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 the extremal condition under the scattering of any mode of the scalar field.
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 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…
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 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 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 …
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 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…
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…
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…
This thesis mainly focuses on the Hawking radiation (HR) evacuating from the surface of the objects that have earned a reputation as the most extraordinary objects existing so far; the black holes (BHs). Throughout this study, quantum tunneling (QT) process serves as the model for the HR of scalar, vector and Dirac particles. The scalar and Dirac particles are anticipated to be tunneling through the horizon of rotating scalar hairy black holes (RHSBHs); whilst the vector particles are associated with a rotating warped anti de-Sitter black hole (WAdS3BH) embedded in a (2+1) dimensional fabric. …
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…
We present the explicit solution to the geodesic equations in a warped de Sitter space-time proposed by Randall-Sundrum. We find that a test particle moves in the bulk and is not restricted on a 3-brane (to be taken as our universe). On the 3-brane, the test particle moves with uniform velocity, giving the appearance that it is not subject to a force. But computing the particle's energy using the energy-momentum tensor yields a time-dependent energy that suggests a time-dependent mass. Thus, the extra force, which is the effect of the warped extra dimension on the particle's motion on the 3-br…
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…
Exploiting a multiply warped product manifold scheme, we study the interior solutions of the Banados-Teitelboim-Zanelli black holes and the exterior solutions of the de Sitter black holes in the (2+1) dimensions.
We apply the warped product spacetime scheme to the Banados-Teitelboim-Zanelli black holes and the Reissner-Nordström-anti-de Sitter black hole to investigate their interior solutions in terms of warped products. It is shown that there exist no discontinuities of the Ricci and Einstein curvatures across event horizons of these black holes.
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…
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 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…
We derive a low-energy effective theory for gravity with anti-D branes, which are essential to get de Sitter solutions in the type IIB string warped compactification, by taking account of gravitational backreactions of anti-D branes. In order to see the effects of the self-gravity of anti-D branes, a simplified model is studied where a 5-dimensional anti-de Sitter ({\it AdS}) spacetime is realized by the bulk cosmological constant and the 5-form flux, and anti-D branes are coupled to the 5-form field by Chern-Simon terms. The {\it AdS} spacetime is truncated by introducing UV and IR cut-off br…
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 …
We interpret the cosmological constant as the energy of the vacuum, and under a minimum amount of assumptions, we show that it is deformed in the vicinity of a black hole. This leads us to reexamine the Kerr-de Sitter solution. We provide a new solution, simpler and geometrically richer, which shows the impact of the rotation in form of a warped curvature. We carry out a detailed and exact study on the new black hole solution, and we conclude with a conjecture regarding the possible impact of our results on alternative theories.
We initiate a comprehensive study of a set of solutions of topologically massive gravity known as null warped anti-de Sitter spacetimes. These are pp-wave extensions of three-dimensional anti-de Sitter space. We first perform a careful analysis of the linearized stability of black holes in these spacetimes. We find two qualitatively different types of solutions to the linearized equations of motion: the first set has an exponential time dependence, the second - a polynomial time dependence. The solutions polynomial in time induce severe pathologies and moreover survive at the non-linear level.…
General relativity can be unambiguously formulated with Lorentz, de Sitter and anti-de Sitter tangent groups, which determine the fermionic representations. We show that besides of the Lorentz group only anti-de Sitter tangent group is consistent with all physical requirements.
It is pointed out that in the warped string compactification, motion of anti-D-branes near the bottom of a throat behaves like dark matter. Several scenarios for production of the dark matter are suggested, including one based on the D/anti-D interaction at the late stage of D/anti-D inflation.
Despite the recent evidence that anti-de Sitter spacetime is nonlinearly unstable, we argue that many asymptotically anti-de Sitter solutions are nonlinearly stable. This includes geons, boson stars, and black holes. As part of our argument, we calculate the frequencies of long-lived gravitational quasinormal modes of AdS black holes in various dimensions. We also discuss a new class of asymptotically anti-de Sitter solutions describing noncoalescing black hole binaries.
We extend the derivation of the Hawking temperature of a Schwarzschild black hole via the Heisenberg uncertainty principle to the de Sitter and anti-de Sitter spacetimes. The thermodynamics of the Schwarzschild-(anti-)de Sitter black holes is obtained from the generalized uncertainty principle of string theory and non-commutative geometry. This may explain why the thermodynamics of (anti-)de Sitter-like black holes admits a holographic description in terms of a dual quantum conformal field theory, whereas the thermodynamics of Schwarzschild-like black holes does not.
Anti-de Sitter space with identified points give rise to black-hole structures. This was first pointed out in three dimensions, and generalized to higher dimensions by Aminneborg et al. In this paper, we analyse several aspects of the five dimensional anti-de Sitter black hole including, its relation to thermal anti-de Sitter space, its embedding in a Chern-Simons supergravity theory, its global charges and holonomies, and the existence of Killing spinors.
We construct new axially symmetric solutions of SU(2) Yang-Mills theory in a four dimensional anti-de Sitter spacetime. Possessing nonvanishing nonabelian charges, these regular configurations have also a nonzero angular momentum. Numerical arguments are also presented for the existence of rotating solutions of Einstein-Yang-Mills equations in an asymptotically anti-de Sitter spacetime.
The stability of the modular field in a warped brane world scenario has been a subject of interest for a long time. Goldberger \& Wise ( GW ) proposed a mechanism to achieve this by invoking a massive scalar field in the bulk space-time neglecting the back-reaction. In this work, we examine the possibility of stabilizing the modulus without bringing in any external scalar field. We show that instead of flat 3-branes as considered in Randall-Sundrum ( RS ) warped braneworld model, if one considers a more generalized version of warped geometry with de-Sitter 3-brane, then the brane vacuum energy…
We first briefly discuss the relation between black hole thermodynamics and the entropy function formalism. We find that an equation which governs the relationship between Sen's entropy function and black hole entropy, can quickly give higher order corrections to entropy of pure (anti-) de Sitter space without knowing the corrected metric. We also show that near horizon geometry and the entropy function extremization is no longer required for pure (anti-)de Sitter space. The entropy of (anti-)de Sitter space and Schwarzschild-(anti-) de Sitter black holes together with Gauss-Bonnet terms, $R^2…
Cosmological acceleration is difficult to accommodate in theories of fundamental interactions involving supergravity and superstrings. An alternative is that the acceleration is not universal but happens in a large localized region, which is possible in theories admitting regular black holes with de Sitter-like interiors. We considerably strengthen this scenario by placing it in a global anti-de Sitter background, where the formation of 'de Sitter bubbles' will be enhanced by mechanisms analogous to the Bizon-Rostworowski instability in general relativity. This opens an arena for discussing th…
We consider global monopoles in asymptotic de Sitter/ Anti- de Sitter space-time. We present the by our numerical analysis confirmed asymptotic behaviour of the metric and Goldstone field functions. We find that the appearance of horizons in this model depends strongly on the sign and value of the cosmological constant as well as on the value of the gravitational coupling. In Anti-de Sitter (AdS) space, we find that for a fixed value of the cosmological constant, global monopoles without horizons exist only up to a critical value of the gravitational coupling. Moreover, we observe (in contrast…
Fermions in (anti) de Sitter gravity theory in four dimensions are considered. Especially we propose new fermion actions to derive a Weyl or Majorana fermion action if we break the AdS (dS) group to the Lorentz group in curved spacetime.
It is shown how the results of Deser and Levin on the response of accelerated detectors in anti-de Sitter space can be understood from the same general perspective as other thermality results in spacetimes with bifurcate Killing horizons.
We show how to compute the mass of a Kerr-anti-de Sitter spacetime with respect to the anti-de Sitter background in any dimension, using a superpotential which has been derived from standard Noether identities. The calculation takes no account of the source of the curvature and confirms results obtained for black holes via the first law of thermodynamics.
The deep reason why the equations describing axial and polar perturbations of Schwarzschild black holes have the same spectrum is far from trivial. In this article, we revisit the original proof and try to make it clearer. Still focusing on uncharged and non-rotating black holes, we extend the results to spacetimes including a cosmological constant, which have so far mostly been investigated numerically from this perspective.
We compute the mass and angular momenta of rotating anti-de Sitter spacetimes in Einstein-Gauss-Bonnet theory of gravity using a superpotential derived from standard Noether identities. The calculation relies on the fact that the Einstein and Einstein-Gauss-Bonnet vacuum equations are the same when linearized on maximally symmetric backgrounds and uses the recently discovered D-dimensional Kerr-anti-de Sitter solutions to Einstein's equations.
Hawking radiation (HR) of massive vector particles from a rotating Warped Anti-de Sitter black hole in 2+1 dimensions (WAdS$_{\text{3}}$BH) is studied in detail. The quantum tunneling approach with the Hamilton-Jacobi method (HJM) is applied in the Proca equation (PE), and we show that the radial function yields the tunneling rate of the outgoing particles. Comparing the result obtained with the Boltzmann factor, we satisfactorily reproduce the Hawking temperature (HT) of the WAdS$_{\text{3}}$BH.
We prove that five-dimensional extreme anti-de Sitter black ring solutions to the vacuum Einstein equations that admit biaxial symmetry do not exist. This is established by demonstrating the nonexistence of five-dimensional, biaxisymmetric, vacuum near-horizon geometries of extreme horizons with a nonzero cosmological constant and ring topology.
We investigate aspects of the four-dimensional effective description of brane world scenarios based on warped compactification on anti-de Sitter space. The low-energy dynamics is described by visible matter gravitationally coupled to a ``dark'' conformal field theory. We give the linearized description of the 4d stress tensor corresponding to an arbitrary 5d matter distribution. In particular a 5d falling particle corresponds to a 4d expanding shell, giving a 4d interpretation of a trajectory that misses a black hole only by moving in the fifth dimension. Breakdown of the effective description…
A class of five-dimensional warped solutions is presented. The geometry is everywhere regular and tends to five-dimensional anti-de Sitter space for large absolute values of the bulk coordinate. The physical features of the solutions change depending on the value of an integer parameter. In particular, a set of solutions describes generalized gravitating kinks where the scalar field interpolates between two different minima of the potential. The other category of solutions describes instead gravitating defects where the scalar profile is always finite and reaches the same constant asymptote bo…
We discuss several aspects of the relation between asymptotically AdS and asymptotically dS spacetimes including: the continuation between these types of spaces, the global stability of asymptotically dS spaces and the structure of limits within this class, holographic renormalization, and the maximal mass conjecture of Balasubramanian-deBoer-Minic.
We review several aspects of anti-De Sitter (AdS) spaces in different dimensions, and of four dimensional Schwarzschild anti-De Sitter (SAdS) black hole.
In this paper time machines are constructed from anti-de Sitter space. One is constructed by identifying points related via boost transformations in the covering space of anti-de Sitter space and it is shown that this Misner-like anti-de Sitter space is just the Lorentzian section of the complex space constructed by Li, Xu, and Liu in 1993. The others are constructed by gluing an anti-de Sitter space to a de Sitter space, which could describe an anti-de Sitter phase bubble living in a de Sitter phase universe. Self-consistent vacua for a massless conformally coupled scalar field are found for …
Superradiance in black hole spacetimes can trigger instabilities. Here we show that, due to superradiance, small Kerr-anti-de Sitter black holes are unstable. Our demonstration uses a matching procedure, in a long wavelength approximation.
We propose new braneworld models arising from a scalar field in the bulk. In these examples, the induced on--brane line element is de Sitter (or anti de Sitter) and the bulk (five dimensional) Einstein equations can be exactly solved to obtain warped spacetimes. The solutions thus derived are single and two-brane models -- one with {\em thin} branes while the other one of the {\em thick} variety. The field profiles and the potentials are obtained and analysed for each case. We note that for the {\em thick} brane scenario the field profile resembles a kink, whereas for one or more {\em thin} br…
We study the asymptotic behavior of the bulk spacetimes with the negative cosmological constant in the context of the brane-world scenario. We show that, in Euclidean bulk, or in Lorentzian static bulk, some sequences of hypersurfaces with the positive Ricci scalar evolve to the warped geometries like the anti-de Sitter spacetime. Based on the AdS/CFT correspondence, we discuss that the positivity of the Ricci scalar is related to the stability of CFT on the brane. In addition, the brane-world is described from the holographic point of view. The asymptotic local structure of the conformal infi…
In a recent paper we investigated stationary, relativistic Bondi-type accretion in Schwarzschild-(anti-)de Sitter spacetimes. Here we study their stability, using the method developed by Moncrief. The analysis applies to perturbations satisfying the potential flow condition. We prove that global isothermal flows in Schwarzschild-anti-de Sitter spacetimes are stable, assuming the test-fluid approximation. Isothermal flows in Schwarzschild-de Sitter geometries and polytropic flows in Schwarzschild-de Sitter and Schwarzschild-anti-de Sitter spacetimes can be stable, under suitable boundary condit…
We revisit the principal arguments for interpreting the free quantum fields on anti-de Sitter or de Sitter spacetimes of any dimensions as oscillators or respectively anti-oscillators. In addition, we point out that there exists a chart on the de Sitter background where the free Dirac field becomes a genuine anti-oscillator in the non-relativistic limit in the sense of special relativity.
In this paper we add a compact dimension to Schwarzschild-(anti-) de sitter and Kerr-(anti-) de sitter spacetimes, which describes (rotating) black string-(anti-) de sitter spacetime. We study the geodesic motion of test particles and light rays in this spacetime. We present the analytical solutions of the geodesic equations in terms of Weierstrass elliptic and Kleinian sigma hyperelliptical functions. We also discuss the possible orbits and classify them according to particle's energy and angular momentum. Moreover, the obtained results, are compared to Schwarzschild-(anti-) de sitter and Ker…
Quasinormal mode spectra for gravitational perturbations of black holes in four dimensional de Sitter and anti-de Sitter space are investigated. The anti-de Sitter case is relevant to the ADS-CFT correspondence in superstring theory. The ADS-CFT correspondence suggests a prefered set of boundary conditions.
The group theoretical approach to the relativistic wave equations in the de Sitter and Anti-de Sitter spaces for spin~0 and 1/2 massive particles is considered. The invariant wave equations which determines the appropriate irreducible representations are constructed. The explicit solutions of these equations possessing a simplicity and physical transparency are obtained without use of the separation of variables method. The connection with the general-covariant approach to wave equations in a curved space is established. It is shown that the Anti-de Sitter space is the solution of the Einstein…
In this paper, static electrically charged black hole solutions with cosmological constant are investigated in an Einstein-Hilbert theory of gravity with additional quadratic curvature terms. Beside the analytic Schwarzschild (Anti-) de Sitter solutions, non-Schwarzschild (Anti-) de Sitter solutions are also obtained numerically by employing the shooting method. The results show that there exist two groups of asymptotically (Anti-) de Sitter spacetimes for both charged and uncharged black holes. In particular, it was found that for uncharged black holes the first group can be reduced to the Sc…
