The Inflaton and Time in the Matter-Gravity System

The emergence of time in the matter-gravity system is addressed within the context of the inflationary paradigm. A quantum minisuperspace-homogeneous minimally coupled inflaton system is studied with suitable initial conditions leading to inflation and the system is approximately solved in the limit for large scale factor. Subsequently normal matter (either non homogeneous inflaton modes or lighter matter) is introduced as a perturbation and it is seen that its presence requires the coarse averaging of a gravitational wave function (which oscillates at trans-Planckian frequencies) having suitable initial conditions. Such a wave function, which is common for all types of normal matter, is associated with a ``time density'' in the sense that its modulus is related to the amount of time spent in a given interval (or the rate of flow of time). One is then finally led to an effective evolution equation (Schroedinger Schwinger-Tomonaga) for ``normal'' matter. An analogy with the emergence of a temperature in statistical mechanics is also pointed out.Comment: 14 pages, late

The Born-Oppenheimer Approach to the Matter-Gravity System and Unitarity

The Born-Oppenheimer approach to the matter-gravity system is illustrated and the unitary evolution for matter, in the absence of phenomena such as tunnelling or other instabilities, verified. The Born-Oppenheimer approach to the matter-gravity system is illustrated in a simple minisuperspace model and the corrections to quantum field theory on a semiclassical background exhibited. Within such a context the unitary evolution for matter, in the absence of phenomena such as tunnelling or other instabilities, is verified and compared with the results of other approaches. Lastly the simplifications associated with the use of adiabatic invariants to obtain the solution of the explicitly time dependent evolution equation for matter are evidenced.Comment: Latex, 12 pages. Revised version as accepted for publication by Class. and Quant. Grav. Some points explained and misprints correcte

Fluctuation Effects on the Quadrupolar Ordering in Magnetic Field

Effects of magnetic field on the quadrupolar ordering are investigated with inclusion of fluctuation of order parameters. For the simplest model with the nearest-neighbor quadrupolar interaction, the transition temperature and the specific heat are derived by the use of the recently proposed effective medium theory. It is shown that magnetic field H has two competing effects on the quadrupolar ordering; one is to encourage the ordering by suppressing the fluctuation among different components of order parameters, and the other is to block the ordering as in antiferromagnets. The former is found to be of order H^2 and the latter of order H^4. Hence the fluctuation is suppressed for weak fields, and the transition temperature increases with magnetic field. The fluctuation effect is so strong that the entropy released at the quadrupolar ordering is only about half of the full value ln 4 even without the Kondo effect.Comment: 10 pages including 3 Postscript figure

Minimal Length Uncertainty Relation and Hydrogen Atom

We propose a new approach to calculate perturbatively the effects of a particular deformed Heisenberg algebra on energy spectrum. We use this method to calculate the harmonic oscillator spectrum and find that corrections are in agreement with a previous calculation. Then, we apply this approach to obtain the hydrogen atom spectrum and we find that splittings of degenerate energy levels appear. Comparison with experimental data yields an interesting upper bound for the deformation parameter of the Heisenberg algebra.Comment: 7 pages, REVTe

Effective inhomogeneous inflation: curvature inhomogeneities of the Einstein vacuum

We consider spatially averaged inhomogeneous universe models and argue that, already in the absence of sources, an effective scalar field arises through foliating and spatially averaging inhomogeneous geometrical curvature invariants of the Einstein vacuum. This scalar field (the `morphon') acts as an inflaton, if we prescribe a potential of some generic form. We show that, for any initially negative average spatial curvature, the morphon is driven through an inflationary phase and leads - on average - to a spatially flat, homogeneous and isotropic universe model, providing initial conditions for pre-heating and, by the same mechanism, a possibly natural self-exit.Comment: 9 pages, 2 figures, to appear in Class. Quant. Grav. as Fast Track Communicatio

The Schwinger Mechanism, the Unruh Effect and the Production of Accelerated Black Holes

We compute the corrections to the transition amplitudes of an accelerated Unruh ``box'' that arise when the accelerated box is replaced by a ``two level ion'' immersed in a constant electric field and treated in second quantization. There are two kinds of corrections, those due to recoil effects induced by the momentum transfers and those due to pair creation. Taken together, these corrections show that there is a direct relationship between pair creation amplitudes described by the Heisenberg-Euler-Schwinger mechanism and the Unruh effect, i.e. the thermalisation of accelerated systems at temperature $a/ 2 \pi$ where $a$ is the acceleration. In particular, there is a thermodynamical consistency between both effects whose origin is that the euclidean action governing pair creation rates acts as an entropy in delivering the Unruh temperature. Upon considering pair creation of charged black holes in an electric field, these relationships explain why black holes are created from vacuum in thermal equilibrium, i.e. with their Hawking temperature equal to their Unruh temperature.Comment: Revised version: expanded introduction and discussion of pair creation of black holes, 2figures added, 22 pages, Late

Entropy generation in 2+1-dimensional Gravity

The tunneling approach, for entropy generation in quantum gravity, is shown to be valid when applied to 3-D general relativity. The entropy of de Sitter and Reissner-Nordstr\"om external event horizons and of the 3-D black hole obtained by Ba\~nados et. al. is rederived from tunneling of the metric to these spacetimes. The analysis for spacetimes with an external horizon is carried out in a complete analogy with the 4-D case. However, we find significant differences for the black hole. In particular the initial configuration that tunnels to a 3-D black hole may not to yield an infinitely degenerate object, as in 4-D Schwarzschild black hole. We discuss the possible relation to the evaporation of the 3-D black hole.Comment: 22 pages, Tex, TAUP-2102-9

State-Space Based Approach to Particle Creation in Spatially Uniform Electric Fields

Our formalism described recently in (Dolby et al, hep-th/0103228) is applied to the study of particle creation in spatially uniform electric fields, concentrating on the cases of a time-invariant electric field and a so-called `adiabatic' electric field. Several problems are resolved by incorporating the `Bogoliubov coefficient' approach and the `tunnelling' approaches into a single consistent, gauge invariant formulation. The value of a time-dependent particle interpretation is demonstrated by presenting a coherent account of the time-development of the particle creation process, in which the particles are created with small momentum (in the frame of the electric field) and are then accelerated by the electric field to make up the `bulge' of created particles predicted by asymptotic calculations. An initial state comprising one particle is also considered, and its evolution is described as being the sum of two contributions: the `sea of current' produced by the evolved vacuum, and the extra current arising from the initial particle state.Comment: 36 pages, 16 figure

Black Hole Lasers Revisited

Contribution to "Quantum Analogues: From Phase Transitions to Black Holes and Cosmology" edited by William G. Unruh and Ralf Schutzhold. (Lecture Notes in Physics Vol. 718)The production of Hawking radiation by a single horizon is not dependent on the high-frequency dispersion relation of the radiated field. When there are two horizons, however, Corley and Jacobson have shown that superluminal dispersion leads to an amplification of the particle production in the case of bosons. The analytic theory of this "black hole laser" process is quite complicated, so we provide some numerical results in the hope of aiding understanding of this interesting phenomenon. Specifically, we consider sonic horizons in a moving fluid. The theory of elementary excitations in a Bose-Einstein condensate provides an example of "superluminal" (Bogoliubov) dispersion, so we add Bogoliubov dispersion to Unruh's equation for sound in the fluid. A white-hole/black-hole horizon pair will then display black hole lasing. Numerical analysis of the evolution of a wave packet gives a clear picture of the amplification process. By utilizing the similarity of a radiating horizon to a parametric amplifier in quantum optics we also analyze the black hole laser as a quantum-optical network