Three dimensional spacelike warped anti-de Sitter space is studied in the context of Einstein theories of gravity and string theory, where there is no gravitational Chern-Simons term in the action. We propose that it is holographically dual to a two-dimensional conformal field theory with equal left and right moving central charges. Various checks of the central charges are offered, based on the Bekenstein-Hawking entropy of the stretched warped black holes and warped self-dual solutions. The proposed central charges are applied to compute the Bekenstein-Hawking entropy of the Hopf T-dual of six-dimensional dyonic black strings which have a near horizon consisting of three dimensional warped anti-de Sitter space times a three-sphere. We find that the Hopf T-duality is a map between thermal states with equal entropy of the CFTs dual to the dyonic black string and the Hopf T-dualized black string.
Three-dimensional warped anti-de Sitter space in topologically massive gravity with a negative cosmological constant has been proposed to be holographically dual to a two-dimensional conformal field theory. We extend this proposal to both positive and vanishing values of the cosmological constant where stretched warped anti-de Sitter space is found to be a solution. For positive cosmological constant, another class of warped solutions is obtained by a spacelike (timelike) line fibration over Lorentzian (Euclidean) two-dimensional de Sitter space. These solutions exhibit a cosmological horizon …
We comment on the ubiquity of the so-called warped anti-de Sitter spacetimes in three-dimensional (2,0) supergravity theory. By using isometry-invariant tensors and simple counting, we prove their existence for arbitrary $(2,0)$ supergravity models suitably defined close to a minimal model. We also analyze their offshell supersymmetry and the supersymmetry of two geometric orbifolds.
We consider explicit type II string constructions of backgrounds containing warped and squashed anti de Sitter spaces. These are obtained via T duality from brane intersections including dyonic black strings, plane waves and monopoles. We also study the supersymmetry of these solutions and discuss special values of the deformation parameters.
The solutions of 10 and 11 dimensional supergravity that are warped products of de Sitter space with a non-compact `internal' space are investigated. A convenient form of the metric is found and it is shown that in each case the internal space is asymptotic to a cone over a product of spheres. A consistent truncation gives gauged supergravities with non-compact gauge groups. The BPS domain wall solutions of the non-compact gauged supergravities are lifted to warped solutions in 10 or 11 dimensions.
We investigate the stability of a new warped black string with nontrivial topologies in five-dimensional Anti-de Sitter spacetime. After studying the linear gravitational perturbation, we find that this black string is unstable when the Kaluza-Klein mass falls in a certain range and the instability exists for all topological spacetimes.
Besides black holes, the phase space of three-dimensional massive gravity about Warped-Anti de Sitter (WAdS) space contains solutions that decay exponentially in time. They describe evanescent graviton configurations that, while governed by a wave equation with non-vanishing effective mass, do not carry net gravitational energy. Explicit examples of such solutions have been found in the case of Topologically Massive Gravity; here, we generalize them to a much more general ghost-free massive deformation, with the difference being that the decay rate gets corrected due to the presence of higher-…
We classify all warped product de-Sitter backgrounds in heterotic supergravity, up to two loops. We find that warped $dS_n$ backgrounds, with $n\ge 3$, are $\mathbb{R}^{1,n}\times M_{9-n}$, where $M_{9-n}$ is a $(9-n)$-dimensional Riemannian manifold. Moreover, we establish that warped $dS_2$ backgrounds are $AdS_3\times M_7$, where $M_7$ is a 7-dimensional Riemannian manifold.
In this paper we show that warped AdS$_{3}$ black hole spacetime is a solution of the generalized minimal massive gravity (GMMG) and introduce suitable boundary conditions for asymptotically warped AdS$_{3}$ spacetimes. Then we find the Killing vector fields such that transformations generated by them preserve the considered boundary conditions. We calculate the conserved charges which correspond to the obtained Killing vector fields and show that the algebra of the asymptotic conserved charges is given as the semi direct product of the Virasoro algebra with $U(1)$ current algebra. We use a pa…
We test the robustness of the conditions required for the existence of (supersymmetric) warped flux anti-de Sitter, de Sitter, and Minkowski backgrounds in supergravity theories using as examples suitable foliations of anti-de Sitter spaces. We find that there are supersymmetric de Sitter solutions in supergravity theories including maximally supersymmetric ones in 10- and 11-dimensional supergravities. Moreover, warped flux Minkowski backgrounds can admit Killing spinors which are not Killing on the Minkowski subspace and therefore cannot be put in a factorized form.
We show that the warped de Sitter compactifications are possible under certain conditions in D-dimensional gravitational theory coupled to a dilaton, a form field strength, and a cosmological constant. We find that the solutions of field equations give de Sitter spacetime with the warped structure, and discuss cosmological models directly obtained from these solutions. We also construct a cosmological model in the lower-dimensional effective theory. If there is a field strength having non-vanishing components along the internal space, the moduli can be fixed at the minimum of the effective pot…
We present new solutions of warped compactifications in the higher-dimensional gravity coupled to the scalar and the form field strengths. These solutions are constructed in the D-dimensional spacetime with matter fields, with the internal space that has a finite volume. Our solutions give explicit examples where the cosmological constant or 0-form field strength leads to a de Sitter spacetime in arbitrary dimensions.
We discuss the integrability of 2d non-linear sigma models with target space being the squashed three-sphere, warped anti-de Sitter space and the Schroedinger spacetime. These models can be obtained via T-duality from integrable models. We construct an infinite family of non-local conserved charges from the T-dual Lax currents, enhancing the symmetry of warped anti-de Sitter space and the Schroedinger spacetime to sl2(R)+sl2(R).
For spacetimes that are not asymptotic to anti-de Sitter Space (non AAdS), we adapt the Lewkowycz-Maldacena procedure to find the holographic entanglement entropy. The key observation, which to our knowledge is not very well appreciated, is that asymptotic boundary conditions play an essential role on extending the replica trick to the bulk. For non AAdS, we expect the following three main modifications: (1) the expansion near the special surface has to be compatible with the asymptotic expansion; (2) periodic conditions are imposed to coordinates on the phase space with diagonalized symplecti…
We give a direct computation of the mass of black holes in Warped Anti-de Sitter space (WAdS) in terms of the Brown-York stress-tensor at the boundary. This permits to explore to what extent the holographic renormalization techniques can be applied to such type of deformation of AdS. We show that, despite some components of the boundary stress-tensor diverge and resist to be regularized by the introduction of local counterterms, the precise combination that gives the quasilocal energy density yields a finite integral. The result turns out to be in agreement with previous computations of the bl…
We discuss the spectrum of the tensor metric perturbations and the stability of warped compactifications with the de Sitter spacetime in the higher-dimensional gravity. The spacetime structure is given in terms of the warped product of the non-compact direction, the spherical internal dimensions and the four-dimensional de Sitter spacetime. To realize a finite bulk volume, we construct the brane world model, using the cut-copy-paste method. Then, we compactify the spherical directions on the brane. In any case, we show the existence of the massless zero mode and the mass gap of it with massive…
We present a simple class of warped-product vacuum (Ricci-flat) solutions to ten and eleven-dimensional supergravity, where the internal space is flat and the warp factor supports de Sitter (dS) and anti-de Sitter (AdS) vacua in addition to trivial Minkowski vacua. We outline the construction of consistent Kaluza-Klein (KK) reductions and show that, although our vacuum solutions are non-supersymmetric, these are closely related to the bosonic part of well-known maximally supersymmetric reductions on spheres. We comment on the stability of our solutions, noting that (A)dS$_3$ vacua pass routine…
We investigate the thermodynamics and stability of the horizons in warped anti-de Sitter black holes of the new massive gravity under the scattering of a massive scalar field. Under scattering, conserved quantities can be transferred from the scalar field to the black hole, which change the state of the black hole. We determine that the changes in the black hole are well coincident with the laws of thermodynamics. In particular, the Hawking temperature of the black hole cannot be zero in the process as per the third law of thermodynamics. Furthermore, the black hole cannot be overspun beyond t…
We propose the use of D-brane realizations of Dynamical Supersymmetry Breaking (DSB) gauge sectors as sources of uplift in compactifications with moduli stabilization onto de Sitter vacua. This construction is fairly different from the introduction of anti D-branes, yet allows for tunably small contributions to the vacuum energy via their embedding into warped throats. The idea is explicitly exemplified by the embedding of the 1-family $SU(5)$ DSB model in a local warped throat with fluxes, which we discuss in detail in terms of orientifolds of dimer diagrams.
Asymptotically warped AdS spacetimes in topologically massive gravity with negative cosmological constant are considered in the case of spacelike stretched warping, where black holes have been shown to exist. We provide a set of asymptotic conditions that accommodate solutions in which the local degree of freedom (the "massive graviton") is switched on. An exact solution with this property is explicitly exhibited and possesses a slower fall-off than the warped AdS black hole. The boundary conditions are invariant under the semidirect product of the Virasoro algebra with a u(1) current algebra.…
We continue our study of codimension two solutions of warped space-time varying compactifications of string theory. In this letter we discuss a non-supersymmetric solution of the classical type IIB string theory with de Sitter gravity on a codimension two uncompactified part of spacetime. A non-zero positive value of the cosmological constant is induced by the presence of non-trivial stringy moduli, such as the axion-dilaton system for the type IIB string theory. Furthermore, the naked singularity of the codimension two solution is resolved by the presence of a small but non-zero cosmological …
Thermodynamic properties of Schwarzschild-Anti de-Sitter (Sch-AdS) and Reissner-Nordström-Anti de-Sitter (RN-AdS) blackholes in 3+1 dimensional spacetime are studied critically with special reference to the warped braneworld black holes with non-vanishing cosmological constant on the brane. Explicit dependence of the thermodynamic variables on the parameters of the braneworld model such as the induced three brane cosmological constant as well as the bulk cosmological constant have been determined. Hawking-Page phase transition has been discussed for both Sch-AdS and RN-AdS black holes. At the …
We investigate the asymptotic structure of the three dimensional warped anti de sitter black holes in the Bergshoeff, Hohm and Townsend massive gravity using the canonical Hamiltonian formalism. We define the canonical asymptotic guage generators, which produce the conserved charges and the asymptotic symmetry group for the warped anti de sitter black holes. The attained symmetry group is described by a semi direct sum of a Virasoro and a KacMoody algebra. Using the Sugawara construction, we obtain a direct sum of two Virasoro algebras. We show that not only the asymptotic conserved charges sa…
We consider de Sitter vacua realised in concrete type IIB Calabi-Yau compactifications with an anti D3-brane at the tip of a warped throat of Klebanov-Strassler type. The Kähler moduli are stabilised together with the complex structure modulus of the warped throat. The volume is exponentially large as in the large volume scenario (LVS). We analyse the conditions on the parameters of the EFT such that they are in the region of validity of our approximations, there are no runaway problems and the vacua satisfy all consistency constraints, such as tadpole cancellation. We illustrate our results w…
We revisit moduli stabilisation for type IIB flux compactifications that include a warped throat region corresponding to a warped deformed conifold, with an anti-D3-brane sitting at its tip. The warping induces a coupling between the conifold's deformation modulus and the bulk volume modulus in the Kähler potential. Previous works have studied the scalar potential assuming a strong warping such that this coupling term dominates, and found that the anti-D3-brane uplift may destabilise the conifold modulus and/or volume modulus, unless flux numbers within the throat are large, which makes tadpol…
In this note we outline the arguments against the ten-dimensional consistency of the simplest types of KKLT de Sitter vacua, as given in arXiv:1707.08678. We comment on parametrization proposals within four-dimensional supergravity and express our disagreement with the recent criticism by the authors of arXiv:1808.09428.
The dynamics of warped/flux compactifications is studied, including warping effects, providing a firmer footing for investigation of the "landscape." We present a general formula for the four-dimensional potential of warped compactifications in terms of ten-dimensional quantities. This allows a systematic investigation of moduli-fixing effects and potentials for mobile branes. We provide a necessary criterion, "slope-dominance," for evading "no-go" results for de Sitter vacua. We outline the ten-dimensional derivation of the non-perturbative effects that should accomplish this in KKLT examples…
We explore in detail the prospects of obtaining a four-dimensional de Sitter universe in classical supergravity models with warped and time-independent extra dimensions, presenting explicit cosmological solutions of the $(4+n)$-dimensional Einstein equations with and without a bulk cosmological constant term. For the first time in the literature we show that there may exist a large class of warped supergravity models with a noncompact extra dimension which lead to a finite 4D Newton constant as well as a massless 4D graviton localised on an inflating four-dimensional FLRW universe. This result…
Warped dS$_3$ arises as a solution to topologically massive gravity (TMG) with positive cosmological constant $+1/\ell^2$ and Chern-Simons coefficient $1/μ$ in the region $μ^2 \ell^2 < 27$. It is given by a real line fibration over two-dimensional de Sitter space and is equivalent to the rotating Nariai geometry at fixed polar angle. We study the thermodynamic and asymptotic structure of a family of geometries with warped dS$_3$ asymptotics. Interestingly, these solutions have both a cosmological horizon and an internal one, and their entropy is unbounded from above unlike black holes in regul…
This is the first of two papers studying localization of massive bulk fields on a bane in 5D anti-de Sitter spacetime, and some of their cosmological consequences. Here we focus on a massive 5D scalar, which is known to lack a localized mode, and discuss how a seeming discontinuity between this theory and the massless theory - known to support a localized zero mode - is resolved thanks to peculiar analytic properties of the massive two-point amplitude. Furthermore, we propose a boundary term that leads to the emergence of a massless localized mode in the massive theory. Last but not least, we …
On the Stability of Warped Anti-de Sitter Spaces in Supergravity
Politecnico di Torino（都灵理工大学）；INFN, Sezione di Torino（意大利国家核物理研究所都灵分部）；CEICO, Institute of Physics of the Czech Academy of Sciences（捷克科学院物理研究所）；Universidade de Santiago de Compostela（圣地亚哥德孔波斯特拉大学）；Texas A&M University（德克萨斯农工大学）；ENS de Lyon（里昂高等师范学校）
We study the asymptotic symmetries of three-dimensional Warped Anti-de Sitter (WAdS) spaces in three-dimensional New Massive Gravity (NMG). For a specific choice of asymptotic boundary conditions, we find that the algebra of charges is infinite-dimensional and coincides with the semidirect sum of Virasoro algebra with non-vanishing central charge and an affine $\hat{u}(1)_k$ Kač-Moody algebra. We show that the WAdS black hole configurations organize in terms of two commuting Virasoro algebras. We identify the Virasoro generators that expand the associated representations in the dual Warped Con…
We investigate the stability of the horizon in a warped anti-de Sitter black hole based on the three-dimensional new massive gravity by particle absorption. If a particle moving towards the black hole enters its outer horizon, the black hole changes because it absorbs conserved quantities of the particle. This variation is constrained by the equations of motion for the particle. We prove both the irreducibility of the entropy and stability of the horizon for the black hole through this process. However, the instability of the horizon is found in a near-extremal black hole by considering its se…
We discuss a possible compactification of a higher-dimensional gravitational theory, which give rise to a de Sitter or an accelerating universe, to the extent that it can describe a low energy limit of string theory. Such analysis can be carried out by the usual integration over the internal space in the Einstein equations. The combined field equations in the higher-dimensional supergravity theory after integration give several new terms which may help to realize a de Sitter compactification. After developing the general framework, we describe some specific examples involving the dilaton and m…
We construct a stretched (aka Warped) Anti-de Sitter black hole in 3 dimensions supported by a real scalar field configuration. The latter is regular everywhere outside and on the horizon. No hair theorems in 3 dimensions demand the matter to be coupled to the curvature in a non-minimal way; however, this coupling can still be of the Horndeski type, i.e. yielding second order field equations similar to those appearing in the context of Galileon theories. These Warped-Anti-de Sitter black holes exhibit interesting thermodynamical properties, such as finite Hawking temperature and entropy. We co…
We investigate properties of the inner horizons of certain black holes in higher-derivative three-dimensional gravity theories. We focus on BTZ and Spacelike Warped Anti-de Sitter black holes, as well as on asymptotically Warped de-Sitter solutions exhibiting both a cosmological and a black hole horizon. We verify that a First Law is satisfied at the Inner horizon, in agreement with the proposal of \cite{Castro:2012av}. We then show that, in Topologically Massive Gravity, the product of the areas of the inner and outer horizons fails to be independent on the mass, and trace this to the diffeom…
We provide a simple holographic description for a warped conformal field theory (WCFT) at finite temperature. To this end we study the counterpart of warped anti-de Sitter black holes in three dimensions using a lower-spin $\mathfrak{sl}(2,\mathbb{R})\oplus\mathfrak{u}(1)$ Chern-Simons theory proposed by Hofman and Rollier. We determine the asymptotic symmetries, thermal entropy and holographic entanglement entropy and show that all these quantities are in perfect agreement with the expectations from the dual WCFT perspective. In addition we provide a metric interpretation of our results which…
We develop tools to engineer de Sitter vacua with semi-holographic duals, using elliptic fibrations and orientifolds to uplift Freund-Rubin compactifications with CFT duals. The dual brane construction is compact and constitutes a microscopic realization of the dS/dS correspondence, realizing d-dimensional de Sitter space as a warped compactification down to (d-1)-dimensional de Sitter gravity coupled to a pair of large-N matter sectors. This provides a parametric microscopic interpretation of the Gibbons-Hawking entropy. We illustrate these ideas with an explicit class of examples in three di…
Explicit time-dependent solutions of the 10D vacuum Einstein equations are found for which spacetime is compactified on six-dimensional warped spaces. We explicitly work out an example where the internal manifold is a six-dimensional generalized space having positive, negative or zero scalar curvature, whose base can be a five-sphere $S^5$ or an Einstein space $T^{1,1}=(S^2\times S^2)\rtimes S^1$. In this paper, inflationary de Sitter solutions are found just by solving the 10D vacuum Einstein equations. Our results further show that the limitation with warped models studied to date has arisen…
Free scalar field theory in the sector with a large number of particles can be interpreted as bosonic string theory on anti-de Sitter space of vanishing radius. Different ways of writing the field theory Hamiltonian translate to different ways of reparametrizing the world-sheet sigma coordinate. Adding a mass term in the field theory corresponds to cutting off the warped AdS direction, with cut-off inversely proportional to the mass. The string theory has neither tachyon, nor critical dimension.
The characterization of a six- (or seven)-dimensional internal manifold with metric as having positive, zero or negative curvature is expected to be an important aspect of warped compactifications in supergravity. In this context, Douglas and Kallosh recently pointed out that a compact internal space with negative curvature could help to construct four-dimensional de Sitter solutions only if the extra dimensions are strongly warped or there are large stringy corrections. That is, the problem of finding 4-dimensional de Sitter solutions is well posed, if all extra dimensions are physically comp…
The model of d5 higher derivative (HD) gravity admitting Schwarzschild--anti de Sitter Black Hole (S-AdS BH) as exact solution is considered. The surface counterterms are added to the complete action, they are fixed by the condition of finiteness of bulk AdS spacetime when brane goes to infinity. As a result the brane (observable Universe) is defined dynamically in terms of d5 theory parameters (brane tension is fixed). Brane radius is always bigger than horizon radius and the 4d Universe itself could be static or inflationary. Natural ganeralization of this model gives warped compactification…
In this paper, we discuss the time-dependent brane solutions in higher-dimensional supergravity theories. We particularly focus on the dynamical extensions of the intersecting brane solutions involving three branes. We also show that in the near-horizon limits, where the time dependence is negligible, these branes describe warped anti-de Sitter spacetimes as in the corresponding static solutions. We finally examine the lower-dimensional cosmological dynamics obtained after compactifications of the higher-dimensional solutions and show the solutions we have found give the four-dimensional unive…
We outline the construction of metastable de Sitter vacua of type IIB string theory. Our starting point is highly warped IIB compactifications with nontrivial NS and RR three-form fluxes. By incorporating known corrections to the superpotential from Euclidean D-brane instantons or gaugino condensation, one can make models with all moduli fixed, yielding a supersymmetric AdS vacuum. Inclusion of a small number of anti-D3 branes in the resulting warped geometry allows one to uplift the AdS minimum and make it a metastable de Sitter ground state. The lifetime of our metastable de Sitter vacua is …
Motivated by the AdS_6/CFT_5 correspondence, we study general supersymmetric solutions of massive type IIA supergravity, consisting of a warped product of six-dimensional anti-de Sitter space AdS_6 with a four-dimensional Riemannian manifold M_4, and fluxes compatible with the SO(5,2) symmetry. We find that the only local solution of this form is the warped AdS_6 x_w S^4 solution, originally discovered by Brandhuber and Oz. We discuss the supersymmetric properties of this solution.
Accelerating universe or the existence of a small and positive cosmological constant is probably the most pressing obstacle as well as opportunity to significantly improving the models of four-dimensional cosmology from fundamental theories of gravity, including string theory. In seeking to resolve this problem, one naturally wonders if the real world can somehow be interpreted as an inflating de Sitter brane embedded in a higher-dimensional spacetime described by warped geometry. In this scenario, the four-dimensional cosmological constant may be uniquely determined in terms of two length sca…
We investigate stability of two branches of Freund-Rubin compactification from thermodynamic and dynamical perspectives. Freund-Rubin compactification allows not only trivial solutions but also warped solutions describing warped product of external de Sitter space and internal deformed sphere. We study dynamical stability by analyzing linear perturbations around solutions in each branch. Also we study thermodynamic stability based on de Sitter entropy. We show complete agreement of thermodynamic and dynamical stabilities of this system. Finally, we interpret the results in terms of effective e…
We study the extensions of DGP model which are described by five-dimensional Einstein gravity coupled covariantly to 3-brane with induced gravity term and consider warped D=4 de Sitter background field solutions on the brane. The case with included D=5 AdS cosmological term is also considered. Following background field method we obtain the field equations described by the Lagrangean terms bilinear in gravitational field. In such a linear field approximation on curved dS background we calculate explicitly the five-dimensional massive terms as well as the mass-like ones on the brane. We investi…
This article discusses model-building scenarios including anti-D3-/D7-branes, in which supersymmetry is broken spontaneously, despite having no scale at which sparticles appear and standard supersymmetry is restored. If the branes are placed on singularities at the tip of warped throats in Calabi-Yau orientifold flux compactifications, they may give rise to realistic particle spectra, closed- and open-string moduli stabilisation with a Minkowski/de Sitter uplift, and a geometrical origin for the scale hierarchies. The paper derives the low-energy effective field theory description for such sce…
We study the role of the Gauss-Bonnet corrections and two loop higher genus contribution to the gravity action on the Kaluza-Klien modes and their interactions for different bulk fields which enable one to study various phenomenological implications of string loop corrected Gauss-Bonnet modified warped geometry model in one canvas. We have explicitly derived a phenomenological bound on the Gauss-Bonnet parameter so that the required Planck to TeV scale hierarchy can be achieved through the warp factor in the light of recently discovered Higgs like boson at 125 GeV. Moreover due to the presence…
Two ways in which de Sitter space can arise in supergravity theories are discussed. In the first, it arises as a solution of a conventional supergravity, in which case it necessarily has no Killing spinors. For example, de Sitter space can arise as a solution of N=8 gauged supergravities in four or five dimensions. These lift to solutions of 11-dimensional supergravity or D=10 IIB supergravity which are warped products of de Sitter space and non-compact spaces of negative curvature. In the second way, de Sitter space can arise as a supersymmetric solution of an unconventional supergravity theo…
We continue the study of compactifications of massive IIA supergravity on G2 orientifolds and demonstrate that breaking supersymmetry with anti-D2 and anti-D6 sources leads to 3d theories for which the typical tachyons haunting classical dS solutions can be absent. However for a concrete torus example the meta-stable dS window disappears after a quantization of fluxes and charges. We discuss the prospects of more general G2 compactifications and argue that they could potentially alleviate the tachyon problem by introducing larger tadpole numbers and warped throats. However, exactly those ingre…
Time-dependent soliton solutions are explicitly derived in a five-dimensional theory endowed with one (warped) extra-dimension. Some of the obtained geometries, everywhere well defined and technically regular, smoothly interpolate between two five-dimensional anti-de Sitter space-times for fixed value of the conformal time coordinate. Time dependent solutions containing both topological and non-topological sectors are also obtained. Supplementary degrees of freedom can be also included and, in this case, the resulting multi-soliton solutions may describe time-dependent kink-antikink systems.
We revisit the effective low-energy dynamics of the volume modulus in warped flux compactifications with anti-D3-branes in order to analyze the prospects for meta-stable de Sitter vacua and brane inflation along the lines of KKLT/KKLMMT. At the level of the 10d supergravity solution, anti-branes in flux backgrounds with opposite charge are known to source singular terms in the energy densities of the bulk fluxes, which led to a debate on the consistency of such constructions in string theory. A straightforward yet non-trivial check of the singular solution is to verify that its dimensional red…
We reinvestigate the thermodynamics of black objects (holes and strings) in four-dimensional braneworld models that are originally constructed by Emparan, Horowitz and Myers based on the anti-de Sitter (AdS) C-metric. After proving the uniqueness of slicing the AdS C-metric, we derive thermodynamic quantities of the black objects by means of the Euclidean formulation and find that we have no necessity of requiring any regularization to calculate their classical action. We show that there exist the Bekenstein-Hawking law and the thermodynamic first law. The thermodynamic mass of the localized b…
In this paper, we study Ricci-flat and Einstein Lorentzian multiply warped products. We also consider the case of having constant scalar curvatures for this class of warped products. Finally, after we introduce a new class of spacetimes called as generalized Kasner space-times, we apply our results to this kind of space-times as well as other relativistic space-times, i.e., Reissner-Nordstrom, Kasner space-times, Banados-Teitelboim-Zanelli and de Sitter Black hole solutions.
