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
Mining metrics for buried treasure
The same but different: That might describe two metrics. On the surface
CLASSI may show two metrics are locally equivalent, but buried beneath one may
be a wealth of further structure. This was beautifully described in a paper by
M.A.H. MacCallum in 1998. Here I will illustrate the effect with two flat
metrics -- one describing ordinary Minkowski spacetime and the other describing
a three-parameter family of Gal'tsov-Letelier-Tod spacetimes. I will dig out
the beautiful hidden classical singularity structure of the latter (a structure
first noticed by Tod in 1994) and then show how quantum considerations can
illuminate the riches. I will then discuss how quantum structure can help us
understand classical singularities and metric parameters in a variety of exact
solutions mined from the Exact Solutions book.Comment: 16 pages, no figures, minor grammatical changes, submitted to
Proceedings of the Malcolm@60 Conference (London, July 2004