The Einstein-Lovelock theory contains an infinite series of corrections to the Einstein term with an increasing power of the curvature. It is well-known that for large black holes the lowest (Gauss-Bonnet) term is the dominant one, while for smaller black holes higher curvature corrections become important. We will show that if one is limited by positive values of the coupling constants, then the dynamical instability of black holes serves as an effective cut-off of influence of higher curvature corrections in the 4D Einstein-Lovelock approach: the higher is the order of the Lovelock term, the smaller is the maximal value of the coupling constant allowing for stability, so that effectively only a first few orders can deform the observable values seemingly. For negative values of coupling constants this is not so, and, despite some suppression of higher order terms also occurs due to the decreasing threshold values of the coupling constant, this does not lead to an noticeable opportunity to neglect higher order corrections. In the case a lot of orders of Lovelock theory are taken into account, so that the black-hole solution depends on a great number of coupling constants, we propose a compact description of it in terms of only two or three parameters encoding all the observable values.
The regularization procedure for getting the four-dimensional nontrivial Einstein-Gauss-Bonnet effective description of gravity and its Lovelock generalization has been recently developed. Here we propose the regularization for the three-dimensional gravity, which is based on the rescaling of the coupling constants and, afterward, taking the limit $D \to 3$. We obtain the generalization of the Bañados-Teitelboim-Zanelli solution in the presence of the higher curvature (Gauss-Bonnet and Lovelock) corrections of any order. The obtained general solution shows a peculiar behavior: The event horizo…
An interpretation to the physics of stable geodesics of massive particles in black hole backgrounds has been recently proposed in the context of the AdS/CFT correspondence. It was argued that the existence of stable orbits indicates that the dual state does not thermalize on a thermal time scale and the bulk excitations can be interpreted as metastable states in the dual field theory. Here we study motion of massive particles in the background of the D-dimensional asymptotically anti-de Sitter (AdS) black holes in the Einstein-Lovelock theory. We show that, unlike the asymptotically flat case,…
In this work, we provide consistent compactifications of Einstein-Maxwell and Einstein-Maxwell-Lovelock theories on direct product spacetimes of the form $\mathcal{M}_D=\mathcal{M}_d\times\mathcal{K}^{p}$, where $\mathcal{K}^p$ is a Euclidean internal manifold of constant curvature. For these compactifications to take place, it is required the distribution of a precise flux of $p$-forms over the internal manifold. The dynamic of the $p$-forms are demanded to be controlled by two types of interaction. First, by specific couplings with the curvature tensor and, second, by a suitable interaction …
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…
A $(3+1)$-dimensional Einstein-Gauss-Bonnet theory of gravity has been recently formulated in [D. Glavan and C. Lin, Phys. Rev. Lett. {\bf 124}, 081301 (2020)] which is different from the pure Einstein theory, i.e., bypasses the Lovelock's theorem and avoids Ostrogradsky instability. The theory was formulated in $D > 4$ dimensions and its action consists of the Einstein-Hilbert term with a cosmological constant, while the Gauss-Bonnet term multiplied by a factor $1/(D-4)$. Then, the four-dimensional theory is defined as the limit $D \to 4$. Here we generalize this approach to the four-dimensio…
Here we have developed the general parametrization for spherically symmetric and asymptotically flat black-hole spacetimes in an arbitrary metric theory of gravity. The parametrization is similar in spirit to the parametrized post-Newtonian (PPN) approximation, but valid in the whole space outside the event horizon, including the near horizon region. This generalizes the continued-fraction expansion method in terms of a compact radial coordinate suggested by Rezzolla and Zhidenko [Phys.Rev.D 90 8, 084009 (2014)] for the four-dimensional case. As the first application of our higher-dimensional …
In this paper, we investigate the generalized covariant entropy bound in the theory where the Einstein gravity is perturbed by the higher-order Lovelock terms. After replacing the Bekenstein-Hawking entropy with the Jacobson-Myers entropy and introducing two reasonable physical assumptions, we showed that the corresponding generalized covariant entropy bound is satisfied under a higher-order approximation of the perturbation from the higher-order Lovelock terms. Our result implies that the Jacobson-Myers entropy strictly obeys the entropy bound under the perturbation level, and the generalized…
We 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…
Thermodynamic route to Field equations in Lanczos-Lovelock Gravity
具有视界的时空与热力学系统相似，人们可以将温度和熵的概念与它们联系起来。在爱因斯坦-希尔伯特引力的情况下，可以将爱因斯坦方程解释为球对称时空的热力学恒等式TdS = dE + PdV，从而提供了理解引力动力学的热力学途径。我们进一步研究了这种方法，并表明，在球对称时空中的Lanczos-Lovelock作用的场方程也可以表示为TdS = dE + PdV与S和E是由以前在文献中导出的表达式由其他方法。Lanczos-Lovelock拉格朗日量的形式为L=Q_a^{bcd}R^ a_{bcd}，其中\nabla_b Q^{abcd}=0。在这样的模型中，Q^{abcd}在度规张量的导数方面的展开决定了理论的结构，高阶项可以解释为对爱因斯坦引力的量子修正。我们的结果表明视界热力学与标准爱因斯坦引力的量子修正之间有着深刻的联系，并表明TdS = dE + PdV关系比爱因斯坦场方程具有更大的有效域.
It is well known that the Reissner-Norstrom solution of Einstein-Maxwell theory cannot be cylindrically extended to higher dimension, as with the black hole solutions in vacuum. In this paper we show that this result is circumvented in Lovelock gravity. We prove that the theory containing only the quadratic Lovelock term, the Gauss-Bonnet term, minimally coupled to a $U(1)$ field, admits homogeneous black string and black brane solutions characterized by the mass, charge and volume of the flat directions. We also show that theories containing a single Lovelock term of order $n$ in the Lagrangi…
This work is mainly devoted to constructing a multisymplectic description of Lovelock's gravity, which is an extension of General Relativity. We establish a Griffiths variational problem for the Lovelock Lagrangian, obtaining the geometric form of the corresponding field equations. We give the unified Lagrangian--Hamiltonian formulation of this model and we study the correspondence between the unified formulations for the Einstein--Hilbert and the Einstein--Palatini models of gravity.
本文介绍了三阶Lovelock引力的$n$维Lorentz虫洞解。与爱因斯坦引力和高斯-邦尼引力的情况相反，我们发现虫洞的喉道半径$r_0$有一个下限，它取决于Lovelock系数、时空的维数和形函数。研究了喉道附近存在正常物质的条件，发现喉道附近的物质可以在$r_0 \leq r \leq r_{\max}$区域内是正常物质，其中$r_{\max}$依赖于Lovelock系数和形状函数.我们还发现负耦合常数的三阶Lovelock项扩大了正常物质区的半径，而负耦合常数的高阶Lovelock项扩大了正常物质区的半径。
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 …
Brown-York quasilocal energy in Lanczos-Lovelock gravity and black hole horizons
在广义相对论中，准定域能量的标准候选者是布朗-约克能量，它本质上是一个二维的表面积分，其外在曲率位于平坦时空的类空超曲面的两个边界上。几年前，我们中的一个人已经证明，黑洞视界是由引力能和非引力能均分来定义的。利用准定域Brown-York能的上述定义，我们验证了广义相对论中关于静态带电和带电轴对称黑洞的均分猜想。我们进一步将Brown-York形式推广到Lanczos-Lovelock引力理论的所有阶，并验证了d= 2 m +2维纯Lovelock荷电黑洞的猜想，其中m是Lovelock作用量的阶数.事实证明，均分猜想只适用于纯洛夫洛克，而不适用于爱因斯坦-洛夫洛克，黑洞。
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…
We derive the conformal constraints satisfied by classical vertices of a (Einstein) Gauss-Bonnet theory around flat space, in general dimensions and at $d=4$ (4d EGB). In $4d$ EGB they are obtained by a singular limit of the integral of the Euler-Poincarè density. Our analysis exploits the relation between this theory and the conformal anomaly action, which allows to uncover some interesting features of the GB vertex at cubic and quartic level. If we introduce a conformal decomposition of the metric, the resulting theory can be formulated in two different versions, which are regularization dep…
We examine the thermodynamics of a new class of asymptotically AdS black holes with non-constant curvature event horizons in Gauss-Bonnet Lovelock gravity, with the cosmological constant acting as thermodynamic pressure. We find that non-trivial curvature on the horizon can significantly affect their thermodynamic behaviour. We observe novel triple points in 6 dimensions between large and small uncharged black holes and thermal AdS. For charged black holes we find a continuous set of triple points whose range depends on the parameters in the horizon geometry. We also find new generalizations o…
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 construct a plethora of new Euclidean AdS-Taub-NUT and bolt solutions of several four- and six-dimensional higher-curvature theories of gravity with various base spaces $\mathcal{B}$. In $D=4$, we consider Einsteinian cubic gravity, for which we construct solutions with $\mathcal{B}=\mathbb{S}^2,\mathbb{T}^2$. These represent the first generalizations of the Einstein gravity Taub-NUT/bolt solutions for any higher-curvature theory in four dimensions. In $D=6$, we show that no new solutions are allowed for any Generalized quasi-topological gravity at cubic order. They exist however when we co…
