Electromagnetic quasinormal modes of D-dimensional black holes

Using the monodromy method we calculate the asymptotic quasinormal frequencies of an electromagnetic field moving in D-dimensional Schwarzschild and Schwarzschild de Sitter black holes (D ≥ 4). For the D-dimensional Schwarzschild anti-de Sitter black hole we also compute these frequencies with a similar method. Moreover, we calculate the electromagnetic normal modes of the D-dimensional anti-de Sitter spacetime.     

An inflationary scenario taking into account of possible dark energy effects in the early universe

We investigate the possible effect of cosmological-constant type dark energy during the inflation period of the early universe. This is accommodated by a new dispersion relation in de Sitter space. The modified inflation model of a minimally coupled scalar field is still able to yield an observation-compatible scale-invariant primordial spectrum, simultaneously having the potential to generate a spectrum with lower power at large scales. A qualitative match to the WMAP 7-year data is presented. We obtain an Ω _Λ of the same order of that in the Λ-CDM model. Possible relations between the de Sitter scenario and Doubly Special Relativity (DSR) are also discussed.     

Towards a quantization of gauge fields on de Sitter group by functional integral method

A formulation of the de Sitter symmetry as a purely inner symmetry defined on a fixed Minkowski space-time is presented. We define the generators of the de Sitter group and write the structure equations using a constant deformation parameter λ. The conserved gauge currents are calculated, and their physical meaning is given. Local gauge transformations and the corresponding covariant derivative depending on the gauge fields are also obtained. We study the behavior of gauge fields, the torsion and curvature tensors and give a regularization technique in terms of the ζ function.     

Oscillations of the F(R) dark energy in the accelerating universe

Oscillations of the F(R) dark energy around the phantom divide line, ω _DE=−1, both during the matter era and also in the de Sitter epoch are investigated. The analysis during the de Sitter epoch is revisited by expanding the modified equations of motion around the de Sitter solution. Then, during the matter epoch, the time dependence of the dark energy perturbations is discussed by using two different local expansions. For high values of the red shift, the matter epoch is a stable point of the theory, giving the possibility to expand the F(R)-functions in terms of the dark energy perturbations. In the late-time matter era, the realistic case is considered where dark energy tends to a constant. The results obtained are confirmed by precise numerical computation on a specific model of exponential gravity. A novel and very detailed discussion is provided on the critical points in the matter era and on the relation of the oscillations with possible singularities.     

Thermodynamics of Gauss–Bonnet black holes revisited

We investigate the Gauss–Bonnet black hole in five dimensional anti-de Sitter spacetimes (GBAdS). We analyze all thermodynamic quantities of the GBAdS, which is characterized by the Gauss–Bonnet coupling c and mass M, comparing with those of the Born–Infeld-AdS (BIAdS), Reissner–Norstr?m-AdS black holes (RNAdS), Schwarzschild-AdS (SAdS), and BTZ black holes. For c<0 we cannot obtain the black hole with positively definite thermodynamic quantities of mass, temperature, and entropy, because the entropy does not satisfy the area law. On the other hand, for c>0, we find the BIAdS-like black hole, showing that the coupling c plays the role of a pseudo-charge. Importantly, we could not obtain the SAdS in the limit of c→0, which means that the GBAdS is basically different from the SAdS. In addition, we clarify the connections between thermodynamic and dynamical stability. Finally, we also conjecture that if a black hole is big and thus globally stable, its quasi-normal modes may take on analytic expressions.     

Snyder''s quantized space-time and de Sitter special relativity

There is a one-to-one correspondence between Snyder’s model in de Sitter space of momenta and the dS-invariant special relativity as well as a minimum uncertainty-like relation. This indicates that physics at the Planck length ℓ _P and the scale R = (3/Λ)^1/2 should be dual to each other and there is in-between gravity of local dS-invariance characterized by a dimensionless coupling constant g = ℓ _P /R ∼ 10⁻⁶¹.      

De Sitter Relativity: a New Road to Quantum Gravity?

The Poincaré group generalizes the Galilei group for high-velocity kinematics. The de Sitter group is assumed to go one step further, generalizing Poincaré as the group governing high-energy kinematics. In other words, ordinary special relativity is here replaced by de Sitter relativity. In this theory, the cosmological constant Λ is no longer a free parameter, and can be determined in terms of other quantities. When applied to the whole universe, it is able to predict the value of Λ and to explain the cosmic coincidence. When applied to the propagation of ultra-high energy photons, it gives a good estimate of the time delay observed in extragalactic gamma-ray flares. It can, for this reason, be considered a new paradigm to approach the quantum gravity problem.     

Gravitation,thermodynamics, and the bound on viscosity

The anti-de Sitter/conformal field theory (AdS/CFT) correspondence implies that small perturbations of a black hole correspond to small deviations from thermodynamic equilibrium in a dual field theory. For gauge theories with an Einstein gravity dual, the AdS/CFT correspondence predicts a universal value for the ratio of the shear viscosity to the entropy density, η/s = 1/4π. It was conjectured recently that all fluids conform to the lower bound η/s ≥ 1/4π. This conjectured bound has been the focus of much recent attention. However, despite the flurry of research in this field we still lack a proof for the general validity of the bound. In this essay we show that this mysterious bound is actually a direct outcome of the interplay between gravity, quantum theory, and thermodynamics.     

Hadron spectroscopy and structure from AdS/CFT

The AdS/CFT correspondence between conformal field theory and string states in an extended space-time has provided new insights into not only hadron spectra, but also their light-front wave functions. We show that there is an exact correspondence between the fifth-dimensional coordinate of anti-de Sitter space z and a specific impact variable ζ which measures the separation of the constituents within the hadron in ordinary space-time. This connection allows one to predict the form of the light-front wave functions of mesons and baryons, the fundamental entities which encode hadron properties and scattering amplitudes. A new relativistic Schr?dinger light-front equation is found which reproduces the results obtained using the fifth-dimensional theory. Since they are complete and orthonormal, the AdS/CFT model wave functions can be used as an initial ansatz for a variational treatment or as a basis for the diagonalization of the light-front QCD Hamiltonian. A number of applications of light-front wave functions are also discussed.     

Unruh–DeWitt Detectors in Spherically Symmetric Dynamical Space-Times

In the present paper, Unruh–DeWitt detectors are used in order to investigate the issue of temperature associated with a spherically symmetric dynamical space-times. Firstly, we review the semi-classical tunneling method, then we introduce the Unruh–DeWitt detector approach. We show that for the generic static black hole case and the FRW de Sitter case, making use of peculiar Kodama trajectories, semiclassical and quantum field theoretic techniques give the same standard and well known thermal interpretation, with an associated temperature, corrected by appropriate Tolman factors. For a FRW space-time interpolating de Sitter space with the Einstein–de Sitter universe (that is a more realistic situation in the frame of ΛCDM cosmologies), we show that the detector response splits into a de Sitter contribution plus a fluctuating term containing no trace of Boltzmann-like factors, but rather describing the way thermal equilibrium is reached in the late time limit. As a consequence, and unlike the case of black holes, the identification of the dynamical surface gravity of a cosmological trapping horizon as an effective temperature parameter seems lost, at least for our co-moving simplified detectors. The possibility remains that a detector performing a proper motion along a Kodama trajectory may register something more, in which case the horizon surface gravity would be associated more likely to vacuum correlations than to particle creation.     

A discrete nonetheless remarkable brick in de Sitter: The “massless minimally coupled field”

Over the last ten years interest in the physics of de Sitter space—time has been growing very fast. Besides the supposed existence of a “de Sitterian period” in inflation theories, the observational evidence of an acceleration of the universe expansion (interpreted as a positive cosmological constant or a “dark energy” or some form of “quintessence”) has triggered a lot of attention in the physics community. A specific de Sitterian field called “massless minimally coupled field” (mmc) plays a fundamental role in inflation models and in the construction of the de Sitterian gravitational field. A covariant quantization of the mmc field, à la Krein—Gupta—Bleuler was proposed in Class. Quantum. Grav. 17, 1415 (2000). In this talk, we will review this construction and explain the relevance of such a field in the construction of a massless spin-2 field in de Sitter space—time.     

de Sitter branes with a bulk scalar

We propose new brane world 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 thin branes while the other one of the thick variety. The field profiles and the potentials are obtained and analysed for each case. We note that for the thick brane scenario the field profile resembles a kink, whereas for one or more thin branes, it is finite and bounded in the domain of the extra dimension. We have also addressed the localisation of gravity and other matter fields on the brane for these braneworld models.     

Black holes,AdS, and CFTs

This brief conference proceeding attempts to explain the implications of the anti-de Sitter/conformal field theory (AdS/CFT) correspondence for black hole entropy in a language accessible to relativists and other non-string theorists. The main conclusion is that the Bekenstein–Hawking entropy S _BH is the density of states associated with certain superselections sectors, defined by what may be called the algebra of boundary observables. Interestingly while there is a valid context in which this result can be restated as “S _BH counts all states inside the black hole,” there may also be another in which it may be restated as “S _BH does not count all states inside the black hole, but only those that are distinguishable from the outside.” The arguments and conclusions represent the author’s translation of the community’s collective wisdom, combined with a few recent results.     

The IR stability of de Sitter QFT: physical initial conditions

This work uses Lorentz-signature in-in perturbation theory to analyze the late-time behavior of correlators in time-dependent interacting massive scalar field theory in de Sitter space. We study a scenario recently considered by Krotov and Polyakov in which the coupling g turns on smoothly at finite time, starting from g = 0 in the far past where the state is taken to be the (free) Bunch–Davies vacuum. Our main result is that the resulting correlators (which we compute at the one-loop level) approach those of the interacting Hartle–Hawking state at late times. We argue that similar results should hold for other physically-motivated choices of initial conditions. This behavior is to be expected from recent quantum “no hair” theorems for interacting massive scalar field theory in de Sitter space which established similar results to all orders in perturbation theory for a dense set of states in the Hilbert space. Our current work (1) indicates that physically motivated initial conditions lie in this dense set, (2) provides a Lorentz-signature counter-part to the Euclidean techniques used to prove such theorems, and (3) provides an explicit example of the relevant renormalization techniques.     

CMC Hypersurfaces on Riemannian and Semi-Riemannian Manifolds

In this paper we generalize the explicit formulas for constant mean curvature (CMC) immersion of hypersurfaces of Euclidean spaces, spheres and hyperbolic spaces given in Perdomo (Asian J Math 14(1):73–108, 2010; Rev Colomb Mat 45(1):81–96, 2011) to provide explicit examples of several families of immersions with constant mean curvature and non constant principal curvatures, in semi-Riemannian manifolds with constant sectional curvature. In particular, we prove that every h ? [-1,-\frac2?{n-1}n)h\in[-1,-\frac{2\sqrt{n-1}}{n}) can be realized as the constant curvature of a complete immersion of S₁^n-1×\mathbbRS_1^{n-1}\times \mathbb{R} in the (n + 1)-dimensional de Sitter space S₁ⁿ⁺¹\hbox{\bf S}_1^{n+1}. We provide 3 types of immersions with CMC in the Minkowski space, 5 types of immersion with CMC in the de Sitter space and 5 types of immersion with CMC in the anti de Sitter space. At the end of the paper we analyze the families of examples that can be extended to closed hypersurfaces.     

Does entropic force always imply the Newtonian force law?

We investigate propagations of graviton and additional scalar on four-dimensional anti-de Sitter (AdS₄) space using f(R) gravity models with external sources. It is shown that there is the van Dam–Veltman–Zakharov (vDVZ) discontinuity in f(R) gravity models because f(R) gravity implies GR with additional scalar. This clearly indicates a difference between general relativity and f(R) gravity.     

Generalised Chern–Simons actions for 3d gravity and κ-Poincaré symmetry

We consider Chern–Simons theories for the Poincaré, de Sitter and anti-de Sitter groups in three dimensions which generalise the Chern–Simons formulation of 3d gravity. We determine conditions under which κ-Poincaré symmetry and its de Sitter and anti-de Sitter analogues can be associated to these theories as quantised symmetries. Assuming the usual form of those symmetries, with a timelike vector as deformation parameter, we find that such an association is possible only in the de Sitter case, and that the associated Chern–Simons action is not the gravitational one. Although the resulting theory and 3d gravity have the same equations of motion for the gauge field, they are not equivalent, even classically, since they differ in their symplectic structure and the coupling to matter. We deduce that κ-Poincaré symmetry is not associated to either classical or quantum gravity in three dimensions. Starting from the (non-gravitational) Chern–Simons action we explain how to construct a multi-particle model which is invariant under the classical analogue of κ-de Sitter symmetry, and carry out the first steps in that construction.     

Quasinormal modes of D-dimensional de Sitter spacetime

We calculate the exact values of the quasinormal frequencies for an electromagnetic field and a gravitational perturbation moving in D-dimensional de Sitter spacetime (D ≥ 4). We also study the quasinormal modes of a real massive scalar field and compare our results with those of other references.