It is well known that the vacuum in the Einstein gravity, which is linear in the Riemann curvature, is trivial in the critical (2+1=3) dimension because vacuum solution is flat. It turns out that this is true in general for any odd critical $d=2n+1$ dimension where $n$ is the degree of homogeneous polynomial in Riemann defining its higher order analogue whose trace is the nth order Lovelock polynomial. This is the "curvature" for nth order pure Lovelock gravity as the trace of its Bianchi derivative gives the corresponding analogue of the Einstein tensor \cite{bianchi}. Thus the vacuum in the pure Lovelock gravity is always trivial in the odd critical (2n+1) dimension which means it is pure Lovelock flat but it is not Riemann flat unless $n=1$ and then it describes a field of a global monopole. Further by adding Lambda we obtain the Lovelock analogue of the BTZ black hole.
The Horndeski theories are extended into the Lovelock gravity theory. When the canonical scalar field is uniquely kinetically coupled to the Lovelock tensors, it is named after Lovelock scalar field. The Lovelock scalar field model is a subclass of the new Horndeski theories. A most attractive feature of the Lovelock scalar field is its equation of motion is second order. So it is free of ghosts. We study the cosmology of Lovelock scalar field in the background of $7$ dimensional spacetime and present a class of cosmic solutions. These solutions reveal the physics of the scalar field is rather…
Lovelock gravity in $D$-dimensional space-times is considered adopting Cartan's structure equations. In this context, we find out exact solutions in cosmological and spherically symmetric backgrounds. In the latter case, we also derive horizons and the corresponding Bekenstein--Hawking entropies. Moreover, we focus on the topological Chern--Simons theory, providing exact solutions in 5 dimensions. Specifically, it is possible to show that Anti-de Sitter invariant Chern--Simons gravity can be framed within Lovelock--Zumino gravity in 5 dimensions, for particular choices of Lovelock parameters.
We study quasi-stationary physical process for black holes within the context of Lanczos-Lovelock gravity. We show that the Wald entropy of stationary black holes in Lanczos-Lovelock gravity monotonically increases for quasi-stationary physical processes in which the horizon is perturbed by the accretion of positive energy matter and the black hole ultimately settles down to a stationary state. This result reinforces the physical interpretation of Wald entropy for Lanczos-Lovelock models and takes a step towards proving the analogue of the black hole area increase-theorem in a wider class of g…
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…
In this work, we have assumed the generalized Vaidya solution in Lovelock theory of gravity in $(n+2)$-dimensions. It has been shown that Gauss-Bonnet gravity, dimensionally continued Lovelock gravity and pure Lovelock gravity can be constructed by suitable choice of parameters. We have investigated the occurrence of singularities formed by the gravitational collapse in above three particular forms of Lovelock theory of gravity. The dependence of the nature of singularity on the existence of radial null geodesic for Vaidya space-time has been specially considered. In all the three models, we h…
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.
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.
We study gravitational collapse of a spherically symmetric inhomogeneous dust cloud in the Lovelock theory without cosmological constant. We show that the final fate of gravitational collapse in this theory depends on the spacetime dimensions. In odd dimensions the naked singularities formed are found to be massive. In the even dimensions,on the other hand, the naked singularities are found to be massless. We also show that the curvature strength of naked singularity is independent of the spacetime dimensions in odd dimensions. However, it depends on the spacetime dimensions in even dimension.
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.
We present a kind of generalized Vaidya solutions in a generic Lovelock gravity. This solution generalizes the simple case in Gauss-Bonnet gravity reported recently by some authors. We study the thermodynamics of apparent horizon in this generalized Vaidya spacetime. Treating those terms except for the Einstein tensor as an effective energy-momentum tensor in the gravitational field equations, and using the unified first law in Einstein gravity theory, we obtain an entropy expression for the apparent horizon. We also obtain an energy expression of this spacetime, which coincides with the gener…
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.
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.
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 …
According to Lovelock's theorem, the Hilbert-Einstein and the Lovelock actions are indistinguishable from their field equations. However, they have different scalar-tensor counterparts, which correspond to the Brans-Dicke and the \emph{Lovelock-Brans-Dicke} (LBD) gravities, respectively. In this paper the LBD model of alternative gravity with the Lagrangian density $\mathscr{L}_{\text{LBD}}=\frac{1}{16π}\left[ϕ\left( R +\frac{a}{\sqrt{-g}}{}^*RR + b\mathcal{G}\right)-\frac{ω_{\text{L}}}ϕ\nabla_αϕ\nabla^αϕ\right]$ is developed, where ${}^*RR$ and $\mathcal{G}$ respectively denote the topologica…
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.
The Lovelock gravity is a fascinating extension of general relativity, whose action consists of the dimensionally extended Euler densities. Compared to other higher order derivative gravity theories, the Lovelock gravity is attractive since it has a lot of remarkable features such as that there are no more than second order derivatives with respect to metric in its equations of motion, and that the theory is free of ghost. Recently in the study of black string and black brane in the Lovelock gravity, a special class of Lovelock gravity is considered, which is named pure Lovelock gravity, where…
Although gravitational actions diverge in asymptotically AdS spacetimes, boundary counterterms can be added in order to cancel out those divergences; such counterterms are known in general to third order in the Riemann tensor for the Einstein-Hilbert action. Considering foliations of AdS with an $S^m \times H^{d-m}$ boundary, we discuss a simple algorithm which we use to generate counterterms up to sixth order in the Riemann tensor, for the Einstein-Hilbert, Gauss-Bonnet and third-order-Lovelock Lagrangians. We also comment on other theories such as $F(R)$ gravity.
We study the membrane paradigm for horizons in Lanczos-Lovelock models of gravity in arbitrary D dimensions and find compact expressions for the pressure p and viscosity coefficients ηand ζof the membrane fluid. We show that the membrane pressure is intimately connected with the Noether charge entropy S_Wald of the horizon when we consider a specific m-th order Lanczos-Lovelock model, through the relation pA/T=(D-2m)/(D-2)S_Wald, where T is the temperature and A is the area of the horizon. Similarly, the viscosity coefficients are expressible in terms of entropy and quasi-local energy associat…
Spherically symmetric shock waves are shown to exist in Lovelock gravity. They amount to a change of branch of the spherically symmetric solutions across a null hypersurface. The implications of their existence for the status of Birkhoff's theorem in the theory is discussed.
We study the effect of charge on gravitational collapse of inhomogeneous dust cloud in the Einstein, Gauss-Bonnet and Lovelock gravity. Dynamics of the collapsing shell is analyzed. The conditions for the occurrence of bounce during collapse are given. We also show that shell crossing occurs inevitably if the shell near the center is weakly charged.
For any K(=2k+1)th-order Lovelock gravity with fine-tuned Lovelock couplings, we demonstrate the existence of a special isolated critical point characterized by non-standard critical exponents in the phase diagram of hyperbolic vacuum black holes. In the Gibbs free energy this corresponds to a place wherefrom two swallowtails emerge, giving rise to two first-order phase transitions between small and large black holes. We believe that this is a first example of a critical point with non-standard critical exponents obtained in a geometric theory of gravity.
The deep connection between gravitational dynamics and horizon thermodynamics leads to several intriguing features both in general relativity and in Lanczos-Lovelock theories of gravity. Recently in arXiv:1312.3253 several additional results strengthening the above connection have been established within the framework of general relativity. In this work we provide a generalization of the above setup to Lanczos-Lovelock gravity as well. To our expectation it turns out that most of the results obtained in the context of general relativity generalize to Lanczos-Lovelock gravity in a straightforwa…
There is a growing interest in modified gravity theories based on torsion, as these theories exhibit interesting cosmological implications. In this work, inspired by the teleparallel formulation of general relativity, we present its extension to Lovelock gravity known as the most natural extension of general relativity in higher-dimensional space-times. First, we review the teleparallel equivalent of general relativity and Gauss-Bonnet gravity, and then we construct the teleparallel equivalent of Lovelock gravity. In order to achieve this goal we use the vielbein and the connection without imp…
We argue that Lovelock theories of gravity suffer from shock formation, unlike General Relativity. We consider the propagation of (i) a discontinuity in curvature, and (ii) weak, high frequency, gravitational waves. Such disturbances propagate along characteristic hypersurfaces of a "background" spacetime and their amplitude is governed by a transport equation. In GR the transport equation is linear. In Lovelock theories, it is nonlinear and its solutions can blow up, corresponding to the formation of a shock. We show that this effect is absent in some simple cases e.g. a flat background space…
We present a method to analyse black hole hair in the spherical symmetric sector of the Lovelock theory in arbitrary dimensions that is an alternative to solving the equations of motion in their complete form. We explicitly show that the method matches with the known black hole solutions for the vacuum and electro-vacuum spacetimes in Lovelock gravity theories. We further apply the method to the case of minimally coupled non-self-interacting massless scalar field and prove that there is no (non-self-interacting) massless scalar hair for the spherically symmetric Lovelock black holes.
We study the renormalization of Entanglement Entropy in holographic CFTs dual to Lovelock gravity. It is known that the holographic EE in Lovelock gravity is given by the Jacobson-Myers (JM) functional. As usual, due to the divergent Weyl factor in the Fefferman-Graham expansion of the boundary metric for Asymptotically AdS spaces, this entropy functional is infinite. By considering the Kounterterm renormalization procedure, which utilizes extrinsic boundary counterterms in order to renormalize the on-shell Lovelock gravity action for AAdS spacetimes, we propose a new renormalization prescript…
In this paper, we investigate the second law of the black holes in Lovelock gravity sourced by a conformally coupled scalar field under the first-order approximation when the perturbation matter fields satisfy the null energy condition. First of all, we show that the Wald entropy of this theory does not obey the linearized second law for the scalar-hairy Lovelock gravity which contains the higher curvature terms even if we replace the gravitational part of Wald entropy with Jacobson-Myers (JM) entropy. This implies that we cannot naively add the scalar field term of the Wald entropy to the JM …
In the Riemann geometry, the metric's equation of motion for an arbitrary Lagrangian is succinctly expressed in term of the first variation of the action with respect to the Riemann tensor if the Riemann tensor were independent of the metric. Let this variation be called the E-tensor. Noting that the E-tensor and equations of the motion for a general Lovelock gravity have the same differential degree, we define generalized Lovelock gravity as polynomial scalar densities constructed out from the Riemann tensor and its arbitrary covariant derivatives such that they lead to the same differential …
We analyzed static spherically symmetric solutions of the five dimensional (5D) Lovelock gravity in the first order formulation. In the Riemannian sector, when torsion vanishes, Boulware-Deser black hole represents a unique static spherically symmetric black hole solution for the generic choice of the Lagrangian parameters. We showed that the special choice of the Lagrangian parameters, different from the Lovelock Chern-Simons gravity, leads to the existence of the static black hole solution with torsion, which metric is asymptotically AdS. We calculate conserved charges and thermodynamical qu…
We show that the generic solutions of the Lovelock equations with spherical, planar or hyperbolic symmetry are locally isometric to the corresponding static Lovelock black hole. As a consequence, these solutions are locally static: they admit an additional Killing vector that can either be space-like or time-like, depending on the position. This result also holds in the presence of an abelian gauge field, in which case the solutions are locally isometric to a charged static black hole.
We study the entropy evolution of black holes in Lovelock gravity by formulating a thermodynamic generalization of null Raychaudhuri equation. We show that the similarity between the expressions of entropy change of the black hole horizon due to perturbation and that of a fluid, which is out of equilibrium, transcends beyond general relativity to the Lovelock class of theories. Exploiting this analogy we find that the shear and bulk viscosities for the black holes in Lovelock theories exactly match with those obtained in the membrane paradigm and also from holographic considerations.
In this paper, we show that the holographic dark energy density hides in the solutions of Lovelock gravity for black holes. Using the obtained mass and temperature we find density equations. We propose a physical interpretation of the rescaled Lovelock couplings as a topological mass that describes the Lovelock branch. In addition to this, we present new solutions that satisfy the energy conditions according to the Lovelock coupling and the horizon curvatures. This work can be extended to the equation of the state ω_{Λ} of dark energy in third-order Lovelock gravity. We show that the value "-1…
We consider a static self-gravitating system consisting of perfect fluid with isometries of an $(n-2)$-dimensional maximally symmetric space in Lovelock gravity theory. A straightforward analysis of the time-time component of the equations of motion suggests a generalized mass function. Tolman-Oppenheimer-Volkoff like equation is obtained by using this mass function and gravitational equations. We investigate the maximum entropy principle in Lovelock gravity, and find that this Tolman-Oppenheimer-Volkoff equation can also be deduced from the so called "maximum entropy principle" which is origi…
In this paper, we consider logarithmic and exponential forms of nonlinear electrodynamics as a source and obtain magnetic brane solutions of the Lovelock gravity. Although these solutions have no curvature singularity and no horizon, they have a conic singularity with a deficit angle. We investigate the effects of nonlinear electrodynamics and the Lovelock gravity on the value of deficit angle and find that various terms of Lovelock gravity do not affect deficit angle. Next, we generalize our solutions to spinning cases with maximum rotating parameters in arbitrary dimensions and calculate the…
We present an alternative derivation of the gravitational field equations for Lovelock gravity starting from the Newton's law, which is closer in spirit to the thermodynamic description of gravity. As a warm up exercise, we have explicitly demonstrated that projecting the Riemann curvature tensor appropriately and taking a cue from Poisson's equation, the Einstein's equations immediately follow. The above derivation naturally generalizes to Lovelock gravity theories where an appropriate curvature tensor satisfying the symmetries as well as the Bianchi derivative properties of the Riemann tenso…
The first law of thermodynamics at black hole horizons is known to be obtainable from the gravitational field equations. A recent study claims that the contributions at inner horizons should be considered in order to give the conventional first law of black hole thermodynamics. Following this method, we revisit the thermodynamic aspects of field equations in the Lovelock gravity and f(R) gravity by focusing on two typical classes of charged black holes in the two theories.
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 show that the Lovelock type brane gravity is naturally holographic by providing a correspondence between bulk and surface terms that appear in the Lovelock-type brane gravity action functional. We prove the existence of relationships between the $\mathcal{L}_{\mbox{\tiny bulk}}$ and $\mathcal{L}_{\mbox{\tiny surf}}$ allowing $\mathcal{L}_{\mbox{\tiny surf}}$ to be determined completely by $\mathcal{L}_{\mbox{\tiny bulk}}$. In the same spirit, we provide relationships among the various conserved tensors that this theory possesses. We further comment briefly on the correspondence between geom…
In this paper, we consider Lovelock gravity in presence of two Born-Infeld types of nonlinear electrodynamics and study their thermodynamical behavior. We extend the phase space by considering cosmological constant as a thermodynamical pressure. We obtain critical values of pressure, volume and temperature and investigate the effects of both the Lovelock gravity and the nonlinear electrodynamics on these values. We plot $P-v$, $T-v$ and $G-T$ diagrams to study the phase transition of these thermodynamical systems. We show that power of the nonlinearity and gravity have opposite effects. We als…
We study the dual fluid on a finite cutoff surface outside the black brane horizon in the third order Lovelock gravity. Using nonrelativistic long-wavelength expansion, we obtain the incompressible Navier-Stokes equations of dual fluid with external force density on the finite cutoff surface. The viscosity to entropy density ratio $η/s$ is independent of cutoff surface and does not get modification from the third order Lovelock gravity influence. The obtained ratio agrees with the results obtained by using other methods, such as the Kubo formula at the AdS boundary and the membrane paradigm at…
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…
In this work we aim at discussing the effects of higher order corrections to curvature on the Lovelock AdS black holes quasinormal spectrum and, in the context of gauge/gravity correspondence, their consequences for the formation of holographic superconductors. We also explore the hydrodynamic limit of the $U(1)$ gauge field perturbations in $d$ dimensions.
In this paper, we combine Lovelock gravity with gravity's rainbow to construct Lovelock gravity's rainbow. Considering the Lovelock gravity's rainbow coupled to linear and also nonlinear electromagnetic gauge fields, we present two new classes of topological black hole solutions. We compute conserved and thermodynamic quantities of these black holes (such as temperature, entropy, electric potential, charge and mass) and show that these quantities satisfy the first law of thermodynamics. In order to study the thermal stability in canonical ensemble, we calculate the heat capacity and determinan…
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…
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,…
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…
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 …
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 …
