International Journal of Modern Physics A

In the first part of the review, I discuss ways of obtaining Lorentz-Invariance Violating (LIV) space–time foam in the modern context of string theory, involving brane world scenarios. The foamy structures are provided by lower-dimensional background brane defects in a D3-brane universe, whose density is a free parameter to be constrained phenomenologically. Such constraining can be provided by high energy gamma ray photon tests, including ultra-high energy/infrared photon–photon scattering. In the second part, I analyze the currently available data from MAGIC and FERMI telescopes on delayed cosmic photon arrivals in this context. It is understood of course that conventional astrophysics source effects, which currently are far from being understood, might be the dominant reason for the observed delayed arrivals. I also discuss how the stringent constraints from studies of synchrotron-radiation from distant Nebulae, absence of cosmic birefringence and nonobservation of ultra-high energy cosmic photons can be accommodated within the aforementioned stringy space–time foam model. I argue that, at least within the currently available sets of astrophysical data, the stringy foam model can avoid all theses constraints in a natural range of the string coupling and mass scale. The key features are: (i) transparency of the foam to electrons and charged probes in general, (ii) absence of birefringence effects and (iii) a breakdown of the local effective Lagrangian formalism. However, in order to accommodate, in this theoretical framework, the data of the FERMI satellite on the delayed arrival of photons from the short intense Gamma Ray Burst GRB 090510, in a way consistent with the findings of the MAGIC telescope, a nonuniform density of brane foam defects must be invoked.

We continue our discussion of the general bosonic prototype of the new orbifold-string theories of permutation-type. Supplementing the extended physical-state conditions of the previous paper, we construct here the extended Virasoro generators with cycle central charge , where f_j(σ) is the length of cycle j in twisted sector σ. We also find an equivalent, reduced formulation of each physical-state problem at reduced cycle central charge c_j(σ) = 26. These tools are used to begin the study of the target space–time dimension of cycle j in sector σ, which is naturally defined as the number of zero modes (momenta) of each cycle. The general model-dependent formulae derived here will be used extensively in succeeding papers, but are evaluated in this paper only for the simplest case of the "pure" permutation orbifolds.

We consider excitations around the recently introduced near-NHEK metric describing the near-horizon geometry of the near-extremal four-dimensional Kerr black hole. This geometry has a U(1)_L × U(1)_R isometry group which can be enhanced to a pair of commuting Virasoro algebras. We present boundary conditions for which the conserved charges of the corresponding asymptotic symmetries are well defined and nonvanishing and find the central charges c_L = 12J/ℏ and c_R = 0 where J is the angular momentum of the black hole. Applying the Cardy formula reproduces the Bekenstein–Hawking entropy of the black hole. This suggests that the near-extremal Kerr black hole is holographically dual to a nonchiral two-dimensional conformal field theory.

The Cardy–Verlinde formula is analyzed in the contest of the gravitational collapse. Starting from the holographic principle, we show how the equations for a homogeneous and isotropic gravitational collapse describe the formation of the black hole entropy. Some comments on the role of the entangled entropy and the connection with the c-theorem are made.

We apply the tunneling process of charged massive particles through the quantum horizon of a Reissner–Nordström black hole in a new noncommutative gravity scenario. In this model, the tunneling amplitude on account of noncommutativity influences in the context of coordinate coherent states is modified. Our calculation points out that the emission rate satisfies the first law of black hole thermodynamics and is consistent with an underlying unitary theory.

In the present work we investigated the validity of the generalized second law (GSL) of thermodynamics in the presence of interaction between DBI-essence and other four candidates of dark energy, namely the modified Chaplygin gas, hessence, tachyonic field and new agegraphic dark energy. It has been observed that the GSL breaks down in the presence of the interactions. However, the event horizon remains to be an increasing function of time.

The quantum H₃ integrable system is a three-dimensional system with rational potential related to the noncrystallographic root system H₃. It is shown that the gauge-rotated H₃ Hamiltonian as well as one of the integrals, when written in terms of the invariants of the Coxeter group H₃, is in algebraic form: it has polynomial coefficients in front of derivatives. The Hamiltonian has infinitely-many finite-dimensional invariant subspaces in polynomials, they form the infinite flag with the characteristic vector . One among possible integrals is found (of the second order) as well as its algebraic form. A hidden algebra of the H₃ Hamiltonian is determined. It is an infinite-dimensional, finitely-generated algebra of differential operators possessing finite-dimensional representations characterized by a generalized Gauss decomposition property. A quasi-exactly-solvable integrable generalization of the model is obtained. A discrete integrable model on the uniform lattice in a space of H₃-invariants "polynomially"-isospectral to the quantum H₃ model is defined.