Quantum Singularities in Spacetimes with Spherical and Cylindrical Topological Defects

Exact solutions of Einstein equations with null Riemman-Christoffel curvature tensor everywhere, except on a hypersurface, are studied using quantum particles obeying the Klein-Gordon equation. We consider the particular cases when the curvature is represented by a Dirac delta function with support either on a sphere or on a cylinder (spherical and cylindrical shells). In particular, we analyze the necessity of extra boundary conditions on the shells.Comment: 7 page,1 fig., Revtex, J. Math. Phys, in pres

Boundary conditions and renormalized stress-energy tensor on a Poincar\'e patch of AdS2\textrm{AdS}_2

Quantum field theory on anti-de Sitter spacetime requires the introduction of boundary conditions at its conformal boundary, due essentially to the absence of global hyperbolicity. Here we calculate the renormalized stress-energy tensor $T_{\mu\nu}$ for a scalar field $\phi$ on the Poincar\'e patch of $\text{AdS}_2$ and study how it depends on those boundary conditions. We show that, except for the Dirichlet and Neumann cases, the boundary conditions break the maximal $\textrm{AdS}$ invariance. As a result, $\langle\phi^2\rangle$ acquires a space dependence and $\langle T_{\mu\nu}\rangle$ is no longer proportional to the metric. When the physical quantities are expanded in a parameter $\beta$ which characterizes the boundary conditions (with $\beta=0$ corresponding to Dirichlet and $\beta=\infty$ corresponding to Neumann), the singularity of the Green's function is entirely subtracted at zeroth order in $\beta$. As a result, the contribution of nontrivial boundary conditions to the stress-energy tensor is free of singular terms.Comment: 7 pages. Minor Correction. Matches published versio

Quantum Singularities Around a Global Monopole

The behavior of a massive scalar particle on the spacetime surrounding a monopole is studied from a quantum mechanical point of view. All the boundary conditions necessary to turn into self-adjoint the spatial portion of the wave operator are found and their importance to the quantum interpretation of singularities is emphasized.Comment: 5 pages, revte

Robin boundary conditions in acoustic BTZ black holes

We introduce an analog model for the conformally coupled scalar field on the BTZ black hole. The model is based on the propagation of acoustic waves in a Laval nozzle. Since the BTZ black hole is not a globally hyperbolic spacetime, the dynamics of the scalar field is not well defined until extra boundary conditions are prescribed at its spatial infinity. We show that quasinormal modes (QNMs) satisfying Dirichlet, Neumann, and Robin boundary conditions in the BTZ black hole can be interpreted in terms of ordinary QNMs defined with respect to an appropriately extended nozzle. We also discuss the stability of our model with respect to small perturbations.Comment: 12 pages, 6 figure

Quantum Singularities in Horava-Lifshitz Cosmology

The recently proposed Horava-Lifshitz (HL) theory of gravity is analyzed from the quantum cosmology point of view. By employing usual quantum cosmology techniques, we study the quantum Friedmann-Lemaitre-Robertson-Walker (FLRW) universe filled with radiation in the context of HL gravity. We find that this universe is quantum mechanically nonsingular in two different ways: the expectation value of the scale factor $(t)$ never vanishes and, if we abandon the detailed balance condition suggested by Horava, the quantum dynamics of the universe is uniquely determined by the initial wave packet and no boundary condition at $a=0$ is indeed necessary.Comment: 13 pages, revtex, 1 figure. Final version to appear in PR

Quantum singularities in the BTZ spacetime

The spinless Ba\~nados-Teiltelboim-Zanelli (BTZ) spacetime is considered in the quantum theory context. Specially, we study the case of negative mass parameter using quantum test particles obeying the Klein-Gordon and Dirac equations. We study if this classical singular spacetime, with a naked singularity at the origin, remains singular when tested with quantum particles. The need of additional information near the origin is confirmed for massive scalar particles and all the possible boundary conditions necessary to turn the spatial portion of the wave operator self-adjoint are found. When tested by massless scalar particles or fermions, the singularity is ``healed'' and no extra boundary condition are needed. Near infinity, no boundary conditions are necessary.Comment: 6 pages, rvtex, accepted for publication in PR

Quantum singularities in FRW universe revisited

The components of the Riemann tensor in the tetrad basis are quantized and, through the Einstein equation, we find the local expectation value in the ontological interpretation of quantum mechanics of the energy density and pressure of a perfect fluid with equation of state $p=\frac{1}{3}\rho$ in the flat Friedmann-Robertson-Walker quantum cosmological model. The quantum behavior of the equation of state and energy conditions are then studied and it is shown that the later is violated since the singularity is removed with the introduction of quantum cosmology, but in the classical limit both the equation of state and the energy conditions behave as in the classical model. We also calculate the expectation value of the scale factor for several wave packets in the many-worlds interpretation in order to show the independence of the non singular character of the quantum cosmological model with respect to the wave packet representing the wave function of the Universe. It is also shown that, with the introduction of non-normalizable wave packets, solutions of the Wheeler-DeWitt equation, the singular character of the scale factor, can be recovered in the ontological interpretation.Comment: 15 pages, revtex, accepted for publication in PR

n-Dimensional FLRW Quantum Cosmology

We introduce the formalism of quantum cosmology in a Friedmann-Lema\^itre-Robertson-Walker (FLRW) universe of arbitrary dimension filled with a perfect fluid with $p=\alpha\rho$ equation of state. First we show that the Schutz formalism, developed in four dimensions, can be extended to a n-dimensional universe. We compute the quantum representant of the scale factor $a(t)$, in the Many-Worlds, as well as, in the de Broglie-Bohm interpretation of quantum mechanics. We show that the singularities, which are still present in the n-dimensional generalization of FLRW universe, are excluded with the introduction of quantum theory. We quantize, via the de Broglie-Bohm interpretation of quantum mechanics, the components of the Riemann curvature tensor in a tetrad basis in a n-dimensional FLRW universe filled with radiation ($p=\frac{1}{n-1}\rho$). We show that the quantized version of the Ricci scalar are perfectly regular for all time $t$. We also study the behavior of the energy density and pressure and show that the ratio $_L/_L$ tends to the classical value $1/(n-1)$ only for $n=4$, showing that $n=4$ is somewhat privileged among the other dimensions. Besides that, as $n\to\infty$, $_L/_L\to 1$.Comment: 12 pages, revtex, minor modification

Modeling the quantum evolution of the universe through classical matter

It is well known that the canonical quantization of the Friedmann-Lema\^itre-Robertson-Walker (FLRW) filled with a perfect fluid leads to nonsingular universes which, for later times, behave as their classical counterpart. This means that the expectation value of the scale factor $(t)$ never vanishes and, as $t\to\infty$, we recover the classical expression for the scale factor. In this paper, we show that such universes can be reproduced by classical cosmology given that the universe is filled with an exotic matter. In the case of a perfect fluid, we find an implicit equation of state (EoS). We then show that this single fluid with an implict EoS is equivalent to two non-interacting fluids, one of them representing stiff matter with negative energy density. In the case of two non-interacting scalar fields, one of them of the phantom type, we find their potential energy. In both cases we find that quantum mechanics changes completely the configuration of matter for small values of time, by adding a fluid or a scalar field with negative energy density. As time passes, the density of negative energy decreases and we recover the ordinary content of the classical universe. The more the initial wave function of the universe is concentrated around the classical big bang singularity, the more it is necessary to add negative energy, since this type of energy will be responsible for the removal of the classical singularity.Comment: updated version as accepted by Gen. Relativ. Gravi