7 research outputs found
Classical and Quantum Equations of Motion for a BTZ Black String in AdS Space
We investigate gravitational collapse of a -dimensional BTZ black
string in AdS space in the context of both classical and quantum mechanics.
This is done by first deriving the conserved mass per unit length of the
cylindrically symmetric domain wall, which is taken as the classical
Hamiltonian of the black string. In the quantum mechanical context, we take
primary interest in the behavior of the collapse near the horizon and near the
origin (classical singularity) from the point of view of an infalling observer.
In the absence of radiation, quantum effects near the horizon do not change the
classical conclusions for an infalling observer, meaning that the horizon is
not an obstacle for him/her. The most interesting quantum mechanical effect
comes in when investigating near the origin. First, quantum effects are able to
remove the classical singularity at the origin, since the wave function is
non-singular at the origin. Second, the Schr\"odinger equation describing the
behavior near the origin displays non-local effects, which depend on the energy
density of the domain wall. This is manifest in that derivatives of the
wavefunction at one point are related to the value of the wavefunction at some
other distant point.Comment: 9 pages, 1 figure. Minor Clarification and corrections. Accepted for
Publication in JHE
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
never vanishes and, as , 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