Red-shifts near black holes

A simple ordinary differential equation is derived governing the red-shifts of wave-fronts propagating through a non-stationary spherically symmetric space-time. Approach to an event horizon corresponds to approach to a fixed point; in general, the phase portrait of the equation illuminates the qualitative features of the geometry. In particular, the asymptotics of the red-shift as a horizon is approached, a critical ingredient of Hawking's prediction of radiation from black holes, are easily brought out. This asympotic behavior has elements in common with the universal behavior near phase transitions in statistical physics. The validity of the Unruh vacuum for the Hawking process can be understood in terms of this universality. The concept of surface gravity is extended to to non-stationary spherically symmetric black holes. Finally, it is shown that in the non-stationary case, Hawking's predicted flux of radiation from a black hole would be modified.Comment: 20 pages, plain Tex, IOP macros, 4 eps figures, accepted by CQ

The Gauge Fields and Ghosts in Rindler Space

We consider 2d Maxwell system defined on the Rindler space with metric ds^2=\exp(2a\xi)\cdot(d\eta^2-d\xi^2) with the goal to study the dynamics of the ghosts. We find an extra contribution to the vacuum energy in comparison with Minkowski space time with metric ds^2= dt^2-dx^2. This extra contribution can be traced to the unphysical degrees of freedom (in Minkowski space). The technical reason for this effect to occur is the property of Bogolubov's coefficients which mix the positive and negative frequencies modes. The corresponding mixture can not be avoided because the projections to positive -frequency modes with respect to Minkowski time t and positive -frequency modes with respect to the Rindler observer's proper time \eta are not equivalent. The exact cancellation of unphysical degrees of freedom which is maintained in Minkowski space can not hold in the Rindler space. In BRST approach this effect manifests itself as the presence of BRST charge density in L and R parts. An inertial observer in Minkowski vacuum |0> observes a universe with no net BRST charge only as a result of cancellation between the two. However, the Rindler observers who do not ever have access to the entire space time would see a net BRST charge. In this respect the effect resembles the Unruh effect. The effect is infrared (IR) in nature, and sensitive to the horizon and/or boundaries. We interpret the extra energy as the formation of the "ghost condensate" when the ghost degrees of freedom can not propagate, but nevertheless do contribute to the vacuum energy. Exact computations in this simple 2d model support the claim made in [1] that the ghost contribution might be responsible for the observed dark energy in 4d FLRW universe.Comment: Final version to appear in Phys. Rev. D. Comments on relation with energy momentum computations and few new refs are adde

Twist and teleportation analogy of the black hole final state

Mathematical connection between the quantum teleportation, the most unique feature of quantum information processing, and the black hole final state is studied taking into account the non trivial spacetime geometry. We use the twist operatation for the generalized entanglement measurement and the final state boundary conditions to obtain transfer theorems for the black hole evaporation. This would enable us to put together the universal quantum teleportation and the black hole evaporation in the unified mathematical footing. For a renormalized post selected final state of outgoing Hawking radiation, we found that the measure of mixedness is preserved only in the special case of final-state boundary condition in the micro-canonical form, which resmebles perfect teleportation channel.Comment: version_

Creation of a brane world with Gauss-Bonnet term

We study a creation of a brane world using an instanton solution. We analyze a brane model with a Gauss-Bonnet term in a bulk spacetime. The curvature of 3-brane is assumed to be closed, flat, or open. We construct instanton solutions with branes for those models, and calculate the value of the actions to discuss an initial state of a brane universe.Comment: 9 pages, 10 figure

Diffeomorphism on Horizon as an Asymptotic Isometry of Schwarzschild Black Hole

It is argued that the diffeomorphism on the horizontal sphere can be regarded as a nontrivial asymptotic isometry of the Schwarzschild black hole. We propose a new boundary condition of asymptotic metrics near the horizon and show that the condition admits the local time-shift and diffeomorphism on the horizon as the asymptotic symmetry.Comment: 18 pages, no figures, corrected some typo

Matter in Toy Dynamical Geometries

One of the objectives of theories describing quantum dynamical geometry is to compute expectation values of geometrical observables. The results of such computations can be affected by whether or not matter is taken into account. It is thus important to understand to what extent and to what effect matter can affect dynamical geometries. Using a simple model, it is shown that matter can effectively mold a geometry into an isotropic configuration. Implications for "atomistic" models of quantum geometry are briefly discussed.Comment: 8 pages, 1 figure, paper presented at DICE 200

Classical and quantum radiation from a moving charge in an expanding universe

We investigate photon emission from a moving particle in an expanding universe. This process is analogous to the radiation from an accelerated charge in the classical electromagnetic theory. Using the framework of quantum field theory in curved spacetime, we demonstrate that the Wentzel-Kramers-Brillouin (WKB) approximation leads to the Larmor formula for the rate of the radiation energy from a moving charge in an expanding universe. Using exactly solvable models in a radiation-dominated universe and in a Milne universe, we examine the validity of the WKB formula. It is shown that the quantum effect suppresses the radiation energy in comparison with the WKB formula.Comment: 16 pages, JCAP in pres

Multidimensional world, inflation and modern acceleration

Starting from pure multidimensional gravity with curvature-nonlinear terms but no matter fields in the initial action, we obtain a cosmological model with two effective scalar fields related to the size of two extra factor spaces. The model includes both an early inflationary stage and that of modern accelerated expansion and satisfies the observational data. There are no small parameters; the effective inflaton mass depends on the initial conditions which explain its small value as compared to the Planck mass. At the modern stage, the size of extra dimensions slowly increases, therefore this model predicts drastic changes in the physical laws of our Universe in the remote future.Comment: 7 two-column revtex pages, 2 figure

Self-stabilization of extra dimensions

We show that the problem of stabilization of extra dimensions in Kaluza-Klein type cosmology may be solved in a theory of gravity involving high-order curvature invariants. The method suggested (employing a slow-change approximation) can work with rather a general form of the gravitational action. As examples, we consider pure gravity with Lagrangians quadratic and cubic in the scalar curvature and some more complex ones in a simple Kaluza-Klein framework. After a transition to the 4D Einstein conformal frame, this results in effective scalar field theories with certain effective potentials, which in many cases possess positive minima providing stable small-size extra dimensions. Estimates made in the original (Jordan) conformal frame show that the problem of a small value of the cosmological constant in the present Universe is softened in this framework but is not solved completely.}Comment: 10 pages, 4 figures, revtex4. Version with additions and corrections, accepted at Phys. Rev.