Geodésicas e momento angular constante no espaço Anti-de Sitter (2,3)

Considering generalised action for dilaton coupled Maxwell–Einstein theory in four dimensions, Gao and Zhang obtained black holes solutions for asymptotically anti de Sitter (Ads) and de Sitter (ds) spacetimes. We study the Hawking radiation in Parikh–Wilczek's tunneling formalism as well as using Bogoliubov transformations. We compare the expression of the Hawking temperature obtained from these two different approaches. Stability and the extremality conditions for such black holes are discussed. The exact dependences of the Hawking temperature and flux on the dilaton coupling parameter are determined. It is shown that the Hawking flux increases with the dilaton coupling parameter. Finally we show that the expression for the Hawking flux obtained using Bogoliubov transformation matches exactly with flux calculated via chiral gauge and gravitational anomalies. This establishes a correspondence among all these different approaches of estimating Hawking radiation from these classes of black holes.

Stability of black holes and solitons in Anti-de Sitter space-time

We study the quasi-normal modes (QNM) of scalar, electromagnetic and gravitational perturbations of black holes in general relativity whose horizons have toroidal, cylindrical or planar topology in an asymptotically anti-de Sitter (AdS) spacetime. The associated QNM frequencies describe the decay in time of the corresponding test field in the vicinities of the black hole. In terms of the AdS/CFT conjecture, the inverse of the frequency is a measure of the dynamical timescale of approach to thermal equilibrium of the corresponding conformal field theory.

The time-scale of thermalization in holographic dual models with a chemical potential in diverse number of dimensions is systematically investigated using the gauge/gravity duality. We consider a model with a thin-shell of charged dust collapsing from the boundary toward the bulk interior of asymptotically anti-de Sitter (AdS) spaces. In the outer region there is a Reissner-Nordstr\"om-AdS black hole (RNAdS-BH), while in the inner region there is an anti-de Sitter space. We consider renormalized geodesic lengths and minimal area surfaces as probes of thermalization, which in the dual quantum field theory (QFT) correspond to two-point functions and expectation values of Wilson loops, respectively. We show how the behavior of these extensive probes changes for charged black holes in comparison with Schwarzschild-AdS black holes (AdS-BH), for different values of the black hole mass and charge. The full range of values of the chemical potential over temperature ratio in the dual QFT is investigated. In all cases, the structure of the thermalization curves shares similar features with those obtained from the AdS-BH. On the other hand, there is an important difference in comparison with the AdS-BH: the thermalization times obtained from the renormalized geodesic lengths and the minimal area surfaces are larger for the RNAdS-BH, and they increase as the black hole charge increases.

We develop a formalism to calculate the effective action of the strongly coupled conformal field theory (CFT) in curved spacetime. The effective action of the CFT is obtained from AdS/CFT correspondence. The anti de-Sitter (AdS) spacetime has various slicing which give various curved spacetime on its boundary. We show the de Sitter spacetime and the Friedmann-Robertson-Walker (FRW) universe can be embedded in the AdS spacetime and derive the scalar two-point function of the conformal fields in those spacetime. In curved spacetime, the two-point function depends on the vacuum state of the CFT. A method to specify the vacuum state in AdS/CFT calculations is shown. Because the classical action in AdS spacetime diverges near the boundary, we need the counter terms to regulate the result. The simple derivation of the counter terms using the Hamilton-Jacobi equation is also presented in the appendix.

In three dimensions, it is known that field theories possessing extended $(p,q)$ anti-de Sitter (AdS) supersymmetry with ${\cal N}=p+q \geq 3$ can be realised in (2,0) AdS superspace. Here we present a formalism to reduce every field theory with (2,0) AdS supersymmetry to ${\cal N}=1$ AdS superspace. As nontrivial examples, we consider supersymmetric nonlinear sigma models formulated in terms of ${\cal N}=2$ chiral and linear supermultiplets. The $(2,0) \to (1,0)$ AdS reduction technique is then applied to the off-shell massless higher-spin supermultiplets in (2,0) AdS superspace constructed in [1]. As a result, for each superspin value $\hat s$, integer $(\hat s= s)$ or half-integer $(\hat s= s+1/2)$, with $s=1,2,\dots $, we obtain two off-shell formulations for a massless ${\cal N}=1$ superspin-$\hat s$ multiplet in AdS${}_3$. These models prove to be related to each other by a superfield Legendre transformation in the flat superspace limit, but the duality is not lifted to the AdS case. Two out of the four series of ${\cal N}=1$ supersymmetric higher-spin models thus derived are new. The constructed massless ${\cal N}=1$ supersymmetric higher-spin actions in AdS${}_3$ are used to formulate (i) higher-spin supercurrent multiplets in ${\cal N}=1$ AdS superspace; and (ii) new topologically massive higher-spin off-shell supermultiplets. Examples of ${\cal N}=1$ higher-spin supercurrents are given for models of a complex scalar supermultiplet. We also present two new off-shell formulations for a massive ${\cal N}=1$ gravitino supermultiplet in AdS${}_3$.

The stress-energy tensors are computed for scalar and spinor fields with arbitrary mass in anti-de Sitter spacetime using the $\ensuremath{\zeta}$-function technique. The results are compared with those obtained by Pauli-Villars regularization. It is found that they agree with one another. The trace anomaly for the Wess-Zumino model (the scalar supermultiplet) in anti-de Sitter spacetime is studied. It is concluded that the trace anomaly must take the conventional value in this model although the physical significance of the stress-energy tensor is not clear in anti-de Sitter spacetime. The relation between the $\ensuremath{\zeta}$-function and Pauli-Villars methods in an arbitrary space is also clarified.

The supertwistor and bi-supertwistor formulations for N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document}-extended anti-de Sitter (AdS) superspace in four dimensions, AdS4∣4N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ Ad{S}^{4\\mid 4\\mathcal{N}} $$\\end{document}, were derived two years ago in [1]. In the present paper, we introduce a novel realisation of the N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document}-extended AdS supergroup OSp(N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document}|4; ℝ) and apply it to develop a coset construction for AdS4∣4N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\ extrm{AdS}}^{4\\mid 4\\mathcal{N}} $$\\end{document} and the corresponding differential geometry. This realisation naturally leads to an atlas on AdS4∣4N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\ extrm{AdS}}^{4\\mid 4\\mathcal{N}} $$\\end{document} (that is a generalisation of the stereographic projection for a sphere) that consists of two charts with chiral transition functions for N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} > 0. A manifestly OSp(N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document}|4; ℝ) invariant model for a superparticle in AdS4∣4N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\ extrm{AdS}}^{4\\mid 4\\mathcal{N}} $$\\end{document} is proposed. Additionally, by employing a conformal superspace approach, we describe the most general conformally flat N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document}-extended supergeometry. This construction is then specialised to the case of AdS4∣4N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\ extrm{AdS}}^{4\\mid 4\\mathcal{N}} $$\\end{document}.

We derive a map between Einstein spaces of positive and negative curvature,\nincluding scalar matter. Starting from a space of positive curvature with some\ndimensions compactified on a sphere and analytically continuing the number of\ncompact dimensions, we obtain a space of negative curvature with a compact\nhyperbolic subspace, and vice versa. Prime examples of such spaces are de\nSitter (dS) and anti-de Sitter (AdS) space, as well as black hole spacetimes\nwith (A)dS asymptotics and perturbed versions thereof, which play an important\nrole in holography. This map extends work done by Caldarelli et al., who map\nasymptotically AdS spaces to Ricci-flat ones. A remarkable result is that the\nboundary of asymptotically AdS spaces is mapped to a brane in the bulk of de\nSitter, and perturbations near the AdS boundary are sourced by a stress tensor\nconfined to this brane. We also calculate the Brown-York stress tensor for the\nperturbed AdS metric, which turns out to be the negative of the stress tensor\non the de Sitter brane. The map can also be used as a solution generator, and\nwe obtain a Kerr/AdS solution with hyperbolic horizon from a known Kerr/dS one.\n

In this work, test particle dynamics around a static regular Bardeen black hole (BH) in Anti-de Sitter spacetime has been studied. It has been shown for neutral test particles that parameters of a regular Bardeen black hole in Anti-de Sitter spacetime can mimic the rotation parameter of the Kerr metric up to the value a≈0.9 providing the same innermost stable circular orbit (ISCO) radius. We have also explored the dynamics of magnetized particles with a magnetic dipole moment around a magnetically charged regular Bardeen black hole in Anti-de Sitter spacetime. As a realistic astrophysical scenario of the study, we have treated neutron stars orbiting a supermassive black hole (SMBH), in particular, the magnetar PSR J1745-2900 orbiting Sgr A* with the parameter β=10.2, as magnetized test particles. The magnetized particles dynamics shows that the parameter β, negative values of cosmological constant and magnetic charge parameter of the central BH cause a decrease in the ISCO radius. We have compared the effects of the magnetic charge of the Bardeen BH with the spin of rotating Kerr BH and shown that magnetic charge parameter can mimic the spin in the range a/M≃(0,0.7896) when Λ=0 at the range of its values g/M≃(0,0.648).

The goal of the present note is to understand whether it is possible to define interacting quantum field theory in global anti de Sitter space-time with Lorentzian signature, in its covering space-time (whose time coordinate is not periodic) and in its Poincare patch. We show that in global anti de Sitter space-time there are certain problems to define quantum field theory properly. This is due to an additional UV singularity of the Feynman propagator which is sitting on the light-cone emanating from the antipodal point of the source. There is no such singularity in flat space-time. At the same time quantum field theory in Poincare region of the AdS space-time can be well defined and is related to the one in Euclidean AdS via the analytical continuation. In principle one can also define and analytically continue quantum field theory in the covering anti de Sitter space-time. However, to do that one has to use an unusual $i\epsilon$-prescription in the Feynman propagator, which cannot be used in loop calculations in non-stationary situations.

Gravitational collapse of radiation in an anti-de Sitter background is studied. For the spherical case, the collapse proceeds in much the same way as in the Minkowski background, i.e., massless naked singularities may form for a highly inhomogeneous collapse, violating the cosmic censorship, but not the hoop conjecture. The toroidal, cylindrical and planar collapses can be treated together. In these cases no naked singularity ever forms, in accordance with the cosmic censorship. However, since the collapse proceeds to form toroidal, cylindrical or planar black holes, the hoop conjecture in an anti-de Sitter spacetime is violated.

For generic field theories at finite temperature, a power-law falloff of correlation functions of conserved currents at long times is a prediction of non-linear hydrodynamics. We demonstrate, through a one-loop computation in Einstein gravity in Anti de Sitter space, that this effect is reproduced by the dynamics of black hole horizons. The result is in agreement with the gauge-gravity correspondence.

We investigate the vacuum expectation value (VEV) of the energy-momentum tensor for the electromagnetic field in anti-de Sitter (AdS) spacetime in the presence of a boundary parallel to the AdS horizon. On the boundary, the field obeys the generalized perfect conductor boundary condition. The VEV of the energy-momentum tensor is decomposed into the boundary-free and boundary-induced contributions. In this way, for points away from the boundary, the renormalization is reduced to that for AdS spacetime without the boundary. The boundary-induced energy density is negative everywhere, and the normal stress is positive in the region between the boundary and the AdS boundary and is negative in the region between the boundary and the AdS horizon. Near both the AdS boundary and horizon, the boundary-induced VEV decays exponentially as a function of the corresponding proper distance. Applications are given for even and odd vector fields in Randall–Sundrum model with a single brane.

Vacuum expectation value of the energy-momentum tensor and the vacuum interaction forces are evaluated for a massive scalar field with general curvature coupling parameter satisfying Robin boundary conditions on two codimension one parallel branes embedded in ($D+1$)-dimensional background spacetime ${\mathrm{AdS}}_{{D}_{1}+1}\ifmmode\times\else\texttimes\fi{}\ensuremath{\Sigma}$ with a warped internal space $\ensuremath{\Sigma}$. The vacuum energy-momentum tensor is presented as a sum of boundary-free, single brane-induced, and interference parts. The latter is finite everywhere including the points on the branes and is exponentially small for large interbrane distances. Unlike to the purely anti--de Sitter (AdS) bulk, the part induced by a single brane, in addition to the distance from the brane, depends also on the position of the brane in the bulk. The asymptotic behavior of this part is investigated for the points near the brane and for the position of the brane close to the AdS horizon and AdS boundary. The contribution of Kaluza-Klein modes along $\ensuremath{\Sigma}$ is discussed in various limiting cases. The vacuum forces acting on the branes are presented as a sum of the self-action and interaction terms. The first one contains well-known surface divergences and needs a further renormalization. The interaction forces between the branes are finite for all nonzero interbrane distances and are investigated as functions of the brane positions and the length scale of the internal space. We show that there is a region in the space of parameters in which these forces are repulsive for small distances and attractive for large distances. As an example, the case $\ensuremath{\Sigma}={S}^{{D}_{2}}$ is considered. An application to the higher dimensional generalization of the Randall-Sundrum brane model with arbitrary mass terms on the branes is discussed. Taking the limit with infinite curvature radius for the AdS bulk, from the general formulas we derive the results for two parallel Robin plates on background of ${R}^{({D}_{1},1)}\ifmmode\times\else\texttimes\fi{}\ensuremath{\Sigma}$ spacetime.