Hadi Godazgar, Mahdi Godazgar, C. N. Pope
We consider the consequences of the dual gravitational charges for the phase space of radiating modes, and find that they imply a new soft NUT theorem. In particular, we argue that the existence of these new charges removes the need for imposing boundary conditions at spacelike infinity that would otherwise preclude the existence of NUT charges.
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For non-abelian non-supersymmetric gauge theories, generic dual theories have been constructed. In these theories the couplings appear inverted. However, they do not possess a Yang-Mills structure but rather are a kind of non-linear sigma model. It is shown that for a topological gravitational model an analog to this duality exists.
Gravitational S-duality is defined by the contraction of two indices of the Riemann tensor with the epsilon tensor. We review its realization in linearized gravity, and study its generalization to full non-linear gravity by means of explicit examples: Up to a rescaling of the coordinates, it relates two Taub-NUT-Schwarzschild metrics by interchanging m with l, provided both parameters are non-zero. In the presence of a cosmological constant gravitational S-duality can be implemented at the expense of the introduction of a three-form field whose value turns out to be dual to the cosmological co…
Soft zero for cylindrical gravitational waves
本文证明柱面引力波 S 矩阵存在由渐近无穷远处 Geroch 对称性的 Ward 恒等式导致的软零点，而非普通引力子的软极点，因此不产生记忆效应。
Strong-weak duality invariance can only be defined for particular sectors of supersymmetric Yang-Mills theories. Nevertheless, for full non-Abelian non-supersymmetric theories, dual theories with inverted couplings, have been found. We show that an analogous procedure allows to find the dual action to the gauge theory of gravity constructed by the MacDowell-Mansouri model plus the superposition of a $Θ$ term.
We study how the supersymmetry algebra copes with gravitational duality. As a playground, we consider a charged Taub-NUT solution of D=4, N=2 supergravity. We find explicitly its Killing spinors, and the projection they obey provides evidence that the dual magnetic momenta necessarily have to appear in the supersymmetry algebra. The existence of such a modification is further supported using an approach based on the Nester form. In the process, we find new expressions for the dual magnetic momenta, including the NUT charge. The same expressions are then rederived using gravitational duality.
We show that there are a further infinite number of, previously unknown, supertranslation charges. These can be viewed as duals of the known BMS charges corresponding to supertranslations. In Newman-Penrose language, these new supertranslation charges roughly correspond to the imaginary part of the leading term in $ψ_2$. We find these charges by dualising the Barnich-Brandt asymptotic charges and argue that this prescription gives rise to new bona fide charges at null infinity.
Spacetime vacuum as a correlated quantum channel, dual to gravitational memory
本文论证任何规范理论的时空真空可作为关联量子信道且与引力记忆对偶，指出该对偶性有助于解决黑洞信息悖论。
We study how gravitational duality acts on rotating solutions, using the Kerr-NUT black hole as an example. After properly reconsidering how to take into account both electric (i.e. mass-like) and magnetic (i.e. NUT-like) sources in the equations of general relativity, we propose a set of definitions for the dual Lorentz charges. We then show that the Kerr-NUT solution has non-trivial such charges. Further, we clarify in which respect Kerr's source can be seen as a mass M with a dipole of NUT charges.
We provide a Hamiltonian derivation of recently discovered dual BMS charges. In order to do so, we work in the first order formalism and add to the usual Palatini action, the Holst term, which does not contribute to the equations of motion. We give a method for finding the leading order integrable dual charges à la Wald-Zoupas and construct the corresponding charge algebra. We argue that in the presence of fermions, the relevant term that leads to dual charges is the topological Nieh-Yan term.
Log translation invariance of log soft gravitational radiation
该研究针对经典散射引力辐射软频率展开的普适对数项，证明其可显式体现对数平移作用，解释了出射无质量粒子贡献的抵消现象，并导出高阶普适对数软项的递推关系。
We study S-duality transformations that mix the Riemann tensor with the field strength of a 3-form field. The dual of an (A)dS space time - with arbitrary curvature - is seen to be flat Minkowski space time, if the 3-form field has vanishing field strength before the duality transformation. It is discussed whether matter could couple to the dual metric, related to the Riemann tensor after a duality transformation. This possibility is supported by the facts that the Schwarzschild metric can be obtained as a suitable contraction of the dual of a Taub-NUT-AdS metric, and that metrics describing F…
Dual gravitational charges have been recently computed from the Holst term in tetrad variables using covariant phase space methods. We highlight that they originate from an exact 3-form in the tetrad symplectic potential that has no analogue in metric variables. Hence there exists a choice of the tetrad symplectic potential that sets the dual charges to zero. This observation relies on the ambiguity of the covariant phase space methods. To shed more light on the dual contributions, we use the Kosmann variation to compute (quasi-local) Hamiltonian charges for arbitrary diffeomorphisms. We obtai…
Gravitational memory and soft theorems: The local perspective
本文从局域同步坐标视角建立引力记忆与 BMS 变换、残余微分同胚及软定理的联系，并导出等时关联函数的新软定理。
$\mathrm{ISIM}(2)$ gravitational gauge model via Soft Algebra formalism
通过软代数形式规范ISIM(2)洛伦兹子群，构建无挠引力模型并导出不变作用量。
We study the duality of quasilocal energy and charges with non-orthogonal boundaries in the (2+1)-dimensional low-energy string theory. Quasilocal quantities shown in the previous work and some new variables arisen from considering the non-orthogonal boundaries as well are presented, and the boost relations between those quantities are discussed. Moreover, we show that the dual properties of quasilocal variables such as quasilocal energy density, momentum densities, surface stress densities, dilaton pressure densities, and Neuve-Schwarz(NS) charge density, are still valid in the moving observe…
The main focus of this work is to study magnetic soft charges of the four dimensional Maxwell theory. Imposing appropriate asymptotic falloff conditions, we compute the electric and magnetic soft charges and their algebra both at spatial and at null infinity. While the commutator of two electric or two magnetic soft charges vanish, the electric and magnetic soft charges satisfy a complex $U(1)$ current algebra. This current algebra through Sugawara construction yields two $U(1)$ Kac-Moody algebras. We repeat the charge analysis in the electric-magnetic duality-symmetric Maxwell theory and cons…
The thermal duality of E(8) x E(8) and SO(32) heterotic string theories may underpin a mechanism that would convert the kinetic energy of infalling matter during gravitational collapse to form a region of a hot string phase that would expel gravitational gradients. This phase would be the continuation of a Ginzburg-Landau like superconductor in the Euclidean regime. In this scenario, there would be no event horizon or singularity produced in gravitational collapse. Solutions are presented for excitations of the string vacuum that may form during gravitational collapse and drive the transition …
Plane Gravitational Waves in String Theory
本文分析了陪集模型$(E_2^c \ti E_2^c)/E_2^c$，构造了一类描述平面引力波及其传播的精确弦真空，推广了Nappi和Witten的平面波背景。特别是，矢量规范描述了一个双参数族的奇异几何与两个等距，这是对偶的平面引力波。此外，还有一个混合矢量轴向测量，它描述了一个单参数家庭的平面波与五个等距。这两个背景相关的对偶变换，推广了已知的轴向量对偶交换子群。
We provide an exhaustive classification of self-dual four-dimensional gravitational instantons foliated with three-dimensional homogeneous spaces, i.e. homogeneous self-dual metrics on four-dimensional Euclidean spaces admitting a Bianchi simply transitive isometry group. The classification pattern is based on the algebra homomorphisms relating the Bianchi group and the duality group SO(3). New and general solutions are found for Bianchi III.
The transit of a gravitating radiation pulse past arrays of detectors stationed near future null infinity in the vacuum is considered. It is shown that the relative positions and clock times of the detectors before and after the radiation transit differ by a BMS supertranslation. An explicit expression for the supertranslation in terms of moments of the radiation energy flux is given. The relative spatial displacement found for a pair of nearby detectors reproduces the well-known and potentially measurable gravitational memory effect. The displacement memory formula is shown to be equivalent t…
Brans-Dicke theory contains an additional propagating mode which causes homogeneous expansion and contraction of test bodies in transverse directions. This "breathing" mode is associated with novel memory effects in addition to those of general relativity. Standard tensor mode memories are related to a symmetry principle: they are determined by the balance equations corresponding to the BMS symmetries. In this paper, we show that the leading and subleading breathing memory effects are determined by the balance equations associated with the leading and "overleading" asymptotic symmetries of a d…
Axial gravitational quasinormal modes of a self-dual black hole in loop quantum gravity
本文研究了圈量子引力中自对偶黑洞的轴向引力准正规模式，通过求解类薛定谔方程计算准正规频率，发现量子修正参数$P$正向影响频率实虚部绝对值，并验证了eikonal极限下圆类光测地线参数与频率的关系。
Classical soft photon and soft graviton theorems determine long wavelength electromagnetic and gravitational waveforms for a general classical scattering process in terms of the electric charges and asymptotic momenta of the ingoing and outgoing macroscopic objects. Performing Fourier transformation of the electromagnetic and gravitational waveforms in the frequency variable one finds electromagnetic and gravitational waveforms at late and early retarded time. Here extending the formalism developed in \cite{1912.06413}, we derive sub-subleading electromagnetic and gravitational waveforms which…
We consider and derive the gravitational soft theorem up to the sub-subleading power from the perspective of effective Lagrangians. The emergent soft gauge symmetries of the effective Lagrangian provide a transparent explanation of why soft graviton emission is universal to sub-subleading power, but gauge boson emission is not. They also suggest a physical interpretation of the form of the soft factors in terms of the charges related to the soft transformations and the kinematics of the multipole expansion. The derivation is done directly at Lagrangian level, resulting in an operatorial form o…
We derive the leading spin-dependent gravitational tail memory, which appears at the second post-Minkowskian (2 PM) order and behaves as $u^{-2}$ for large retarded time $u$. This result follows from classical soft graviton theorem at order $ω\lnω$ as a low-frequency expansion of gravitational waveform with frequency $ω$. First, we conjecture the result from the classical limit of quantum soft graviton theorem up to sub-subleading order in soft expansion and then we derive it for a classical scattering process without any reference to the soft graviton theorem. The final result of the gravitat…
The gravitational dual to the grand canonical ensemble of a large $N$ holographic theory is a charged black hole. These spacetimes -- for example Reissner-Nordström-AdS -- can have Cauchy horizons that render the classical gravitational dynamics of the black hole interior incomplete. We show that a (spatially uniform) deformation of the CFT by a neutral scalar operator generically leads to a black hole with no inner horizon. There is instead a spacelike Kasner singularity in the interior. For relevant deformations, Cauchy horizons never form. For certain irrelevant deformations, Cauchy horizon…
The fluid/gravity correspondence establishes how gravitational dynamics, as dictated by Einstein's field equations, are related to the fluid dynamics, governed by the relativistic Navier-Stokes equations. In this work the correspondence is extended, where the duality between incompressible fluids and gravitational backgrounds with soft hair excitations is implemented. This construction is set through appropriate boundary conditions to the gravitational background, leading to a correspondence between generalized incompressible Navier-Stokes equations and soft hairy horizons.
We study self-duality in the context of the 3+1-split formalism of gravity with non-zero cosmological constant. Lorentzian self-dual configurations are conformally flat spacetimes and have boundary data determined by classical solutions of the three-dimensional gravitational Chern-Simons. For Euclidean self-dual configurations, the relationship between their boundary initial positions and initial velocity is also determined by the three-dimensional gravitational Chern-Simons. Our results imply that bulk self-dual configurations are holographically described by the gravitational Chern-Simons th…
The question of graviton cloning in the context of the bulk/boundary correspondence is considered. It is shown that multi-graviton theories can be obtained from products of large-N CFTs. No more than one interacting massless graviton is possible. There can be however, many interacting massive gravitons. This is achieved by coupling CFTs via multi-trace marginal or relevant perturbations. The geometrical structure of the gravitational duals of such theories is that of product manifolds with their boundaries identified. The calculational formalism is described and the interpretation of such theo…
Hydrodynamical duals of the gravitational axial anomaly and the cosmological constant
本文在弯曲时空中构造旋转加速介质的流体力学展开，建立宇宙学常数与加速度相关流的对偶，并将引力轴反常的推导推广到外尔张量与里奇张量非零的更一般情形。
In this thesis we study several problems in the context of AdS/CFT. The first is that of gravitational phase transitions between AdS and dS geometries in the Gauss-Bonnet theory of gravity. Such transitions are mediated by thermalons and do not require matter fields. The phenomenon is strongly expected to be generic in higher curvatures theories of gravity. The second problem is the generation of new Supergravity backgrounds and the study of their holographic duals. We generate new examples of supersymmetric flows from $AdS_5$ in the UV to $AdS_3$ in the IR. The new solutions are found to be h…
Classical soft theorems meet the post-Newtonian expansion
该工作在后牛顿框架下研究致密双星引力波形的软结构，分离红外对数并建立引力记忆效应与Sahoo-Sen软定理的直接对应，同时探讨紫外对数及其重整化群跑动。
This thesis deals with the construction of conserved charges for asymptotically flat spacetimes at spatial infinity in four spacetime dimensions in a hopefully pedagogical way. As a first motivation of this work, it highlights the difficulties one encounters when trying to understand the gravitational duality, present at the linearized level, in the full non-linear Einstein's theory or even just in an asymptotic regime of it. In the first part, we restrict the discussion to the Noetherian surface charges, called "electric charges", and study the existence of a larger phase space, than previous…
We study the black hole - black string phase transitions of gravitational theories compactified on a circle using the holographic duality conjecture. The gauge theory duals of these theories are maximally supersymmetric and strongly coupled 1 + 1 dimensional SU(N) Yang-Mills theories compactified on a circle, in the large $N$ limit. We perform the strongly coupled finite temperature gauge theory calculations on a lattice, using the recently developed exact lattice supersymmetry methods based on topological twisting and orbifolding. The spatial Polyakov line serves as relevant order parameter o…
We investigate four-dimensional, self-dual gravitational instantons endowed with a product structure RxM_3, where M_3 is homogeneous of Bianchi type. We analyze the general conditions under which Euclidean-time evolution in the gravitational instanton can be identified with a geometric flow of a metric on M_3. This includes both unimodular and non-unimodular groups, and the corresponding geometric flow is a general Ricci plus Yang-Mills flow accompanied by a diffeomorphism.
We study a system of N D3-branes in which open string tachyons survive in the low energy alpha' -> 0 limit. We compute the height of the tachyon potential both in the weak and strong couplings by using N=4 super Yang-Mills and the dual AdS_5 descriptions respectively. We find an exact agreement between the two descriptions in the large N limit. This provides an example of gravitational duals of open string tachyon condensation.
In de Sitter space, the gravitational fluctuation at the super-horizon scale may make physical quantities time dependent by breaking the de Sitter symmetry. We adopt the Kadanoff-Baym approach to evaluate soft gravitational effects in a matter system at the sub-horizon scale. This investigation proves that only the local terms contribute to the de Sitter symmetry breaking at the one-loop level. The IR singularities in the non-local terms cancel after summing over degenerate states between real and virtual processes. The corresponding IR cut-off is given by the energy resolution like QED. Since…
Exact Solutions for Self--Dual Yang--Mills and Self--Dual Tensor Multiplets on Gravitational Instanton Background
本文给出了最近发展的$~(2+2)\-$维~ $N=1$ ~局部超对称自对偶规范理论的精确解。本文给出了引力瞬子背景下$~SL(2)$ ~自对偶Yang-Mills多重态和Eguchi-Hanson的“自对偶张量多重态”的精确解.我们用一般的方法从已知的自对偶引力解得到一个$~SL(2)$ ~自对偶Yang-Mills解。我们的结果是第一个在~ $(2+2)\-$维中得到$~N=1$ ~局部超对称自对偶多重态耦合系统精确解的例子，这对于适当降维或截断的低维可积模型具有重要意义.我们还检查了我们的精确解的一致性作为背景的$~N=2$ ~超弦耦合到Wess-Zumino-Witten项在$~\s\-$模型制定。
We derive a manifestly duality-invariant formulation of the action principle for linearized gravity on anti de Sitter background. The analysis is based on the two-potential formalism, obtained upon resolution of the constraints in the Hamiltonian formulation. We discuss the relevance of our result in the context of holography.
We apply the recently developed formalism by Kosower, Maybee and O'Connell (KMO) to analyse the soft electromagnetic and soft gravitational radiation emitted by particles without spin in Four and higher dimensions. We use this formalism in conjunction with quantum soft theorems to derive radiative electro-magnetic and gravitational fields in low frequency expansion and to next to leading order in the coupling. We show that in all dimensions, the classical limit of sub-leading soft (photon and graviton) theorems is consistent with the classical soft theorems proved by Sen et al in a series of p…
The "gravitational memory effect" due to an exact plane wave provides us with an elementary description of the diffeomorphisms associated with soft gravitons. It is explained how the presence of the latter may be detected by observing the motion of freely falling particles or other forms of gravitational wave detection. Numerical calculations confirm the relevance of the first, second and third time integrals of the Riemann tensor pointed out earlier. Solutions for various profiles are constructed. It is also shown how to extend our treatment to Einstein-Maxwell plane waves and a midi-superspa…
We derive the asymptotic symmetries of the manifestly duality invariant formulation of electromagnetism in Minkoswki space. We show that the action is invariant under two algebras of angle-dependent $u(1)$ transformations, one electric and the other magnetic. As in the standard electric formulation, Lorentz invariance requires the addition of additional boundary degrees of freedom at infinity, found here to be of both electric and magnetic types. A notable feature of this duality symmetric formulation, which we comment upon, is that the on-shell values of the zero modes of the gauge generators…
Using soft-graviton theorems a well-known zero-frequency limit (ZFL) for the gravitational radiation flux $dE^{GW}/d ω$ is re-derived and extended to order ${\cal O}(ω)$ and ${\cal O}(ω^2)$ for arbitrary massless multi-particle collisions. The (angle-integrated, unpolarized) ${\cal O}(ω)$ correction to the flux turns out to be absent in the case of two-particle elastic collisions. The ${\cal O}(ω^2)$ correction is instead non-vanishing and takes a simple general expression which is then applied to bremsstrahlung from two-particle elastic collisions. For a tree-level process the outcome is fini…
The action for the su(N) SDYM equations is shown to give in the limit $N \to \infty$ the action for the six-dimensional version of the second heavenly equation. The symmetry reductions of this latter equation to the well known equations of self-dual gravity are given. The Moyal deformation of the heavenly equations are also considered.
In this work, we have calculated the polar gravitational quasinormal modes for a quantum corrected black hole model, that arises in the context of Loop Quantum Gravity, known as Self-Dual Black Hole. In this way, we have calculated the characteristic frequencies using the WKB approach, where we can verify a strong dependence with the Loop Quantum Gravity parameters. At the same time we check that the Self-Dual Black Hole is stable under polar gravitational perturbations, we can also verify that the spectrum of the polar quasinormal modes differs from the axial one \cite{Cruz:2015bcj}. Such a r…
We study gravitational lensing by a recently proposed black hole solution in Loop Quantum Gravity. We highlight the fact that the quantum gravity corrections to the Schwarzschild metric in this model evade the `mass suppression' effects (that the usual quantum gravity corrections are susceptible to) by virtue of one of the parameters in the model being dimensionless, which is unlike any other quantum gravity motivated parameter. Gravitational lensing in the strong and weak deflection regimes is studied and a sample consistency relation is presented which could serve as a test of this model. We…
In gauge theories and gravity, field variables are generally not gauge-invariant observables, but such observables may be constructed by "dressing" these or more general operators. Dressed operators create particles, together with their gauge or gravitational fields which typically extend to infinity. This raises an important question of how well quantum information can be localized; one version of this is the question of whether soft charges fully characterize a given localized charge or matter distribution. This paper finds expressions for the non-trivial soft charges of such dressed operato…
Gravitational decoherence from soft-graviton $S$-matrix
本文利用软引力子S矩阵推导规范不变的退相干指数，证明真空退相干消失，并分析压缩态及遗迹背景下的增强效应，连接红外量子信息与引力退相干。
By virtue of their sub-hour orbital periods, ultra-compact X-ray binaries are promising sources for the space-borne gravitational-wave interferometers LISA, Taiji, and TianQin. Some of these systems contain a neutron star primary, whose spin period can be measured directly via pulse timing, or indirectly through rotational modulations of burst phenomena. It is pointed out here that since actively accreting stars, with spin frequencies in the hundreds of Hz, may continuously emit appreciable gravitational waves due to the presence of accretion-built mountains, toroidal magnetic fields, and/or $…
The construction of dual theories for linearized gravity in four dimensions is considered. Our approach is based on the parent Lagrangian method previously developed for the massive spin-two case, but now considered for the zero mass case. This leads to a dual theory described in terms of a rank two symmetric tensor, analogous to the usual gravitational field, and an auxiliary antisymmetric field. This theory has an enlarged gauge symmetry, but with an adequate partial gauge fixing it can be reduced to a gauge symmetry similar to the standard one of linearized gravitation. We present examples …
Applying the recently obtained results on the renormalization of soft supersymmetry-breaking parameters, we investigate the infrared behaviour of the softly broken supersymmetric QCD as well as its dual theory in the conformal window. Under general assumptions on $β$-functions, it is shown that the soft supersymmetry-breaking parameters asymptotically vanish in the infrared limit so that superconformal symmetry in softly broken supersymmetric QCD and in its dual theory revives at the infrared fixed point, provided the soft scalar masses satisfy certain renormalization group invariant relations…
On toric self-dual Einstein gravitational instantons
研究具有负宇宙常数的环面自对偶爱因斯坦引力瞬子的分类，证明若与环面基灵场相关的共形凯勒结构全局且扩展到无额外不动点的ALE流形，则瞬子由Calderbank-Pedersen-Singer构造的多极解给出。
We discuss four-dimensional "spatially homogeneous" gravitational instantons. These are self-dual solutions of Euclidean vacuum Einstein's equations with potentially non-vanishing cosmological constant. They are endowed with a product structure R \times M_3 leading to a natural foliation into three-dimensional subspaces evolving in Euclidean time. For a large class of three-dimensional subspaces, the dynamics coincides with the geometric flow on the three-dimensional homogeneous slice, driven by the Ricci tensor plus an so(3) gauge connection. The metric on the three-dimensional space is relat…
Gravitational Wave Tails from Soft Theorem: A Short Review
本文短评基于经典软引力子定理，阐述碰撞碎片过程引力波波形在早晚期时间的幂律衰减及对数修正，仅依赖入射和出射动量，并简述推导。
Using a five-dimensional warped model including a scalar potential with an exponential behavior in the infrared, and strong back-reaction over the metric, we study the electroweak phase transition, and explore parameter regions that were previously inaccessible. The model exhibits gravitational waves and predicts a stochastic gravitational wave background observable, both at the Laser Interferometer Space Antenna and at the Einstein Telescope. Moreover, concerning the collider signatures predictions, the radion evades current constraints but may show up in future LHC runs.
The gravitational shock waves have provided crucial insights into entanglement structures of black holes in the AdS/CFT correspondence. Recent progress on the soft hair physics suggests that these developments from holography may also be applicable to geometries beyond negatively curved spacetime. In this work, we derive a remarkably simple thermodynamic relation which relates the gravitational shock wave to a microscopic area deformation. Our treatment is based on the covariant phase space formalism and is applicable to any Killing horizon in generic static spacetime which is governed by arbi…
In this paper we examine a certain threebrane solution of type IIB string theory whose long-wavelength dynamics are those of a supersymmetric gauge theory in 2+1 continuous and 1 discrete dimension, all of infinite extent. Low-energy processes in this background are controlled by dimensional deconstruction, a strict limit in which gravity decouples but the lattice spacing stays finite. Relating this limit to the near-horizon limit of our solution we obtain an exact, continuum gravitational dual of a lattice gauge theory with nonzero lattice spacing. H-flux in the translationally invariant solu…
Gravitational instantons ''Lambda-instantons'' are defined here for any given value Lambda of the cosmological constant. A multiple of the Euler characteristic appears as an upper bound for the de Sitter action and as a lower bound for a family of quadratic actions. The de Sitter action itself is found to be equivalent to a simple and natural quadratic action. In this paper we also describe explicitly the reparameterization and duality invariances of gravity (in 4 dimensions) linearized about de Sitter space. A noncovariant doubling of the fields using the Hamiltonian formalism leads to first …
Following the membrane paradigm, we explore the effect of the gravitational $Θ$-term on the behavior of the stretched horizon of a black hole in (3+1)-dimensions. We reformulate the membrane paradigm from a quantum path-integral point of view where we interpret the macroscopic properties of the horizon as effects of integrating out the region inside the horizon. The gravitational $Θ$-term is a total derivative, however, using our framework we show that this term affects the transport properties of the horizon. In particular, the horizon acquires a third order parity violating, dimensionless tr…
The particular model of d5 higher derivative gravity which is dual to ${\cal N}=2$ $Sp(N)$ SCFT is considered. A (perturbative) AdS black hole in such theory is constructed in the next-to-leading order of the AdS/CFT correspondence. The surface counterterms are fixed by the conditions required for a well-defined variational procedure and the finiteness of AdS space (when the brane goes to infinity). A dynamical brane is realized at the boundary of an AdS black hole with a radius that is larger than the horizon radius. The AdS/CFT correspondence dictates the parameters of the gravitational dual…
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