565 research outputs found
General Relativity as a Theory of Two Connections
We show in this paper that it is possible to formulate General Relativity in
a phase space coordinatized by two connections. We analyze first the
Husain-Kucha\v{r} model and find a two connection description for it.
Introducing a suitable scalar constraint in this phase space we get a
Hamiltonian formulation of gravity that is close to the Ashtekar one, from
which it is derived, but has some interesting features of its own. Among them a
possible mechanism for dealing with the degenerate metrics and a neat way of
writing the constraints of General Relativity.Comment: 18 pages, LATEX, Preprint CGPG-93/09-
From Euclidean to Lorentzian General Relativity: The Real Way
We study in this paper a new approach to the problem of relating solutions to
the Einstein field equations with Riemannian and Lorentzian signatures. The
procedure can be thought of as a "real Wick rotation". We give a modified
action for general relativity, depending on two real parameters, that can be
used to control the signature of the solutions to the field equations. We show
how this procedure works for the Schwarzschild metric and discuss some possible
applications of the formalism in the context of signature change, the problem
of time, black hole thermodynamics...Comment: 20 pages uuencoded gzipped tar format. Accepted in Phys. Rev. D. Some
references adde
A Comment on the Degrees of Freedom in the Ashtekar Formulation for 2+1 Gravity
We show that the recent claim that the 2+1 dimensional Ashtekar formulation
for General Relativity has a finite number of physical degrees of freedom is
not correct.Comment: 6 pages LaTex, to appear in Classical and Quantum Gravit
Statistical description of the black hole degeneracy spectrum
We use mathematical methods based on generating functions to study the
statistical properties of the black hole degeneracy spectrum in loop quantum
gravity. In particular we will study the persistence of the observed effective
quantization of the entropy as a function of the horizon area. We will show
that this quantization disappears as the area increases despite the existence
of black hole configurations with a large degeneracy. The methods that we
describe here can be adapted to the study of the statistical properties of the
black hole degeneracy spectrum for all the existing proposals to define black
hole entropy in loop quantum gravity.Comment: 41 pages, 12 figure
Quantum isolated horizons and black hole entropy
We give a short introduction to the approaches currently used to describe
black holes in loop quantum gravity. We will concentrate on the classical
issues related to the modeling of black holes as isolated horizons, give a
short discussion of their canonical quantization by using loop quantum gravity
techniques, and a description of the combinatorial methods necessary to solve
the counting problems involved in the computation of the entropy.Comment: 28 pages in A4 format. Contribution to the Proceedings of the 3rd
Quantum Geometry and Quantum Gravity School in Zakopane (2011
Quantum Geometry and Quantum Gravity
The purpose of this contribution is to give an introduction to quantum
geometry and loop quantum gravity for a wide audience of both physicists and
mathematicians. From a physical point of view the emphasis will be on
conceptual issues concerning the relationship of the formalism with other more
traditional approaches inspired in the treatment of the fundamental
interactions in the standard model. Mathematically I will pay special attention
to functional analytic issues, the construction of the relevant Hilbert spaces
and the definition and properties of geometric operators: areas and volumes.Comment: To appear in the AIP Conference Proceedings of the XVI International
Fall Workshop on Geometry and Physics, Lisbon - Portugal, 5-8 September 200
Classical and quantum behavior of dynamical systems defined by functions of solvable Hamiltonians
We discuss the classical and quantum mechanical evolution of systems
described by a Hamiltonian that is a function of a solvable one, both
classically and quantum mechanically. The case in which the solvable
Hamiltonian corresponds to the harmonic oscillator is emphasized. We show that,
in spite of the similarities at the classical level, the quantum evolution is
very different. In particular, this difference is important in constructing
coherent states, which is impossible in most cases. The class of Hamiltonians
we consider is interesting due to its pedagogical value and its applicability
to some open research problems in quantum optics and quantum gravity.Comment: Accepted for publication in American Journal of Physic
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