the parameters, reentrant phase transitions (RPTs) appear. For odd-dimensi…
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.…
For a given Lovelock order $N$, it turns out that static fluid solutions of the pure Lovelock equation for a star interior have the universal behavior in all $n\geq 2N+2$ dimensions relative to an appropriately defined variable and the Vaidya-Tikekar parameter $K$, indicating deviation from sphericity of $3$-space geometry. We employ the Buchdahl metric ansatz which encompasses almost all the known physically acceptable models including in particular the Vaidya-Tikekar and Finch-Skea. Further for a given star radius, the constant density star, always described by the Schwarzschild interior sol…
We study the zeroth law for Killing horizon in scalar-hairy Lovelock gravity, and show that the surface gravity of a general Killing horizon in the scalar-hairy Lovelock gravity is constant, provided that the dominant energy condition is obeyed by the matter field.
By employing the higher (N\TEXTsymbol{>}5) dimensional version of the Wu-Yang Ansatz we obtain magnetically charged new black hole solutions in the Einstein-Yang-Mills-Lovelock (EYML) theory with second ($α_{2}$) and third ($α_{3}$)order parameters. These parameters, where $α_{2}$ is also known as the Gauss-Bonnet parameter, modify the horizons (and the resulting thermodynamical properties) of the black holes. It is shown also that asymptotically ($r\to \infty $), these parameters contribute to an effective cosmological constant -without cosmological constant- so that the solution behaves de-S…
In this work two new families of non-singular or regular black hole solutions are displayed. These black holes behave as de Sitter space near its center and have a well defined AdS asymptotic region for negative cosmological constant. These solutions are constructed on a general ground through the introduction of a finite density of mass/energy. This removes the usual singularity of a black hole and also introduces a new internal geometry. The thermodynamic properties of these solutions are discussed as well.
In this work it is shown that the thermodynamics of regular black holes with a cosmological horizon, which are solutions of Lovelock gravity, determines that they must evolve either into a state where the black hole and cosmological horizons have reached thermal equilibrium or into an extreme black hole geometry where the black hole and cosmological horizons have merged. This differs from the behavior of Schwarzschild de Sitter geometry which evolves into a de Sitter space, the ground state of the space of solutions. This occurs due to a phase transition of the heat capacity 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.
We study the zeroth law for Killing horizons in Lanczos-Lovelock gravity. We show that the surface gravity of a general Killing horizon in Lanczos-Lovelock gravity (except for general relativity) may not be constant even when the matter source satisfies dominant energy condition.
Gödel universe is a homogeneous rotating dust with negative $Λ$ which is a direct product of three dimensional pure rotation metric with a line. We would generalize it to higher dimensions for Einstein and pure Lovelock gravity with only one $N$th order term. For higher dimensional generalization, we have to include more rotations in the metric, and hence we shall begin with the corresponding pure rotation odd $(d=2n+1)$-dimensional metric involving $n$ rotations, which eventually can be extended by a direct product with a line or a space of constant curvature for yielding higher dimensional G…
In this paper we propose a scheme which allows one to find all possible exponential solutions of special class -- non-constant volume solutions -- in Lovelock gravity in arbitrary number of dimensions and with arbitrate combinations of Lovelock terms. We apply this scheme to (6+1)- and (7+1)-dimensional flat anisotropic cosmologies in Einstein-Gauss-Bonnet and third-order Lovelock gravity to demonstrate how our scheme does work. In course of this demonstration we derive all possible solutions in (6+1) and (7+1) dimensions and compare solutions and their abundance between cases with different L…
In this work the \textit{chemistry} of asymptotically AdS black hole, charged and uncharged, solutions of Pure Lovelock gravity is discussed. For this the mass parameter of black holes is identified with the enthalpy of the system together with the promotion of the cosmological constant to a thermodynamics variable proportional to the \textit{pressure} of the system. The equations of state for both, charged and uncharged, are obtained. It is shown that the charged case behaves as a Van der Waals fluid. The existence of a first order phase transition between small stable/large stable black hole…
To understand the effect of third order Lovelock gravity, $P-V$ criticality of topological AdS black holes in Lovelock-Born-Infeld gravity is investigated. The thermodynamics is further explored with some more extensions and details than the former literature. A detailed analysis of the limit case $β\rightarrow\infty$ is performed for the seven-dimensional black holes. It is shown that for the spherical topology, $P-V$ criticality exists for both the uncharged and charged cases. Our results demonstrate again that the charge is not the indispensable condition of $P-V$ criticality. It may be att…
Conserved currents and related superpotentials for perturbations on arbitrary backgrounds in the Lovelock theory are constructed. We use the Lagrangian based field-theoretical method where perturbations are considered as dynamical fields propagating on a given background. Such a formulation is exact (not approximate) and equivalent to the theory in the original metric form. From the very start, using Noether theorem, we derive the Noether-Klein identities and adopt them for the purposes of the current work. Applying these identities in the framework of Lovelock theory, we construct conserved c…
It has been shown in an earlier work [arXiv:1303.1535] that there exists a pair of canonically conjugate variables $(f^{ab},N^a_{bc})$ in general relativity which also act as thermodynamically conjugate variables on any horizon. In particular their variations $(f^{bc}δN^a_{bc}, N^a_{bc}δf^{bc})$, which occur in the surface term of the Einstein-Hilbert action, when integrated over a null surface, have direct correspondence with $(SδT,TδS)$ where $(T,S)$ are the temperature and entropy. We generalize these results to Lanczos-Lovelock models in this paper. We identify two such variables in Lanczo…
We present a generalization of the n-dimensional (pure) Lovelock Gravity theory based on an enlarged Lorentz symmetry. In particular, we propose an alternative way to introduce a cosmological term. Interestingly, we show that the usual pure Lovelock gravity is recovered in a matter-free configuration. The five and six-dimensional cases are explicitly studied.
Here we give an extended review of the quasilinear reformulation of the Lovelock gravitational field equations in harmonic gauge presented in 1409.6656 [gr-qc]. This is important in order to establish rigorously well-posedness of the theory perturbed about certain backgrounds. The resulting system is not quasidiagonal, therefore analysis of causality is complicated in general. The conditions for the equations to be Leray hyperbolic are elucidated. The relevance to some recent results regarding the stability analysis of black holes is presented.
Starting from the SO(2,2n) Chern-Simons form in (2n+1) dimensions we calculate the variation of conserved quantities in Lovelock gravity and Lovelock-Maxwell gravity through the covariant formalism developed in gr-qc/0305047. Despite the technical complexity of the Lovelock Lagrangian we obtain a remarkably simple expression for the variation of the charges ensuing from the diffeomorphism covariance of the theory. The viability of the result is tested in specific applications and the formal expression for the entropy of Lovelock black holes is recovered.
It is known that spatial curvature can stabilize extra dimensions in Lovelock gravity. In the present paper we study stability of the stabilization solutions in 3-d order Lovelock gravity. We show that in the case of negative spatial curvature of extra dimension space the stabilization solution is always stable. On the contrary, for positive spatial curvature the stability depends on the coupling constant values.
Constructs from conformal geometry are important in low dimensional gravity models, while in higher dimensions the higher curvature interactions of Lovelock gravity are similarly prominent. Considering conformal invariance in the context of Lovelock gravity leads to natural, higher-curvature generalizations of the Weyl, Schouten, Cotton and Bach tensors, with properties that straightforwardly extend those of their familiar counterparts. As a first application, we introduce a new set of conformally invariant gravity theories in D=4k dimensions, based on the squares of the higher curvature Weyl …
We study properties of static, asymptotically AdS black holes in Lovelock gravity. Our main result is a Smarr formula that gives the mass in terms of geometrical quantities together with the parameters of the Lovelock theory. As in Einstein gravity, the Smarr formula follows from applying the first law to an infinitesimal change in the overall length scale. However, because the Lovelock couplings are dimensionful, we must first prove an extension of the first law that includes their variations. Key ingredients in this construction are the Killing-Lovelock potentials associated with each of the…
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.
This thesis is divided in two separate parts, the first concerned with gravitational aspects of Lovelock theories, the second with some of their holographic applications.
Anisotropic exponential cosmological solutions for a space of arbitrary dimension filled with ordinary matter in the 4th and 5th orders of Lovelock gravity are obtained. Also we have supposed a generalization of such solutions on an arbitrary order. All the solutions are represented as a set of conditions on Hubble parameters.
We derive the Hamiltonian for spherically symmetric Lovelock gravity using the geometrodynamics approach pioneered by Kuchař in the context of four-dimensional general relativity. When written in terms of the areal radius, the generalized Misner-Sharp mass and their conjugate momenta, the generic Lovelock action and Hamiltonian take on precisely the same simple forms as in general relativity. This result supports the interpretation of Lovelock gravity as the natural higher-dimensional extension of general relativity. It also provides an important first step towards the study of the quantum mec…
In this paper, we compute the mass and the temperature of the uncharged black holes of third order Lovelock gravity and compute the entropy through the use of first law of thermodynamics. We perform a stability analysis by studying the curves of temperature versus the mass parameter, and find that there exists an intermediate thermodynamically unstable phase for black holes with hyperbolic horizon. The existence of this unstable phase for the uncharged topological black holes of third order Lovelock gravity does not occur in the lower order Lovelock gravity. We also perform a stability analysi…
In this paper, we introduce the $n$-dimensional Lorentzian wormhole solutions of third order Lovelock gravity. In contrast to Einstein gravity and as in the case of Gauss-Bonnet gravity, we find that the wormhole throat radius, $r_0$, has a lower limit that depends on the Lovelock coefficients, the dimensionality of the spacetime and the shape function. We study the conditions of having normal matter near the throat, and find that the matter near the throat can be normal for the region $r_0 \leq r \leq r_{\max}$, where $r_{\max}$ depends on the Lovelock coefficients and the shape function. We …
We investigate Lovelock gravity in five dimensions in first order formalism. We construct a new class of solutions: BTZ black ring with(out) torsion. We show that our solution with torsion exists in the different sector of the Lovelock gravity compared to Lovelock Chern-Simons and the sector investigated by Canfora et al. We compute conserved charges of the solutions by using Nester's formula, and confirm the results by canonical method. We show that the theory linearized around the background with torsion possesses additional degrees of freedom compared to general relativity.
