Quantum singularities in spherically symmetric, conformally static spacetimes

A definition of quantum singularity for the case of static spacetimes has recently been extended to conformally static spacetimes. Here the theory behind quantum singularities in conformally static spacetimes is reviewed, and then applied to a class of spherically symmetric, conformally static spacetimes, including as special cases those studied by Roberts, by Fonarev, and by Husain, Martinez, and N\'u\~nez. We use solutions of the generally coupled, massless Klein-Gordon equation as test fields. In this way we find the ranges of metric parameters and coupling coefficients for which classical timelike singularities in these spacetimes are healed quantum mechanically.Comment: 21 pages, no figure

Definition and classification of singularities in GR: classical and quantum

We will briefly review the definition and classification of classical and quantum singularities in general relativity. Examples of classically singular spacetimes that do not have quantum singularities will be given. We will present results on quantum singularities in quasiregular spacetimes. We will also show that a strong repulsive "potential" near the classical singularity can turn a classically singular spacetime into a quantum mechanically nonsingular spacetime.Comment: 3 pages, no figures, submitted to Proceedings of the Tenth Marcel Grossmann Meeting on General Relativity, Rio de Janeiro, July 20-26, 200

Are classically singular spacetimes quantum mechanically singular as well?

Are the classical singularities of general relativistic spacetimes, normally defined by the incompleteness of classical particle paths, still singular if quantum mechanical particles are used instead? This is the question we will attempt to answer for particles obeying the quantum mechanical wave equations for scalar, null vector and spinor particles. The analysis will be restricted to certain static general relativistic spacetimes that classically contain the mildest true classical singularities, quasiregular singularities.Comment: 3 pages, no figures, submitted to the Proceedings of the Tenth Marcel Grossmann Meeting on General Relativity, Rio de Janeiro, July 20-26, 200

Quantum healing of classical singularities in power-law spacetimes

We study a broad class of spacetimes whose metric coefficients reduce to powers of a radius r in the limit of small r. Among these four-parameter "power-law" metrics we identify those parameters for which the spacetimes have classical singularities as r approaches 0. We show that a large set of such classically singular spacetimes is nevertheless nonsingular quantum mechanically, in that the Hamiltonian operator is essentially self-adjoint, so that the evolution of quantum wave packets lacks the ambiguity associated with scattering off singularities. Using these metrics, the broadest class yet studied to compare classical with quantum singularities, we explore the physical reasons why some that are singular classically are "healed" quantum mechanically, while others are not. We show that most (but not all) of the remaining quantum-mechanically singular spacetimes can be excluded if either the weak energy condition or the dominant energy condition is invoked, and we briefly discuss the effect of this work on the strong cosmic censorship hypothesis.Comment: 14 pages, 1 figure; extensive revision

Classical and quantum properties of a 2-sphere singularity

Recently Boehmer and Lobo have shown that a metric due to Florides, which has been used as an interior Schwarzschild solution, can be extended to reveal a classical singularity that has the form of a two-sphere. Here the singularity is shown to be a scalar curvature singularity that is both timelike and gravitationally weak. It is also shown to be a quantum singularity because the Klein-Gordon operator associated with quantum mechanical particles approaching the singularity is not essentially self-adjoint.Comment: 10 pages, 1 figure, minor corrections, final versio

Nuttier (A)dS Black Holes in Higher Dimensions

We construct new solutions of the vacuum Einstein field equations with cosmological constant. These solutions describe spacetimes with non-trivial topology that are asymptotically dS, AdS or flat. For a negative cosmological constant these solutions are NUT charged generalizations of the topological black hole solutions in higher dimensions. We also point out the existence of such NUT charged spacetimes in odd dimensions and we explicitly construct such spaces in 5 and 7 dimensions. The existence of such spacetimes with non-trivial topology is closely related to the existence of the cosmological constant. Finally, we discuss the global structure of such solutions and possible applications in string theory.Comment: latex, 30 pages, added reference

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