44 research outputs found
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
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
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
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 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