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This review is a contribution to a book dedicated to the memory of Michael E. Fisher. The first example of a quantum many body system not expected to have any quasiparticle excitations was the Wilson-Fisher conformal field theory. The absence of quasiparticles can be established in the compressible, metallic state of the Sachdev-Ye-Kitaev model of fermions with random interactions. The solvability of the latter model has enabled numerous computations of the non-quasiparticle dynamics of chaotic many-body states, such as those expected to describe quantum black holes. We review thermodynamic properties of the SYK model, and describe how they have led to an understanding of the universal structure of the low energy density of states of charged black holes without low energy supersymmetry. [ABSTRACT FROM AUTHOR]

Black holes exert quantum pressure coming from the nonlocal gravity correction. We investigate this nonlocal correction for black holes in anti-de Sitter (AdS) spacetime and its dual boundary field theory. We show that the second order curvature and the nonlocal actions do not backreact on the AdS black hole metric. Thus, the interpretation of quantum pressure holds in the bulk for AdS black hole, generalizing the previous result for the asymptotically flat black hole. We then show that the leading geometric correction comes from the third order in curvature and explicitly calculate the corrections to the metric and to the horizon. For applications to AdS/CFT, we conjectured a nonlocal Gibbons–Hawking–York boundary term along with the necessary counter terms to cancel the ultraviolet divergence of the bulk action. We then calculate the thermodynamic quantities in the bulk and discuss their properties. [ABSTRACT FROM AUTHOR]

We review the role of the spectral condition as a characteristic of Minkowski, de Sitter, and anti-de Sitter quantum field theories. We also discuss the role of plane waves which are compatible with the relevant analyticity domains linked to the spectral condition(s) and discuss harmonic analysis in terms of them. [ABSTRACT FROM AUTHOR]

We review the role of the spectral condition as a characteristic of Minkowski, de Sitter, and anti-de Sitter quantum field theories. We also discuss the role of plane waves which are compatible with the relevant analyticity domains linked to the spectral condition(s) and discuss harmonic analysis in terms of them.

We describe a class of wormholes that generically become traversable afterincorporating gravitational back-reaction from linear quantum fields satisfyingappropriate (periodic or anti-periodic) boundary conditions around anon-contractible cycle, but with natural boundary conditions at infinity (i.e.,without additional boundary interactions). The class includes bothasymptotically flat and asymptotically AdS examples. Simple asymptoticallyAdS$_3$ or asymptotically AdS$_3 \times S^1$ examples with a single periodicscalar field are then studied in detail. When the examples admit a smoothextremal limit, our perturbative analysis indicates the back-reacted wormholeremains traversable at later and later times as this limit is approached. Thissuggests that a fully non-perturbative treatment would find a self-supportingeternal traversable wormhole. While the general case remains to be analyzed indetail, the likely relation of the above effect to other known instabilities ofextreme black holes may make the construction of eternal traversable wormholesmore straightforward than previously expected.

We prove that any metric with curvature less than or equal to $-1$ (in the sense of A. D. Alexandrov) on a closed surface of genus greater than $1$ is isometric to the induced intrinsic metric on a space-like convex surface in a Lorentzian manifold of dimension $(2+1)$ with sectional curvature $-1$. The proof is by approximation, using a result about isometric immersion of smooth metrics by Labourie and Schlenker. [ABSTRACT FROM AUTHOR]

In the same way as the realization of some of the famous gedanken experiments imagined by the founding fathers of quantum mechanics has recently led to the current renewal of the interpretation of quantum physics, it seems that the most recent progress of observational astrophysics can be interpreted as the realization of some cosmological gedanken experiments such as the removal from the universe of the whole visible matter or the cosmic time travel leading to a new cosmological standard model. This standard model involves two dark components of the universe, dark energy and dark matter. Whereas dark energy is usually associated with the cosmological constant, we propose explaining dark matter as a pure QCD effect, namely a gluonic Bose--Einstein condensate, following the transition from the quark gluon plasma phase to the colorless hadronic phase. Our approach not only allows us to assume a Dark/Visible ratio equal to 11/2 but also provides gluons (and di-gluons, viewed as quasi-particles) with an extra mass of vibrational nature. Such an interpretation would support the idea that, apart from the violation of the matter/antimatter symmetry satisfying the Sakharov's conditions, the reconciliation of particle physics and cosmology needs not the recourse to any ad hoc fields, particles or hidden variables. [ABSTRACT FROM AUTHOR]

In this paper, we show how the quasinormal modes (QNMs) arise from the perturbations of massive scalar fields propagating in the curved background by using the artificial neural networks. To this end, we architect a special algorithm for the feedforward neural network method (FNNM) to compute the QNMs complying with the certain types of boundary conditions. To test the reliability of the method, we consider two black hole spacetimes whose QNMs are well known: 4 D pure de Sitter (dS) and five-dimensional Schwarzschild anti-de Sitter (AdS) black holes. Using the FNNM, the QNMs of are computed numerically. It is shown that the obtained QNMs via the FNNM are in good agreement with their former QNM results resulting from the other methods. Therefore, our method of finding the QNMs can be used for other curved spacetimes that obey the same boundary conditions. [ABSTRACT FROM AUTHOR]

We derive the non-relativistic c→∞ and ultra-relativistic c→0 limits of the κ-deformed symmetries and corresponding spacetime in (3+1) dimensions, with and without a cosmological constant. We apply the theory of Lie bialgebra contractions to the Poisson version of the κ-(A)dS quantum algebra, and quantize the resulting contracted Poisson–Hopf algebras, thus giving rise to the κ-deformation of the Newtonian (Newton–Hooke and Galilei) and Carrollian (Para-Poincaré, Para-Euclidean and Carroll) quantum symmetries, including their deformed quadratic Casimir operators. The corresponding κ-Newtonian and κ-Carrollian noncommutative spacetimes are also obtained as the non-relativistic and ultra-relativistic limits of the κ-(A)dS noncommutative spacetime. These constructions allow us to analyze the non-trivial interplay between the quantum deformation parameter κ, the curvature parameter η and the speed of light parameter c.

Initial conditions given on a spacelike, static slice of a non-globally hyperbolic spacetime may not define the fates of classical and quantum fields uniquely. Such lack of global hyperbolicity is a well-known property of the anti-de Sitter solution and led many authors to question how is it possible to develop a quantum field theory on this spacetime. Wald and Ishibashi took a step towards the healing of that causal issue when considering the propagation of scalar fields on AdS. They proposed a systematic procedure to obtain a physically consistent dynamical evolution. Their prescription relies on determining the self-adjoint extensions of the spatial component of the differential wave operator. Such a requirement leads to the imposition of a specific set of boundary conditions at infinity. We employ their scheme in the particular case of the four-dimensional AdS spacetime and compute the expectation values of the field squared and the energy-momentum tensor, which will then bear the effects of those boundary conditions. We are not aware of any laws of nature constraining us to prescribe the same boundary conditions to all modes of the wave equation. Thus, we formulate a physical setup in which one of those modes satisfy a Robin boundary condition, while all others satisfy the Dirichlet condition. Due to our unusual settings, the resulting contributions to the fluctuations of the expectation values will not respect AdS invariance. As a consequence, a back-reaction procedure would yield a non-maximally symmetric spacetime. Furthermore, we verify the violation of weak energy condition as a direct consequence of our prescription for dynamics. [ABSTRACT FROM AUTHOR]

We study warped AdS3 solutions in massive IIA supergravity preserving N=(3,0) and N=(1,0) supersymmetry. We consider solutions whose internal spaces decompose as an S3 × S3 fibration and a interval over which the rest of the solution is foliated. We present necessary and sufficient conditions for these solutions to exist, in terms of systems of ordinary differential equations and find several new analytic and numerical examples with internal spaces bounded between D‐brane and O‐plane behaviors. The authors study warped AdS3 solutions in massive IIA supergravity preserving N = (3; 0) and N = (1; 0) supersymmetry. They consider solutions whose internal spaces decompose as an S3 × S3 fibration and an interval over which the rest of the solution is foliated. Necessary and sufficient conditions for these solutions are presented in terms of systems of ordinary differential equations. Several new analytic and numerical examples with internal spaces bounded between D‐brane and O‐plane behaviors are found. [ABSTRACT FROM AUTHOR]

In the same way as the realization of some of the famous gedanken experiments imagined by the founding fathers of quantum mechanics has recently led to the current renewal of the interpretation of quantum physics, it seems that the most recent progress of observational astrophysics can be interpreted as the realization of some cosmological gedanken experiments such as the removal from the universe of the whole visible matter or the cosmic time travel leading to a new cosmological standard model. This standard model involves two dark components of the universe, dark energy and dark matter. Whereas dark energy is usually associated with the cosmological constant, we propose explaining dark matter as a pure QCD effect, namely a gluonic Bose–Einstein condensate, following the transition from the quark gluon plasma phase to the colorless hadronic phase. Our approach not only allows us to assume a Dark/Visible ratio equal to 11/2 but also provides gluons (and di-gluons, viewed as quasi-particles) with an extra mass of vibrational nature. Such an interpretation would support the idea that, apart from the violation of the matter/antimatter symmetry satisfying the Sakharov’s conditions, the reconciliation of particle physics and cosmology needs not the recourse to any ad hoc fields, particles or hidden variables.

The quantum duality principle is used to obtain explicitly the Poisson analogue of the κ-(A)dS quantum algebra in (3+1) dimensions as the corresponding Poisson–Lie structure on the dual solvable Lie group. The construction is fully performed in a kinematical basis and deformed Casimir functions are also explicitly obtained. The cosmological constant Λ is included as a Poisson–Lie group contraction parameter, and the limit Λ→0 leads to the well-known κ-Poincaré algebra in the bicrossproduct basis. A twisted version with Drinfel'd double structure of this κ-(A)dS deformation is sketched.

En este trabajo se hace una introducción básica acerca de los espacios- tiempo de Sitter y Anti-de Sitter. Para el espacio de Sitter se calcula dos métricas equivalentes una usando coordenadas estáticas y la otra usando coordenadas de Friedmann-Lemaître-Robertson-Walker (FLRW). En el caso del espacio Anti-de Sitter se determina la condición que debe cumplir la constante cosmológica para ser una solución de las ecuaciones de Einstein y nalmente , haciendo uso de coordenadas globales se determina su métrica.

The Cayley–Klein (CK) formalism is applied to the real algebra so(5) by making use of four graded contraction parameters describing, in a unified setting, 81 Lie algebras, which cover the (anti-)de Sitter, Poincaré, Newtonian and Carrollian algebras. Starting with the Drinfel’d–Jimbo real Lie bialgebra for so(5) together with its Drinfel’d double structure, we obtain the corresponding CK bialgebra and the CK r-matrix coming from a Drinfel’d double. As a novelty, we construct the (first-order) noncommutative CK spaces of points, lines, 2-planes and 3-hyperplanes, studying their structural properties. By requiring dealing with real structures, we found that there exist 63 specific real Lie bialgebras together with their sets of four noncommutative spaces. Furthermore, we found 14 classical r-matrices coming from Drinfel’d doubles, obtaining new results for the de Sitter so(4,1) and anti-de Sitter so(3,2) as well as for some of their contractions. These geometric results were exhaustively applied onto the (3 + 1)D kinematical algebras, considering not only the usual (3 + 1)D spacetime but also the 6D space of lines. We established different assignations between the geometrical CK generators and the kinematical ones, which convey physical identifications for the CK contraction parameters in terms of the cosmological constant/curvature Λ and the speed of light c. We, finally, obtained four classes of kinematical r-matrices together with their noncommutative spacetimes and spaces of lines, comprising all κ-deformations as particular cases.

An explanation of the origin of dark matter is suggested in this work. The argument is based on symmetry considerations about the concept of mass. In Wigner’s view, the rest mass and the spin of a free elementary particle in flat space-time are the two invariants that characterize the associated unitary irreducible representation of the Poincaré group. The Poincaré group has two and only two deformations with maximal symmetry. They describe respectively the de Sitter (dS) and anti-de Sitter (AdS) kinematic symmetries. Analogously to their shared flat space-time limit, two invariants, spin and energy scale for de Sitter and rest energy for anti-de Sitter, characterize the unitary irreducible representation associated with dS and AdS elementary systems, respectively. While the dS energy scale is a simple deformation of the Poincaré rest energy and so has a purely mass nature, AdS rest energy is the sum of a purely mass component and a kind of zero-point energy derived from the curvature. An analysis based on recent estimates on the chemical freeze-out temperature marking in Early Universe the phase transition quark–gluon plasma epoch to the hadron epoch supports the guess that dark matter energy might originate from an effective AdS curvature energy.

We discuss the algebraic quantization of a real, massive scalar field in the Poincaré patch of the -dimensional anti-de Sitter spacetime, with arbitrary boundary conditions. By using the functional formalism, we show that it is always possible to associate to such system an algebra of observables enjoying the standard properties of causality, time-slice axiom and F-locality. In addition, we characterize the wavefront set of the ground state associated to the system under investigation. As a consequence, we are able to generalize the definition of Hadamard states and construct a global algebra of Wick polynomials. [ABSTRACT FROM AUTHOR]

We review several aspects of anti-De Sitter (AdS) spaces in different dimensions, and of four dimensional Schwarzschild anti-De Sitter (SAdS) black hole. [ABSTRACT FROM AUTHOR]

The covariant free fields of any spin on anti-de Sitter (AdS) spacetimes are studied, pointing out that these transform under isometries according to covariant representations (CRs) of the AdS isometry group, induced by those of the Lorentz group. Applying the method of ladder operators, it is shown that the CRs with unique spin are equivalent with discrete unitary irreducible representations (UIRs) of positive energy of the universal covering group of the isometry one. The action of the Casimir operators is studied finding how the weights of these representations (reps.) may depend on the mass and spin of the covariant field. The conclusion is that on AdS spacetime, one cannot formulate a universal mass condition as in special relativity. [ABSTRACT FROM AUTHOR]

We study the problem of construction of global isometric embedding for spherically symmetric black holes with negative cosmological constant in various dimensions. Firstly, we show that there is no such embedding for 4D RN-AdS black hole in 6D flat ambient space, completing the classification which we started earlier. Then we construct an explicit embedding of non-spinning BTZ black hole in 6D flat ambient space. Using this embedding as an anzats, we then construct a global explicit embedding of d-dimensional Schwarzschild-AdS black hole in a flat ( d + 3 ) -dimensional ambient space.

The quantum duality principle is used to obtain explicitly the Poisson analogue of the κ -(A)dS quantum algebra in ( 3 + 1 ) dimensions as the corresponding Poisson–Lie structure on the dual solvable Lie group. The construction is fully performed in a kinematical basis and deformed Casimir functions are also explicitly obtained. The cosmological constant Λ is included as a Poisson–Lie group contraction parameter, and the limit Λ → 0 leads to the well-known κ -Poincaré algebra in the bicrossproduct basis. A twisted version with Drinfel'd double structure of this κ -(A)dS deformation is sketched. [ABSTRACT FROM AUTHOR]

We study the dynamics of a spherically symmetric thin shell of perfect fluid embedded in d-dimensional Anti-de Sitter (AdS) spacetime. In global coordinates, besides collapsing solutions, oscillating solutions are found where the shell bounces back and forth between two radii. The parameter space where these oscillating solutions exist is scanned in arbitrary number of dimensions. As expected, AdS3 appears to be singled out. [ABSTRACT FROM AUTHOR]

We present the generalisation to ( 3 + 1 ) dimensions of a quantum deformation of the ( 2 + 1 ) (Anti)-de Sitter and Poincaré Lie algebras that is compatible with the conditions imposed by the Chern–Simons formulation of ( 2 + 1 ) gravity. Since such compatibility is automatically fulfilled by deformations coming from Drinfel'd double structures, we believe said structures are worth being analysed also in the ( 3 + 1 ) scenario as a possible guiding principle towards the description of ( 3 + 1 ) gravity. To this aim, a canonical classical r -matrix arising from a Drinfel'd double structure for the three ( 3 + 1 ) Lorentzian algebras is obtained. This r -matrix turns out to be a twisted version of the one corresponding to the ( 3 + 1 ) κ -deformation, and the main properties of its associated noncommutative spacetime are analysed. In particular, it is shown that this new quantum spacetime is not isomorphic to the κ -Minkowski one, and that the isotropy of the quantum space coordinates can be preserved through a suitable change of basis of the quantum algebra generators. Throughout the paper the cosmological constant appears as an explicit parameter, thus allowing the (flat) Poincaré limit to be straightforwardly obtained. [ABSTRACT FROM AUTHOR]

We construct unique local solutions for the spherically-symmetric Einstein-Klein-Gordon-anti-de Sitter (AdS) system subject to a large class of initial and boundary conditions including some considered in the context of the AdS-CFT correspondence. The proof relies on estimates developed for the linear wave equation by the second author and involves a careful renormalization of the dynamical variables, including a renormalization of the well-known Hawking mass. For some of the boundary conditions considered this system is expected to exhibit rich global dynamics, including the existence of hairy black holes. This paper furnishes a starting point for such global investigations. [ABSTRACT FROM AUTHOR]

We study hyperideal polyhedra in the 3-dimensional anti-de Sitter space A d S 3 , which are defined as the intersection of the projective model of A d S 3 with a convex polyhedron in RP 3 whose vertices are all outside of A d S 3 and whose edges all meet A d S 3 . We show that hyperideal polyhedra in A d S 3 are uniquely determined by their combinatorics and dihedral angles, as well as by the induced metric on their boundary together with an additional combinatorial data, and describe the possible dihedral angles and the possible induced metrics on the boundary. [ABSTRACT FROM AUTHOR]

We investigate the existence of black hole solutions of four dimensional $$\mathfrak {su}(N)$$ EYM theory with a negative cosmological constant. Our analysis differs from previous works in that we generalise the field equations to certain non-spherically symmetric spacetimes. The work can be divided into two sections. In the first half, we use theorems of Wang's to derive a new topologically general $$\mathfrak {su}(N)$$ -invariant one-form connection which may serve as the ansatz for our gauge potential. The second half is devoted to proving the existence of non-trivial solutions to the field equations for any integer $$N$$ , with $$N-1$$ gauge degrees of freedom. Specifically, we prove existence in two separate regimes: for fixed values of the initial parameters and as $$|\varLambda |\rightarrow \infty $$ ; and for any $$\varLambda <0$$ , in some neighbourhood of existing trivial solutions. In both cases we can prove the existence of 'nodeless' solutions, i.e. such that all gauge field functions have no zeroes; this fact is of interest as we anticipate that some of them may be stable. [ABSTRACT FROM AUTHOR]

Abstract: We show that the Drinfel'd double associated to the standard quantum deformation is isomorphic to the -dimensional AdS algebra with the initial deformation parameter η related to the cosmological constant . This gives rise to a generalisation of a non-commutative Minkowski spacetime that arises as a consequence of the quantum double symmetry of gravity to non-vanishing cosmological constant. The properties of the AdS quantum double that generalises this symmetry to the case are sketched, and it is shown that the new non-commutative AdS spacetime is a nonlinear Λ-deformation of the Minkowskian one. [Copyright &y& Elsevier]

Scaling arguments are generalized to discuss the existence and the stability of static, spherically symmetric self-gravitating solitons in asymptotically flat and asymptotically anti-de Sitter spacetimes in $$D$$ dimensions. The formulas obtained from the scaling arguments are applied to the Einstein-Yang-Mills solitons with higher order terms in $$D=4$$ and $$D=5$$ dimensions and the Einstein-Yang-Mills-Chern-Simons solitons in $$D=5$$ dimension. We have shown that the negative cosmological constant, in general, improves the stability of the solitons. In $$D=4$$, in fact, the negative cosmological constant is essential for the stability of the solitons. In $$D=5$$, however, the higher order terms or the Chern-Simons term play more crucial role in the stability of the solitons; the possibility of having stable solitons exists in an asymptotically flat spacetime. [ABSTRACT FROM AUTHOR]

This is a short review of work done in common with Jacques Bros, Michel Gaudin, Ugo Moschella, and Vincent Pasquier. Among results are explicit Källén-Lehmann representations for products of two free-field two-point functions in the de Sitter and the anti-de Sitter spaces and applications to particle decay. [ABSTRACT FROM AUTHOR]

Using a holographic proposal for the geometric entropy we study its behavior in the geometry of Schwarzschild black holes in global AdSp for p = 3, 4, 5. Holographically, the entropy is determined by a minimal surface. On the gravity side, due to the presence of a horizon on the background, generically there are two solutions to the surfaces determining the entanglement entropy. In the case of AdS3, the calculation reproduces precisely the geometric entropy of an interval of length l in a two-dimensional conformal field theory with periodic boundary conditions. We demonstrate that in the cases of AdS4 and AdS5 the sign of the difference of the geometric entropies changes, signaling a transition. Euclideanization implies that various embedding of the holographic surface are possible. We study some of them and find that the transitions are ubiquitous. In particular, our analysis renders a very intricate phase space, showing, for some ranges of the temperature, up to three branches. We observe a remarkable universality in the type of results we obtain from AdS4 and AdS5. [ABSTRACT FROM AUTHOR]

We deform the anti-de Sitter algebra by adding additional generators $\mathcal{Z}_{ab}$, forming in this way the negative cosmological constant counterpart of the Maxwell algebra. We gauge this algebra and construct a dynamical model with the help of a constrained BF theory. It turns out that the resulting theory is described by the Einstein-Cartan action with Holst term, and the gauge fields associated with the Maxwell generators $\mathcal{Z}_{ab}$ appear only in topological terms that do not influence dynamical field equations. We briefly comment on the extension of this construction, which would lead to a nontrivial Maxwell fields dynamics. [ABSTRACT FROM AUTHOR]

We study the semiclassical tunneling of scalar and fermion fields from the horizon of a Constant Curvature Black Hole, which is locally AdS and whose five-dimensional analogue is dual to $\mathcal{N} = 4$ super-Yang-Mills. In particular, we highlight the strong reliance of the tunneling method for Hawking radiation on near-horizon symmetries, a fact often hidden behind the algorithmic procedure with which the tunneling approach tends to be used. We ultimately calculate the emission rate of scalars and fermions, and hence the black hole's Hawking temperature. [ABSTRACT FROM AUTHOR]

Abstract: We clarify the map between boundary perturbations of in general relativity, and exactly marginal worldsheet vertex operators in string theory with Neveu–Schwarz Neveu–Schwarz flux. The latter correspond to solutions of the higher derivative low-energy tree level effective action to all orders in the string length over the curvature radius. We calculate the exact expression of the boundary energy–momentum tensor including all these higher derivative corrections in a purely bosonic string theory. The bottom-line is a canonical shift in the normalization of the boundary energy–momentum tensor corresponding to a shift in the curvature radius over the string length squared by the dual Coxeter number of the subalgebra of the space–time Virasoro algebra. That allows us to propose a value for the Brown–Henneaux central charge including all tree level higher derivative corrections in bosonic string theory, in a scheme dictated by the worldsheet conformal field theory. [Copyright &y& Elsevier]

Abstract: We show how the constant curvature spacetimes of 3d gravity and the associated symmetry algebras can be derived from a single quantum deformation of the 3d Lorentz algebra . We investigate the classical Drinfel''d double of a “hybrid” deformation of that depends on two parameters . With an appropriate choice of basis and real structure, this Drinfel''d double agrees with the 3d anti-de Sitter algebra. The deformation parameter η is related to the cosmological constant, while z is identified with the inverse of the speed of light and defines the signature of the metric. We generalise this result to de Sitter space, the three-sphere and 3d hyperbolic space through analytic continuation in η and z; we also investigate the limits of vanishing η and z, which yield the flat spacetimes (Minkowski and Euclidean spaces) and Newtonian models, respectively. [Copyright &y& Elsevier]

We study the formation of marginally trapped surfaces in the head-on collision of two shock waves in anti-de Sitter space-time. We compare the obtained results with the corresponding results for de Sitter space-time. To clarify this comparison, we use coordinates that allow studying AdS/dS cases in a universal way. We also analyze the dependence of the area of the trapped surface on the choice of the regularization of the shock wave metric. [ABSTRACT FROM AUTHOR]

We consider an Anti-de Sitter universe filled by quantum conformal matter with the contribution from the usual tachyon and a perfect fluid. The model represents the combination of a trace-anomaly annihilated and a tachyon driven Anti-de Sitter universe. The influence exerted by the quantum effects and by the tachyon on the AdS space is studied. The radius corresponding to this universe is calculated and the effect of the tachyon potential is discussed, in particular, concerning the possibility to get an accelerated scale factor for the proposed model (which yields an accelerated expansion of the AdS type of universe). Fulfillment of the cosmological energy conditions in the model is also investigated. [ABSTRACT FROM AUTHOR]

It is shown that the free Dirac equation in spherically symmetric static backgrounds of any dimensions can be put in a simple form using a special version of Cartesian gauge in Cartesian coordinates. This is manifestly covariant under the transformations of the isometry group so that the generalized spherical coordinates can be separated in terms of angular spinors like in the flat case, obtaining a pair of radial equations. In this approach the equation of the Dirac free field in AdSd+1 backgrounds is analytically solved obtaining the formula of the energy levels and the corresponding normalized eigenspinors. [ABSTRACT FROM AUTHOR]

A quantum deformation of the conformal algebra of the Minkowskian spacetime in (3+1) dimensions is identified with a deformation of the (4+1)-dimensional AdS algebra. Both Minkowskian and AdS first-order non-commutative spaces are explicitly obtained, and the former coincides with the well-known κ-Minkowski space. Next, by working in the conformal basis, a new non-commutative Minkowskian spacetime is constructed through the full (all orders) dual quantum group spanned by deformed Poincare´ and dilation symmetries. Although Lorentz invariance is lost, the resulting non-commutative spacetime is quantum group covariant, preserves space isotropy and, furthermore, can be interpreted as a generalization of the κ-Minkowski space in which a variable fundamental scale (Planck length) appears. [Copyright &y& Elsevier]

We revisit the non-rotating massive BTZ black hole within a pseudo-Riemannian symmetric space context. Using classical symmetric space techniques we find that every such space intrinsically carries a regular Poisson structure whose symplectic leaves are para-Hermitian symmetric surfaces. We also obtain a global expression of the metric yielding a dynamical description of the black hole from its initial to its final singularity. [Copyright &y& Elsevier]

In the perturbative AdS–CFT correspondence, the dual field whose source are the prescribed boundary values of a bulk field in the functional integral, and the boundary limit of the quantized bulk field are the same thing. This statement is due to the fact that Witten graphs are boundary limits of the corresponding Feynman graphs for the bulk fields, and hence the dual conformal correlation functions are limits of bulk correlation functions. This manifestation of duality is analyzed in terms of the underlying functional integrals of different structure. [ABSTRACT FROM AUTHOR]

Maximally supersymmetric spacetime algebras in eleven dimensions, which are the isometry superalgebras of Minkowski space, AdS7×S4, AdS4×S7 and pp-wave background, are related by Ino¨nu¨–Wigner contractions. The super-AdS4(7)×S7(4) algebras allow to introduce two contraction parameters, the one for the flat limit to the super-Poincare´ algebra and the other for a Penrose limit to the super-pp-wave algebra. Under these contractions supersymmetries are maintained because the Jacobi identity of three supercharges holds for any values of contraction parameters. [Copyright &y& Elsevier]

The isometry algebras of the maximally supersymmetric solutions of IIB supergravity are derived by the Ino¨nu¨–Wigner contractions of the super-AdS5×S5 algebra. The super-AdS5×S5 algebra allows introducing two contraction parameters; the one for the Penrose limit to the maximally supersymmetric pp-wave algebra and the AdS5×S5 radius for the flat limit. The fact that the Jacobi identity of three supercharges holds irrespectively of these parameters reflects the fact that the number of supersymmetry is not affected under both contractions. [Copyright &y& Elsevier]

A class of radiative solutions of Einstein's field equations with a negative cosmological constant and a pure radiation is investigated. The space-times, which generalize the Defrise solution, represent exact gravitational waves which interact with null matter and propagate in the anti–de Sitter universe. Interestingly, these solutions have homogeneous and non-singular wave-fronts for all freely moving observers. We also study properties of sandwich and impulsive waves which can be constructed in this class of space-times. [ABSTRACT FROM AUTHOR]

The renormalised value of〈φ2〉 is calculated for amassless, conformally coupled scalar field in theHartle-Hawking vacuum state. This quantity is used as ameasure of vacuum polarization induced by the presence of gravitation. It isalso a step towards the calculation of the gravitationalback reaction of the field in a black cosmic stringspacetime which is asymptotically anti-de Sitter and possesses a non constant dilaton field. Itis found that the field is divergence free throughoutthe spacetime and attains its maximum value near thehorizon. [ABSTRACT FROM AUTHOR]

The Cayley–Klein (CK) formalism is applied to the real algebra so (5) by making use of four graded contraction parameters describing, in a unified setting, 81 Lie algebras, which cover the (anti-)de Sitter, Poincaré, Newtonian and Carrollian algebras. Starting with the Drinfel'd–Jimbo real Lie bialgebra for so (5) together with its Drinfel'd double structure, we obtain the corresponding CK bialgebra and the CK r-matrix coming from a Drinfel'd double. As a novelty, we construct the (first-order) noncommutative CK spaces of points, lines, 2-planes and 3-hyperplanes, studying their structural properties. By requiring dealing with real structures, we found that there exist 63 specific real Lie bialgebras together with their sets of four noncommutative spaces. Furthermore, we found 14 classical r-matrices coming from Drinfel'd doubles, obtaining new results for the de Sitter so (4 , 1) and anti-de Sitter so (3 , 2) as well as for some of their contractions. These geometric results were exhaustively applied onto the (3 + 1)D kinematical algebras, considering not only the usual (3 + 1)D spacetime but also the 6D space of lines. We established different assignations between the geometrical CK generators and the kinematical ones, which convey physical identifications for the CK contraction parameters in terms of the cosmological constant/curvature Λ and the speed of light c. We, finally, obtained four classes of kinematical r-matrices together with their noncommutative spacetimes and spaces of lines, comprising all κ -deformations as particular cases. [ABSTRACT FROM AUTHOR]

We explain how General Relativity with a cosmological constant arises as a broken symmetry phase of a BF theory. In particular we show how to treat de Sitter and anti-de Sitter cases simultaneously. This is then used to formulate a quantisation of General Relativity through a spin foam perturbation theory. We then briefly discuss how to calculate the effective action in this quantization procedure.

We derive the non-relativistic c → ∞ and ultra-relativistic c → 0 limits of the κ -deformed symmetries and corresponding spacetime in (3+1) dimensions, with and without a cosmological constant. We apply the theory of Lie bialgebra contractions to the Poisson version of the κ -(A)dS quantum algebra, and quantize the resulting contracted Poisson–Hopf algebras, thus giving rise to the κ -deformation of the Newtonian (Newton–Hooke and Galilei) and Carrollian (Para-Poincaré, Para-Euclidean and Carroll) quantum symmetries, including their deformed quadratic Casimir operators. The corresponding κ -Newtonian and κ -Carrollian noncommutative spacetimes are also obtained as the non-relativistic and ultra-relativistic limits of the κ -(A)dS noncommutative spacetime. These constructions allow us to analyze the non-trivial interplay between the quantum deformation parameter κ , the curvature parameter η and the speed of light parameter c. [ABSTRACT FROM AUTHOR]

We study the problem of construction of global isometric embedding for spherically symmetric black holes with negative cosmological constant in various dimensions. Firstly, we show that there is no such embedding for 4D RN-AdS black hole in 6D flat ambient space, completing the classification which we started earlier. Then we construct an explicit embedding of non-spinning BTZ black hole in 6D flat ambient space. Using this embedding as an anzats, we then construct a global explicit embedding of d-dimensional Schwarzschild-AdS black hole in a flat (d + 3) -dimensional ambient space. [ABSTRACT FROM AUTHOR]