International Journal of Modern Physics D

Penrose¹ has emphasized how the initial big bang singularity requires a special low entropy state. We address how recent brane cosmological schemes address this problem and whether they offer any apparent resolution. Pushing the start time back to t = -∞, or utilizing maximally symmetric AdS spaces, simply exacerbates or transfers the problem. Since the entropy of de Sitter space is S ≤ 1/Λ, using the present acceleration of the universe as a low energy (Λ ~ 10^-120) inflationary stage, as in cyclic ekpyrotic models, produces a gravitational heat death after one cycle. Only higher energy driven inflation, together with a suitable, quantum gravity holography style, restriction on ab initio degrees of freedom, gives a suitable low entropy initial state. We question the suggestion that a high energy inflationary stage could be naturally reentered by Poincaré recurrence within a finite causal region of an accelerating universe.

We further give a heuristic argument that the so-called eternal inflation is not consistent with the second law of thermodynamics within a causal patch.

Within a cosmological framework, we provide a Hamiltonian analysis of the Mixmaster Universe dynamics on the base of a standard Arnowitt–Deser–Misner approach, showing how the chaotic behavior characterizing the evolution of the system near the cosmological singularity can be obtained as the semiclassical limit of the canonical quantization of the model in the same dynamical representation. The relation between this intrinsic chaotic behavior and the indeterministic quantum dynamics is inferred through the coincidence between the microcanonical probability distribution and the semiclassical quantum one.

Within the spirit of five-dimensional gravity in the Randall-Sundrum scenario, in this paper we consider cosmological and gravitational implications induced by forcing the spacetime metric to satisfy a Misner-like symmetry. We first show that in the resulting Misner-brane framework the Friedmann metric for a radiation dominated flat universe and the Schwarzschild or anti-de Sitter black hole metrics are exact solutions on the branes, but the model cannot accommodate any inflationary solution. The horizon and flatness problems can however be solved in Misner-brane cosmology by causal and noncausal communications through the extra dimension between distant regions which are outside the horizon. Based on a semiclassical approximation to the path-integral approach, we have calculated the quantum state of the Misner-brane universe and the quantum perturbations induced on its metric by brane propagation along the fifth direction. We have then considered testable predictions from our model. These include a scale-invariant spectrum of density perturbations whose amplitude can be naturally accommodated to the required value 10^-5-10^-6, and a power spectrum of CMB anisotropies whose acoustic peaks are at the same sky angles as those predicted by inflationary models, but having much smaller secondary-peak intensities. These predictions seem to be compatible with COBE and recent Boomerang and Maxima measurements.

We formulate the requirements which lead to the existence of a class of globally regular solutions of the minimally coupled GR equations asymptotically de Sitter at the center. The source term for this class, invariant under boosts in the radial direction, is classified as spherically symmetric vacuum with variable density and pressure associated with an r-dependent cosmological term , whose asymptotic at the origin, dictated by the weak energy condition, is the Einstein cosmological term Λg_μν, while asymptotic at infinity is de Sitter vacuum with λ < Λ or Minkowski vacuum. For this class of metrics the mass m defined by the standard ADM formula is related to both the de Sitter vacuum trapped at the origin and the breaking of space–time symmetry. In the case of the flat asymptotic, space–time symmetry changes smoothly from the de Sitter group at the center to the Lorentz group at infinity through radial boosts in between. Geometry is asymptotically de Sitter as r → 0 and asymptotically Schwarzschild at large r. In the range of masses m ≥ m_crit, the de Sitter–Schwarzschild geometry describes a vacuum nonsingular black hole (ΛBH), and for m < m_crit it describes G-lump — a vacuum selfgravitating particle-like structure without horizons. In the case of de Sitter asymptotic at infinity, geometry is asymptotically de Sitter as r → 0 and asymptotically Schwarzschild–de Sitter at large r. Λ_μν geometry describes, dependently on parameters m and and choice of coordinates, a vacuum nonsingular cosmological black hole, self-gravitating particle-like structure at the de Sitter background λg_μν, and regular cosmological models with cosmological constant evolving smoothly from Λ to λ.

We extend to higher dimensions a recent work of Bonnor, which generalizes the Einstein–Straus model utilizing the inhomogeneous Tolman–Bondi universe in place of the homogeneous Friedmann one. Following Israel's junction conditions, the criteria of matching between the higher dimensional Schwarzschild-like interior and the Tolman–Bondi-like exterior is obtained. We also give a new exact solution for a five-dimensional TB type of metric and use it to study the dynamical behavior of the vacuole boundary. Furthermore the transformation relations which transform the inhomogeneous TB metric to the homogeneous Friedmann model are explicitly given for any arbitrary dimensions. The frequency shift of radiation coming from the boundary surface is calculated and it is found that, depending on initial conditions both redshift and blue-shift are possible for an expanding vacuole. This is at variance with Bonnor's result where only redshift is possible under similar situation. It is also observed that higher dimensional models are less stable against perturbation than the usual 4D ones.

Neutrino asymmetry in general relativistic radiative spacetime exterior to spinning stars is investigating by making use of Newman–Penrose (NP) spin coefficient formalism. It is shown that neutrino current depends on the direction of rotation of the star. The solution is obtained in test field approximation where the neutrinos do not generate gravitational fields.

We consider the evolution of a 4D-universe embedded in a five-dimensional (bulk) world with a large extra dimension and a cosmological constant. The cosmology in 5D possesses "wave-like" character in the sense that the metric coefficients in the bulk are functions of the extra coordinate and time in a way similar to a pulse or traveling wave propagating along the fifth dimension. This assumption is motivated by some recent work presenting the big-bang as a higher dimensional shock wave. We show that this assumption, together with an equation of state for the effective matter quantities in 4D, allows Einstein's equations to be fully integrated. We then recover the familiar FLRW universes, on the four-dimensional hypersurfaces orthogonal to the extra dimension. Regarding the extra dimension we find that it is growing in size if the universe is speeding up its expansion. We also get an estimate for the relative change of the extra dimension over time. This estimate could have important observational implications, notably for the time variation of rest mass, electric charge and the gravitational "constant". Our results extend previous ones in the literature.

An investigation on the subject of evolution of propagation diagrams and obtaining the theoretical frequency spectrum of some δ Scuti star models with masses around 2 M_⊙ has been presented. The variations of some eigenfunctions throughout the star, the variation of ω² with logT_e and the distribution of nodes of eigenfunctions of some modes along with the evolution of the star have been plotted and examined. For the models at the ZAMS phase, pure acoustic modes in the outer stellar layers and pure gravity modes in the interiors were calculated. A mixed character of low degree nonradial modes was found in evolved models. These modes behave like p modes in the envelope and like g modes in the interior.

The entropy of a rotating and arbitrarily accelerating black hole whose metric changes slowly is calculated using the thin film brick-wall model. We obtain the entropy density at every point of the horizon surface and the total entropy of the black hole. The results show that the entropy of the nonstationary black hole is also proportional to the surface area of the black hole's event horizon as in the cases of stationary black holes.

We present cylindrically symmetric, static solutions of the Einstein field equations around a line singularity such that the energy momentum tensor corresponds to infinitely thin photonic shells. Positivity of the energy density of the thin shell and the line singularity is discussed. It is also shown that thick shells containing mostly radiation are possible in a numerical solution.

In this paper, we study in detail a perfect fluid cosmological model with time-varying "constants" using dimensional analysis and the symmetry method. We examine the case of variable "constants" in detail without considering the perfect fluid model as a limiting case of a model with a causal bulk viscous fluid as discussed in a recent paper. We obtain some new solutions through the Lie method and show that when matter creation is considered, these solutions are physically relevant.

A model is proposed for a collapsing radiating star consisting of a fluid with shear motion undergoing radial heat flow with outgoing radiation. The pressure of the star, at the beginning of the collapse, is isotropic but due to the presence of the shear motion of the fluid the pressure becomes more and more anisotropic. The radial and temporal behaviors of the density, the pressure, the total mass, the luminosity, the effective adiabatic index and the Kretschmann scalar are analyzed for a star with 6 M_⊙. The final evolution is a star that radiates all its mass during the collapse, and thus, neither forming a black hole, as in the previous model, nor a naked singularity.