International Journal of Modern Physics D

In this essay it will be shown that Decoherence Model and Einstein Equivalence Principle are conceptually incompatible. In other words, assuming only the validity of the Weak Equivalence Principle the present work concludes that we face two possibilities: (i) if Decoherence Model provides a correct description of nature at quantum level, then there are systems which violate Local Position Invariance, or, (ii) if all the postulates behind Einstein Equivalence Principle are valid, even on quantum realm, then Decoherence Model breaks down in curved spacetimes. Finally, the present results are confronted against Schiff's conjecture.

We discuss a model describing exactly a thin spherically symmetric shell of matter with zero rest mass. We derive the reduced formulation of this system in which the variables are embeddings, their conjugate momenta, and Dirac observables. A nonperturbative quantum theory of this model is then constructed, leading to a unitary dynamics. As a consequence of unitarity, the classical singularity is fully avoided in the quantum theory.

Recent conjectures suggest the universe may have large extra dimensions, through which gravity propagates. This implies gross departures from Newton's law of gravity at small length scales. Here I consider some implications for particle dynamics on scales comparable to the compactification radius, R_c≲1 mm. During planet formation, coalescence of micron sized dust grains to planetesimals is a rate critical step. Blum et al. (2000) found dust grain aggregates form low fractal dimension structures in microgravity, consistent with high angular momentum coalescence. I consider the effects of non-Newtonian gravity on dust aggregation on scales less than R_c and show they naturally coalesce into low-dimensional structures with high specific angular momentum. We infer R_c≈80 microns.

If the topology of the universe is compact we show how it significantly changes our assessment of the naturalness of the observed structure of the universe and the likelihood of its present state of high isotropy and near flatness arising from generic initial conditions. We also identify the most general cosmological models with compact space.

The equation of motion of test particles in the geometry of a black string trapped on a domain wall embedded in a five-dimensional AdS spacetime is studied. With an inversion transformation on the fifth coordinate "w," we obtain a simple form of the geodesics and the geodesics deviation. The equations for the separation vector ξ^α between two nearby geodesics are found, with ξ⁵(λ)=ξ₍₀₎⁵sin(λ/l), where l is the AdS radius, independent of the Schwarzschild potential U(r).

In this essay we marshal evidence suggesting that Einstein gravity may be an emergent phenomenon, one that is not "fundamental" but rather is an almost automatic low-energy long-distance consequence of a wide class of theories. Specifically, the emergence of a curved spacetime "effective Lorentzian geometry" is a common generic result of linearizing a classical scalar field theory around some nontrivial background. This explains why so many different "analog models" of general relativity have recently been developed based on condensed matter physics; there is something more fundamental going on. Upon quantizing the linearized fluctuations around this background geometry, the one-loop effective action is guaranteed to contain a term proportional to the Einstein–Hilbert action of general relativity, suggesting that while classical physics is responsible for generating an "effective geometry," quantum physics can be argued to induce an "effective dynamics." This physical picture suggests that Einstein gravity is an emergent low-energy long-distance phenomenon that is insensitive to the details of the high-energy short-distance physics.

We investigate thermodynamic properties of two types of asymptotically anti-de Sitter spacetimes: black holes and singular scalar field spacetimes. We describe the possibility that thermodynamic phase transitions can transform one spacetime into another, suggesting that black holes can radiate to naked singularities.

The possibility is raised that the observed cosmological matter–antimatter asymmetry may reside in asymmetric spacetime fluctuations and their interplay with the Stückelberg–Feynman interpretation of antimatter. The presented thesis also suggests that the effect of spacetime fluctuations is to diminish the fine structure constant in the past. Recent studies of the QSO absorption lines provide a 4.1 standard deviation support for this prediction. Our considerations suggest that in the presence of spacetime fluctuations, the principle of local gauge invariance, and the related notion of parallel transport, must undergo fundamental changes.

We discuss the phase portrait of the reduced Einstein (3+1)-equations on a compact manifold of Yamabe type -1. We show that the flow for these equations either has a unique fixed point if the underlying manifold M is hyperbolizable or has no fixed points if M is not hyperbolizable. Thus the topology of M is a critical determinant of the phase portrait of the reduced equations. If, additionally, M is rigid, the fixed point is a local attractor, thereby answering an important question regarding the stability of these model universes. In the non-hyperbolizable case, under certain conditions, the reduced Einstein flow predicts that the conformal volume collapses M, in contrast to the physical volume which, as befits an expanding universe, goes to infinity as the coordinate time goes to infinity.

In this review, we summarize exact results for the three-dimensional BTZ black hole. We use rigorous mathematical results to clarify the general structure and properties of this black hole spacetime and its microscopic description. In particular, we study the formation of the black hole by point particle collisions, leading to an exact analytic determination of the Choptuik scaling parameter. We also show that a "No Hair Theorem" follows immediately from a mathematical theorem of hyperbolic geometry, due to Sullivan. A microscopic understanding of the Bekenstein–Hawking entropy, and decay rate for massless scalars, is shown to follow from standard results of conformal field theory.

In this work we obtain a nondemolition variable for the case in which a charged particle moves in the electric and gravitational fields of a spherical body. Afterwards we consider the continuous monitoring of this nondemolition parameter, and calculate, along the ideas of the so called restricted path integral formalism, the corresponding propagator. Using these results the probabilities associated with the possible measurement outputs are evaluated. The limit of our results, as the resolution of the measuring device goes to zero, is analyzed, and the dependence of the corresponding propagator upon the strength of the electric and gravitational fields is commented. The role that mass plays in the corresponding results, and its possible connection with the equivalence principle at quantum level, are studied.

We present a stationary axisymmetric solution belonging to Carter's family [Ã] of spaces and representing an anisotropic fluid configuration

Relativistic prescription is used to study the slow rotation of stars composed by self-gravitating bosons and fermions (fermions may be considered as neutrons). Previous results demand that purely boson stars are unable to display slow rotation, if one uses relativistic prescription with classical scalar fields. In contrast to this, the present work shows that a combined boson-fermion star in its ground-state can rotate. Its structure and stability are analysed under slow rotation approximations.

Models of the universe with a cosmological term which is introduced as a correction of the metric tensor field are studied. By revisiting with these models some of the conventional success, we infer that a model with a linear correction is a favourable candidate for a model of the universe. The cosmological constant and the flatness problems are examined in the model. There might be a possibility to solve the other cosmological problems only with the metric tensor field.

We present technical results which extend previous work and show that the cosmological constant of general relativity is an artefact of the reduction to 4D of 5D Kaluza–Klein theory (or 10D superstrings and 11D supergravity). We argue that the distinction between matter and vacuum is artificial in the context of ND field theory. The concept of a cosmological "constant" (which measures the energy density of the vacuum in 4D) should be replaced by that of a series of variable fields whose sum is determined by a solution of ND field equations in a well-defined manner.

Previously, we have argued that the cosmic magnetic field B_c is attributable to the indeterminacy principle, applied to metric fluctuations at the time t_e≈4.4×10¹⁰h^-4 s of equipartition of energy (the last time of dynamical coupling) between matter and radiation in the Universe, stemming from the intrinsic uncertainty in the initial conditions (the phase of the wave function) at the Planck time t_P≈ 5.4×10^-44 s, which leads to a present-day magnetic field B_c(t₀)≈ 10^-9 G coherent on the length scale ℓ(t₀)≈ 50 Mpc. Here, we discuss this result à propos the ultra-high-energy cosmic rays of energy E ≳ 10²⁰ eV, suggesting that they may be due to nearby radio galaxies within ~ 10 Mpc, the primary components being heavy nuclei of charge Z≳ 10 deflected through large angles.

We compare some features of quintessence cosmological scenarios with the duality symmetry existing in string dilaton cosmologies. Actually, we consider the tracker potential type V = V₀/φ^α and show that duality is only established if α = -2.

The production of Primordial Black Holes (PBH) from inflationary perturbations provides a physical process where the effective classicality of the fluctuations does not hold for certain scales. For adiabatic perturbations produced during inflation, this range of scales corresponds to PBH with masses M≪10¹⁵ g. For PBH with masses M ~ M_H(t_e), the horizon mass at the end of inflation, the generation process during the preheating stage could be classical as well, in contrast to the formation of PBH on these scales by adiabatic inflationary perturbations. For the nonevaporated PBH, the generation process is essentially classical.

We obtain some cosmological model that are exact solutions of Einstein field equations. The metric utilized is the nonstatic Gödel-type cosmological model and the curvature source is a string cloud with scalar field and heat flow. The solutions have nonzero expansion, shear, and rotating. The properties of the solutions are studied and the temperature distribution is also given explicitly.

This paper deals with quantum cosmological phenomena in anisotropic cosmological models with nonminimally coupled scalor field. With proper transformation of the field variables, the Wheeler–Dewitt (WD) equation looks simple in form and solutions are obtained using separable form of the wave function. Using part integral formulation, the wave function of the Universe has been evaluated by the method of steepest descent. Finally, the causal interpretation has been done using quantum Bohmian trajectories and also we study the classical limit of some particular solutions of these quantum models.

This paper deals with vacuum Brans–Dicke theory in an anisotropic Kantowski–Sachs model and Euclidean wormhole solutions have been obtained. The Wheeler–Dewitt (WD) equation has been solved using separable form of the wave function and these solutions have been examined whether wormhole boundary condition due to Hawking is satisfied or not.

In this paper, we present an investigation of the Berry phase that a photon acquired during its propagating through a gravitational field produced by a Kerr black hole. Starting from the Maxwell equation in Kerr–Schild metric form of Kerr black hole, we give the zeroth order Hamiltonian of the photon under geometric optics approximation. The helicity state of the photon is then derived. We demonstrate that there are two factors leading to the Berry phase that the photon acquires in a gravitational field. These are the adiabatic transport of the local comoving tetrad and the rotation of the equivalent magnetic field that we introduce. The straightforward calculation show that the appearance of Berry phase is attributed to the twisted optical path due to the rotation of black hole. It is in fact analogous to the observed optical rotation for a linear polarized light propagating in an helical optical fiber.