Gokhan Alkac, Deniz Olgu Devecioglu
We define a "holographic limit" of Lancsoz-Lovelock theories at the Lagrangian level which gives three-dimensional modified gravity theories. We also show that this limit applies to more general classes of theories in higher dimensions provided that they admit the holographic c-theorem.
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Microscopic entropy of static black holes in 3d Lovelock gravities
本文微观推导了3d Lovelock引力中静态黑洞的半经典熵，通过双重Wick旋转得到孤子基态，并利用无中心荷的Cardy公式重现熵，详细说明了孤子质量的计算方法。
For appropriate choices of the coupling constants, the equations of motion of Lovelock gravities up to order n in the Riemann tensor can be factorized such that the theories admits a single (A)dS vacuum. In this paper we construct two classes of exact rotating metrics in such critical Lovelock gravities of order n in d=2n+1 dimensions. In one class, the n angular momenta in the n orthogonal spatial 2-planes are equal, and hence the metric is of cohomogeneity one. We construct these metrics in a Kerr-Schild form, but they can then be recast in terms of Boyer-Lindquist coordinates. The other cla…
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…
In this work, we provide consistent compactifications of Einstein-Maxwell and Einstein-Maxwell-Lovelock theories on direct product spacetimes of the form $\mathcal{M}_D=\mathcal{M}_d\times\mathcal{K}^{p}$, where $\mathcal{K}^p$ is a Euclidean internal manifold of constant curvature. For these compactifications to take place, it is required the distribution of a precise flux of $p$-forms over the internal manifold. The dynamic of the $p$-forms are demanded to be controlled by two types of interaction. First, by specific couplings with the curvature tensor and, second, by a suitable interaction …
We present a Born-Infeld gravity theory based on generalizations of Maxwell symmetries denoted as $\mathfrak{C}_{m}$. We analyze different configuration limits allowing to recover diverse Lovelock gravity actions in six dimensions. Further, the generalization to higher even dimensions is also considered.
On the maximally symmetric vacua of generic Lovelock gravities
本文考察了 Lovelock 引力的极大对称真空解，利用 Palais 对称临界性原理恢复静态黑洞解，展示了场方程在真空附近的线性化因式分解，并阐述了守恒荷的计算及特殊真空的性质。
We study holographic implications of Lovelock gravities in AdS spacetimes. For a generic Lovelock gravity in arbitrary spacetime dimensions we formulate the existence condition for asymptotically AdS black holes. We consider small fluctuations around these black holes and determine the constraint on Lovelock parameters by demanding causality of the boundary theory. For the case of cubic Lovelock gravity in seven spacetime dimensions we compute the holographic Weyl anomaly and determine the three point functions of the stress energy tensor in the boundary CFT. Remarkably, these correlators happ…
Thin shells in Lovelock and Quasi-topological gravities
本文推导了Lovelock与准拓扑引力中球对称薄壳的衔接条件，澄清了薄壳质量随半径变化的错误结论，为质量通胀分析提供了基础。
We study entanglement entropies of simply connected surfaces in field theories dual to Lovelock gravities. We consider Gauss-Bonnet and cubic Lovelock gravities in detail. In the conformal case the logarithmic terms in the entanglement entropy are governed by the conformal anomalies of the CFT; we verify that the holographic calculations are consistent with this property. We also compute the holographic entanglement entropy of a slab in the Gauss-Bonnet examples dual to relativistic and non-relativistic CFTs and discuss its properties. Finally, we discuss features of the entanglement entropy i…
On the Properties of the Power-Law Cosmological Solutions in Lovelock Gravity
本文研究了洛夫洛克引力中幂律宇宙解的性质，发现高阶解在某些条件下无法作为过去渐近解，影响了过渡和紧致化可能性。
f(Lovelock) gravities are simple generalizations of the usual f(R) and Lovelock theories in which the gravitational action depends on some arbitrary function of the corresponding dimensionally-extended Euler densities. In this paper we study several aspects of these theories in general dimensions. We start by identifying the generalized boundary term which makes the gravitational variational problem well-posed. Then, we show that these theories are equivalent to certain scalar-tensor theories and how this relation is characterized by the Hessian of f. We also study the linearized equations of …
A (3+1)-dimensional Einstein-Gauss-Bonnet effective description of gravity has been recently formulated as the $D \to 4$ limit of the higher dimensional field equations after the rescaling of the coupling constant. This approach has been recently extended to the four-dimensional Einstein-Lovelock gravity. Although validity of the regularization procedure has not been shown for the general case, but only for a wide class of metrics, the black-hole solution obtained as a result of such a regularization is also an exact solution in the well defined 4D Einstein-Gauss-Bonnet theory suggested by Aok…
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 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 consider massless higher-order gravities in general $D=d+1$ dimensions, which are Einstein gravity extended with higher-order curvature invariants in such a way that the linearized spectrum around the AdS vacua involves only the massless graviton. We derive the covariant holographic two-point functions and find that they have a universal structure. In particular, the theory-dependent overall coefficient factor $\mathcal{C}_T$ can be universally expressed by $(d-1) \mathcal{C}_T=\ell (\partial a/\partial\ell)$, where $a$ is the holographic $a$-charge and $\ell$ is the AdS radius. We verify t…
We employ the Noether procedure to derive a general formula for the radially conserved heat current in AdS planar black holes with certain transverse and traceless perturbations, for a general class of gravity theories. For Einstein gravity, the general higher-order Lovelock gravities and also a class of Horndeski gravities, we derive the boundary stress tensor and show that the resulting boundary heat current matches precisely the bulk Noether current.
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…
The equivalence between the Lanczos-Lovelock and teleparallel gravities is discused. It is shown that the teleparallel equivalent of the Lovelock gravity action is generated by dimensional continuation of the teleparallel equivalent of the Euler characteristics associated to all the lower even dimensions. It is also found that the teleparallel equivalent of the (i) d-dimensional Euler characteristic is a closed form and gauge invariant, (ii) Lovelock action are invariant both under the Poincare group and diffeomorphisms.
The holographic entanglement entropy functional for higher-curvature gravities involves a weighted sum whose evaluation, beyond quadratic order, requires a complicated theory-dependent splitting of the Riemann tensor components. Using the splittings of general relativity one can obtain unambiguous formulas perturbatively valid for general higher-curvature gravities. Within this setup, we perform a novel rewriting of the functional which gets rid of the weighted sum. The formula is particularly neat for general cubic and quartic theories, and we use it to explicitly evaluate the corresponding f…
Chern-Simons gravities are theories with a lagrangian given by a Chern-Simons form constructed from a space-time gauge group. In previous investigations we showed that, for some special field configurations that are solutions of the field equations, the extension from Chern-Simons to Transgression forms as lagrangians, motivated by gauge invariance, automatically yields the boundary terms required to regularize the theory, giving finite conserved charges and black hole thermodynamics. Further work by other researchers showed that one of the action functionals considered in the above mentioned …
We review the issue of gauge and gravitational anomalies with backgrounds, maybe offering a new outlook on some aspects of these questions. We compute the holographic anomalies of hypothetical theories dual, in the sense of the AdS-CFT correspondence, to Chern-Simons AdS gravities. Those anomalies are either gauge anomalies associated to the AdS gauge group of the theory or diffeomorphism anomalies, with each kind related to the other. As a result of using suitable action principles por Chern-Simons AdS gravities, coming from Transgression forms, we obtain finite results without the need for f…
We study several aspects of higher-order gravities constructed from general contractions of the Riemann tensor and the metric in arbitrary dimensions. First, we use the fast-linearization procedure presented in arXiv:1607.06463 to obtain the equations satisfied by the metric perturbation modes on a maximally symmetric background in the presence of matter and to classify $\mathcal{L}($Riemann$)$ theories according to their spectrum. Then, we linearize all theories up to quartic order in curvature and use this result to construct quartic versions of Einsteinian cubic gravity (ECG). In addition, …
We review the often forgotten fact that gravitation theories invariant under local de Sitter, anti-de Sitter or Poincare transformations can be constructed in all odd dimensions. These theories belong to the Chern-Simons family and are particular cases of the so-called Lovelock gravities, constructed as the dimensional continuations of the lower dimensional Euler classes. The supersymmetric extensions of these theories exist for the AdS and Poincare groups, and the fields are components of a single connection for the corresponding Lie algebras. In 11 dimensions these supersymmetric theories ar…
Holographic Renormalization of String-Derived Lovelock--Horndeski Theory
针对五维弦导出的洛夫洛克-霍恩德斯基理论，构建了其渐近局域 AdS 分支的重整化生成泛函，证明全息响应可重构高维参数，为弦约化提供边界指纹。
The gravitational Lagrangian can be written as a summation of a bulk and a total derivative term. For some theories of gravity such as Einstein gravity, or more general Lovelock gravities, there are Lagrangian holographic relations between the bulk and the total derivative term such that the latter is fully determined by the former. However at the $D\rightarrow 2\&4$ limit, the bulks of Einstein or Gauss-Bonnet theories become themselves total derivatives. Performing the Kaluza-Klein reduction on Einstein and Gauss-Bonnet gravities gives rise to some two-dimensional or four-dimensional scalar-…
The Komar integral relation of Einstein gravity is generalized to Lovelock theories of gravity. This includes, in particular, a new boundary integral for the Komar mass in Einstein gravity with a nonzero cosmological constant, which has a finite result for asymptotically AdS black holes, without the need for an infinite background subtraction. Explicit computations of the Komar mass are given for black holes in pure Lovelock gravities of all orders and in general Gauss-Bonnet theories.
Can Bekenstein's area law prevail in modified theories of gravity?
本文指出四维Gauss--Bonnet引力中对贝肯斯坦面积定律的对数修正源于忽略平移对称性，正确考虑该对称性并修改黑洞温度后，面积定律在四维及高维Lovelock引力中均可恢复成立。
This is intended as a broad introduction to Chern-Simons gravity and supergravity. The motivation for these theories lies in the desire to have a gauge invariant system --with a fiber bundle formulation-- in more than three dimensions, which could provide a firm ground for constructing a quantum theory of the gravitational field. The starting point is a gravitational action which generalizes the Einstein theory for dimensions D>4 --Lovelock gravity. It is then shown that in odd dimensions there is a particular choice of the arbitrary parameters of the action that makes the theory gauge invaria…
We explore the ultra-relativistic limit of a class of four dimensional gravity theories, known as Lovelock-Cartan gravities, in the first order formalism. First, we review the well known limit of the Einstein-Hilbert action. A very useful scale symmetry involving the vierbeins and the boost connection is presented. Moreover, we explore the field equations in order to find formal solutions. Some remarkable results are obtained: Riemann and Weitzenböck like manifolds are discussed; Birkhoff's theorem is verified for the torsionless case; an explicit solution with non-trivial geometry is discusse…
Logarithmic correction to the entropy of near-extremal higher-curvature black holes
该研究利用二维Horndeski理论对应关系，证明近极端黑洞熵的对数修正具有普适性，并给出其主导尺度的一般形式，适用于多种高曲率引力理论。
Weyl-invariant scalar-tensor gravities from purely metric theories
提出将任意纯度规高导数引力通过共形不变度规替换提升为 Weyl 不变标量–张量理论的方法，并用于 Lovelock、Einsteinian cubic 及 Einstein–AdS 引力。
We show that theories having second-order field equations in the context of higher-dimensional modified gravity are not restricted to the family of Lovelock Lagrangians, but can also be obtained if no a priori assumption on the relation between the metric and affine structures of space-time is made (Palatini approach). We illustrate this fact by considering the case of Palatini $f(R)$ gravities in five dimensions. Our results provide an alternative avenue to explore new domains of the AdS/CFT correspondence without resorting to {\it ad hoc} quasi-topological constructions.
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