We study how the standard definitions of ADM mass and Brown-York quasi-local energy generalize to pure Lovelock gravity. The quasi-local energy is renormalized using the background subtraction prescription and we consider its limit for large surfaces. We find that the large surface limit vanishes for asymptotically flat fall-off conditions except in Einstein gravity. This problem is avoided by focusing on the variation of the quasi-local energy which correctly approaches the variation of the ADM mass for large surfaces. As a result, we obtain a new simple formula for the ADM mass in pure Lovelock gravity. We apply the formula to spherically symmetric geometries verifying previous calculations in the literature. We also revisit asymptotically AdS geometries.
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 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 this paper, we study existence and stability of static black holes in Lovelock theories with a particular focus on pure Lovelock black holes. We derive the equation of stability from action without using S-deformation approach. It turns out that though pure-Lovelock black hole in even dimension is always unstable, however introduction of $Λ$ stablizes it by prescribing a lower threshold mass while there also exists an upper bound on mass which is given by existence of horizon. We also study stability of dimensionally continued black holes as well as of pure Lovelock analogue of BTZ black ho…
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…
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 study pure Lovelock vacuum and perfect fluid equations for Kasner-type metrics. These equations correspond to a single $N$th order Lovelock term in the action in $d=2N+1,\,2N+2$ dimensions, and they capture the relevant gravitational dynamics when aproaching the big-bang singularity within the Lovelock family of theories. Pure Lovelock gravity also bears out the general feature that vacuum in the critical odd dimension, $d=2N+1$, is kinematic; i.e. we may define an analogue Lovelock-Riemann tensor that vanishes in vacuum for $d=2N+1$, yet the Riemann curvature is non-zero. We completely cla…
The gravitational interaction is expected to be modified for very short distances. This is particularly important in situations in which the curvature of spacetime is large in general, such as close to the initial cosmological singularity. The gravitational dynamics is then captured by the higher curvature terms in the action, making it difficult to reliably extrapolate any prediction of general relativity. In this note we review pure Lovelock equations for Kasner-type metrics. These equations correspond to a single $N$th order Lovelock term in the action in $d=2N+1,\,2N+2$ dimensions, and the…
For static fluid interiors of compact objects in pure Lovelock gravity (involving ony one $N$th order term in the equation) we establish similarity in solutions for the critical odd and even $d=2N+1, 2N+2$ dimensions. It turns out that in critical odd $d=2N+1$ dimensions, there can exist no bound distribution with a finite radius, while in critical even $d=2N+2$ dimensions, all solutions have similar behavior. For exhibition of similarity we would compare star solutions for $N =1, 2$ in $d=4$ Einstein and $d=6$ in Gauss-Bonnet theory respectively. We also obtain the pure Lovelock analogue of t…
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 study the bound on the compactness of a stellar object in pure Lovelock theories of arbitrary order in arbitrary spacetime dimensions, involving electromagnetic field. The bound we derive for a generic pure Lovelock theory, reproduces the known results in four dimensional Einstein gravity. Both the case of a charged shell and that of a charge sphere demonstrates that for a given spacetime dimension, stars in general relativity are more compact than the stars in pure Lovelock theories. In addition, as the strength of the Maxwell field increases, the stellar structures become more compact, i.…
It is well known that a rotating black hole in four dimension could be overspun by linear order test particle accretion which however always gets overturned when non-linear perturbations are included. It turns out that in the Einstein gravity, repulsion due to rotation dominates over attraction due to mass in dimensions, $D>5$, and consequently black hole cannot be overspun even for linear order accretion. For the pure Lovelock rotating black hole, this dimensional threshold is $D>4N+1$ where $N$ is degree of single $N$th order term in the Lovelock polynomial in the action. Thus the pure Lovel…
It is well known that vacuum equation of arbitrary Lovelock order for static spacetime ultimately reduces to a single algebraic equation, we show that the same continues to hold true for pure Lovelock gravity of arbitrary order $N$ for topology ${\bf S^{(n)} \times S^{(n)}}$. We thus obtain pure Lovelock static black hole solutions with two-sphere topology for any order $N$, and in particular we study in full detail the third and fourth order Lovelock black holes. It is remarkable that thermodynamical stability of black hole discerns between odd and even $N$, and consequently between negative …
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…
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 …
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 …
In this paper we show that pure Lovelock static Schwarzschild's analogue black hole in dimensions $d>3N+1$, where $N$ is the degree of Lovelock polynomial action, is stable even though pure Gauss-Bonnet $N=2$ black hole is unstable in dimension $d<7$. We also discuss and compare quasinormal modes for pure Lovelock and the corresponding Einstein black hole in the same dimension. We find that perturbations decay with characteristic time which is weakly dimensional dependent as it depends only on the gravitational potential of the background solution, while frequency of oscillations however depen…
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 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.
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…
The necessary and sufficient condition for the thermodynamical universality of the static spherically symmetric Lovelock black hole is that it is the pure Lovelock Λ-vacuum solution. By universality we mean the thermodynamical parameters: temperature and entropy always bear the same relationship to the horizon radius irrespective of the Lovelock order and the spacetime dimension. For instance, the entropy always goes in terms of the horizon radius as rh and r^2 respectively for h odd and even dimensions. This universality uniquely identifies the pure Lovelock black hole with Λ.
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 initial value problem for Lovelock and Horndeski theories of gravity. We show that the equations of motion of these theories can be written in a form that, at weak coupling, is strongly hyperbolic and therefore admits a well-posed initial value problem. This is achieved by introducing a new class of "modified harmonic" gauges for general relativity.
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…
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…
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…
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 …
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…
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…
We define a notion of extrinsic black hole in pure Lovelock gravity of degree $k$ which captures the essential features of the so-called Lovelock-Schwarzschild solutions, viewed as rotationally invariant hypersurfaces with null $2k$-mean curvature in Euclidean space $\mathbb R^{n+1}$, $2\leq 2k\leq n-1$. We then combine a regularity argument with a rigidity result by Araújo-Leite to prove, under a natural ellipticity condition, a global uniqueness theorem for this class of black holes. As a consequence we obtain, in the context of the corresponding Penrose inequality for graphs established by …
It is known that the emission rate of entropy from a Schwarzschild black hole is exactly the same as that of a one dimensional quantum channel \cite{Beken}. We calculate the dimension of entropy emission from a $D$ dimensional pure Lovelock black holes. Our results indicate that the dimension of transmission for odd $D$ dimensional space-times is equal to $D$ and for even $D$ dimensional space-times, the dimension of quantum channel becomes $1+ε(Λ)$, where $ Λ$ is cosmological constant. It is interesting that cosmological constant may put some constraint on dimension of quantum channel in even…
Extending the Comisso-Asenjo Energy Extraction Mechanism to Pure Lovelock Gravity
Harbin Institute of Technology（哈尔滨工业大学）；New Uzbekistan University（新乌兹别克斯坦大学）；Institute of Fundamental and Applied Research, National Research University TIIAME（国立研究型大学TIIAME基础与应用研究所）；Tashkent University of Applied Sciences（塔什干应用科学大学）；National University of Uzbekistan（乌兹别克斯坦国立大学）
We obtain the classical holographic relation for the general Lovelock gravity and decompose the full Lagrangian into the bulk term and the surface term, expressed as a total derivative $\partial_μJ^μ$. By classical holographic relation, we mean that $J^μ$ is determined completely by the bulk term. We find that the bulk term is not degenerate, or first-order in this foliation-independent approach. We then consider the Arnowitt-Deser-Misner (ADM) formalism where the foliation coordinate $w$ is treated as special. We obtain the classical holographic-degenerate relation with the first-order bulk t…
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…
In this paper we study circular orbits around higher dimensional rotating Myers-Perry and pure Gauss-Bonnet (GB) black holes. It turns out that for the former there occurs no potential well to harbour bound and thereby stable circular orbits. The only circular orbits that could occur are all unstable and their radius is bounded from the below by that of the photon circular orbit. On the other hand bound and stable circular orbits do exist for pure GB/Lovelock rotating black holes (the metric is though not an exact solution of pure Lovelock vacuum equation but it satisfies the equation in the l…
We show that the scalar-tensor theory that arises in a rigorous $D \to 3$ limit of Lovelock gravity up to cubic order admits a holographic c-theorem and verify that the value of the c-function at the UV fixed point matches with the Weyl anomaly coefficient (up to an irrelevant factor). The constructed c-function is the same as one that follows from the "naive limit", which is obtained by scaling the couplings by a factor of $\frac{1}{D-3}$, and then setting $D=3$.
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 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.
Based on the insight gained by many authors over the years on the structure of the Einstein-Hilbert, Gauss-Bonnet and Lovelock gravity Lagrangians, we show how to derive -- in an elementary fashion -- their first-order, generalized "ADM" Lagrangian and associated Hamiltonian. To do so, we start from the Lovelock Lagrangian supplemented with the Myers boundary term, which guarantees a Dirichlet variational principle with a surface term of the form $π^{ij}δh_{ij}$, where $π^{ij}$ is the canonical momentum conjugate to the boundary metric $h_{ij}$. Then, the first-order Lagrangian density is obta…
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 perform a space-time analysis of the D>4 quadratic curvature Lanczos-Lovelock (LL) model, exhibiting its dependence on intrinsic/extrinsic curvatures, lapse and shifts. As expected from general covariance, the field equations include D constraints, of zeroth and first time derivative order. In the "linearized" - here necessarily cubic - limit, we give an explicit formulation in terms of the usual ADM metric decomposition, incidentally showing that time derivatives act only on its transverse-traceless spatial components. Unsurprisingly, pure LL has no Hamiltonian formulation, nor are even it…
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…
An explicit formula for the ADM mass of an asymptotically AdS black hole in a generic Lovelock gravity theory is presented, identical in form to that in Einstein gravity, but multiplied by a function of the Lovelock coupling constants and the AdS curvature radius. A Gauss' law type formula relates the mass, which is an integral at infinity, to an expression depending instead on the horizon radius. This and other thermodynamic quantities, such as the free energy, are then analyzed in the limits of small and large horizon radius, yielding results that are independent of the detailed choice of Lo…
It is well-known that Einstein gravity is kinematic (no non-trivial vacuum solution;i.e. Riemann vanishes whenever Ricci does so) in $3$ dimension because Riemann is entirely given in terms of Ricci. Could this property be universalized for all odd dimensions in a generalized theory? The answer is yes, and this property uniquely singles out pure Lovelock (it has only one $N$th order term in action) gravity for which $N$th order Lovelock Riemann tensor is indeed given in terms of corresponding Ricci for all odd $d=2N+1$ dimensions. This feature of gravity is realized only in higher dimensions a…
In this paper, we investigate the existence of Lifshitz solutions in Lovelock gravity, both in vacuum and in the presence of a massive vector field. We show that the Lovelock terms can support the Lifshitz solution provided the constants of the theory are suitably chosen. We obtain an exact black hole solution with Lifshitz asymptotics of any scaling parameter $z$ in both Gauss-Bonnet and in pure 3rd order Lovelock gravity. If matter is added in the form of a massive vector field, we also show that Lifshitz solutions in Lovelock gravity exist; these can be regarded as corrections to Einstein g…
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…
In this note we classify a certain family of solutions of Lovelock gravity in the Chern-Simons (CS) case, in arbitrary (odd) dimension greater than four. The spacetime is characterized by admitting a metric that is a warped product of a two-dimensional spacetime M2 and an (a priori) arbitrary Euclidean base manifold Sigma(d-2) of dimension d-2. We show that the solutions are naturally classified in terms of the equations that restrict the base manifold. According to the strength of such constraints we found the following branches in which Sigma(d-2) has to fulfill: a Lovelock equation with a s…
In this note we perform the $n+1$ decomposition, or Arnowitt Deser Misner (ADM) formulation of $f($Lovelock$)$ gravity theory. The hamiltonian form of Lovelock gravity was known since the work of C. Teitelboim and J. Zanelli in 1987, but this result had not yet been extended to $f($Lovelock$)$ gravity. Besides, field equations of $f($Lovelock$)$ have been recently be computed by P. Bueno et al., though without ADM decomposition. We focus on the non-degenerate case, ie. when the Hessian of $f$ is invertible. Using the same Legendre transform as for $f(\mathrm{R})$ theories, we can identify the …
In four space-time dimensions, there are good theoretical reasons for believing that General Relativity is the correct geometrical theory of gravity, at least at the classical level. If one admits the possibility of extra space-time dimensions, what would we expect classical gravity to be like? It is often stated that the most natural generalisation is Lovelock's theory, which shares many physical properties with GR. But there are also key differences and problems. A potentially serious problem is the breakdown of determinism, which can occur when the matrix of coefficients of second time deri…
There has recently been an increasing interest in regularizations of Lovelock-Lanczos gravity (LLG) in four dimensions, in which dimensional poles and possibly counter-terms are introduced to compensate the vanishing of the Lovelock field equations in critical and lower dimensions. In this paper, we review and extend some of these results. We first find a class of LLG theories whose perturbative expansion around a given (A)dS vacuum can be regularized up to arbitrary order, the simplest one being close to Lovelock gravities with a unique vacuum. If well-defined, these models might be interpret…
We investigate the existence and nature of classical maximum force bound between two black holes with touching horizons. Besides general relativity, the maximum force bound is independent of black hole masses only in Moffat's theory, Brans Dicke theory (which is the same as Einstein's for vacuum) and the higher dimensional generalization of Einstein's theory, pure Lovelock gravity which is characterised by having single $n$th order term in Lovelock polynomial without sum over lower orders in the action. Further if the bound is to exist in higher dimensions and is entirely in terms of the veloc…
It has long been known that Lovelock gravity, being of Cauchy-Kowalevskaya type, admits a well defined initial value problem for analytic data. However, this does not address the physically important issues of continuous dependence of the solution on the data and the domain of dependence property. In this note we fill this gap in our understanding of the (local) dynamics of the theory. We show that, by a known mathematical trick, the fully nonlinear harmonic-gauge-reduced Lovelock field equations can be made equivalent to a quasilinear PDE system. Due to this equivalence, an analysis of the pr…
Static asymptotically Lifshitz wormholes and black holes in vacuum are shown to exist for a class of Lovelock theories in d=2n+1>7 dimensions, selected by requiring that all but one of their n maximally symmetric vacua are AdS of radius l and degenerate. The wormhole geometry is regular everywhere and connects two Lifshitz spacetimes with a nontrivial geometry at the boundary. The dynamical exponent z is determined by the quotient of the curvature radii of the maximally symmetric vacua according to n(z^2-1)+1=(l/L)^2, where L corresponds to the curvature radius of the nondegenerate vacuum. Lig…
