433 research outputs found
Note on Self-Duality and the Kodama State
An interesting interplay between self-duality, the Kodama (Chern-Simons)
state and knot invariants is shown to emerge in the quantum theory of an
Abelian gauge theory. More precisely, when a self-dual representation of the
CCR is chosen, the corresponding vacuum in the Schroedinger representation is
precisely given by the Kodama state. Several consequences of this construction
are explored.Comment: 4 pages, no figures. References and discussion added. Final version
to appear in PR
Energy of test objects on black hole spacetimes: A brief review
In this paper, we review the issue of defining energy for test particles on a
background stationary spacetime. We revisit the different notions of energy as
defined by different observers. As is well known, the existence of a time-like
isometry allows for the notion of total conserved energy to be well defined. We
use this well known quantity to show that a gravitational potential energy can
be consistently defined. As examples, we study the case of the exterior regions
of an asymptotically flat black hole and of the Schwarzschild de
Sitter case, where an asymptotic region is not available. We then consider the
situation in which the test particle is absorbed by the black hole, and analyze
the energetics in detail. In particular, we show that the notion of horizon
energy as defined by the isolated horizons formalism provides a satisfactory
notion of energy compatible with the particle's total conserved energy. With
these choices, there is a global conservation of energy. Finally, we comment on
a recent proposal to define energy of the black hole as seen by a nearby
observer at rest, for which this feature is lost.Comment: 16 pages, no figures. Discussion expanded, de Sitter BH case
included. Matches published versio
Loop quantum gravity and Planck-size black hole entropy
The Loop Quantum Gravity (LQG) program is briefly reviewed and one of its
main applications, namely the counting of black hole entropy within the
framework is considered. In particular, recent results for Planck size black
holes are reviewed. These results are consistent with an asymptotic linear
relation (that fixes uniquely a free parameter of the theory) and a logarithmic
correction with a coefficient equal to -1/2. The account is tailored as an
introduction to the subject for non-experts.Comment: 21 pages, 5 figures. Contribution to the Proceedings of the NEB XII
International Conferenc
Quantum Superposition Principle and Geometry
If one takes seriously the postulate of quantum mechanics in which physical
states are rays in the standard Hilbert space of the theory, one is naturally
lead to a geometric formulation of the theory. Within this formulation of
quantum mechanics, the resulting description is very elegant from the
geometrical viewpoint, since it allows to cast the main postulates of the
theory in terms of two geometric structures, namely a symplectic structure and
a Riemannian metric. However, the usual superposition principle of quantum
mechanics is not naturally incorporated, since the quantum state space is
non-linear. In this note we offer some steps to incorporate the superposition
principle within the geometric description. In this respect, we argue that it
is necessary to make the distinction between a 'projective superposition
principle' and a 'decomposition principle' that extend the standard
superposition principle. We illustrate our proposal with two very well known
examples, namely the spin 1/2 system and the two slit experiment, where the
distinction is clear from the physical perspective. We show that the two
principles have also a different mathematical origin within the geometrical
formulation of the theory.Comment: 10 pages, no figures. References added. V3 discussion expanded and
new results added, 14 pages. Dedicated to Michael P. Ryan on the occasion of
his sixtieth bithda
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