1,734 research outputs found
Fock representations from U(1) holonomy algebras
We revisit the quantization of U(1) holonomy algebras using the abelian C*
algebra based techniques which form the mathematical underpinnings of current
efforts to construct loop quantum gravity. In particular, we clarify the role
of ``smeared loops'' and of Poincare invariance in the construction of Fock
representations of these algebras. This enables us to critically re-examine
early pioneering efforts to construct Fock space representations of linearised
gravity and free Maxwell theory from holonomy algebras through an application
of the (then current) techniques of loop quantum gravity.Comment: Latex file, 30 pages, to appear in Phys Rev
Notes on Isolated Horizons
A general analysis for characterizing and classifying `isolated horizons' is
presented in terms of null tetrads and spin coefficients. The freely
specifiable spin coefficients corresponding to isolated horizons are identified
and specific symmetry classes are enumerated. For isolated horizons admitting
at least one spatial isometry, a standard set of spherical coordinates are
introduced and associated metric is obtained. An angular momentum is also
defined.Comment: 45 pages, Latex, no figures. Explained approach better. To appear in
Class. Quant. Gra
Dynamical Horizons and their Properties
A detailed description of how black holes grow in full, non-linear general
relativity is presented. The starting point is the notion of dynamical
horizons. Expressions of fluxes of energy and angular momentum carried by
gravitational waves across these horizons are obtained. Fluxes are local and
the energy flux is positive. Change in the horizon area is related to these
fluxes. A notion of angular momentum and energy is associated with
cross-sections of the horizon and balance equations, analogous to those
obtained by Bondi and Sachs at null infinity, are derived. These in turn lead
to generalizations of the first and second laws of black hole mechanics. The
relation between dynamical horizons and their asymptotic states --the isolated
horizons-- is discussed briefly. The framework has potential applications to
numerical, mathematical, astrophysical and quantum general relativity.Comment: 44 pages, 2 figures, RevTeX4. Minor typos corrected. Final PRD
versio
Generic isolated horizons in loop quantum gravity
Isolated horizons model equilibrium states of classical black holes. A
detailed quantization, starting from a classical phase space restricted to
spherically symmetric horizons, exists in the literature and has since been
extended to axisymmetry. This paper extends the quantum theory to horizons of
arbitrary shape. Surprisingly, the Hilbert space obtained by quantizing the
full phase space of \textit{all} generic horizons with a fixed area is
identical to that originally found in spherical symmetry. The entropy of a
large horizon remains one quarter its area, with the Barbero-Immirzi parameter
retaining its value from symmetric analyses. These results suggest a
reinterpretation of the intrinsic quantum geometry of the horizon surface.Comment: 13 page
Laws of Black Hole Mechanics from Holst Action
The formulation of Weak Isolated Horizons (WIH) based on the Isolated Horizon
formulation of black hole horizons is reconsidered. The first part of the paper
deals with the derivation of laws of mechanics of a WIH. While the zeroth law
follows from the WIH boundary conditions, first law depends on the action
chosen. We construct the covariant phase space for a spacetime having an WIH as
inner boundary for the Holst action. This requires the introduction of new
potential functions so that the symplectic structure is foliation independent.
We show that a precise cancellation among various terms leads to the usual
first law for WIH. Subsequently, we show from the same covariant phase space
that for spherical horizons, the topological theory on the inner boundary is a
U(1) Chern-Simons theory.Comment: References added, Minor Corrections 25 pages 1 fi
Gauss Linking Number and Electro-magnetic Uncertainty Principle
It is shown that there is a precise sense in which the Heisenberg uncertainty
between fluxes of electric and magnetic fields through finite surfaces is given
by (one-half times) the Gauss linking number of the loops that bound
these surfaces. To regularize the relevant operators, one is naturally led to
assign a framing to each loop. The uncertainty between the fluxes of electric
and magnetic fields through a single surface is then given by the self-linking
number of the framed loop which bounds the surface.Comment: 13 pages, Revtex file, 3 eps figure
Laws Governing Isolated Horizons: Inclusion of Dilaton Couplings
Mechanics of non-rotating black holes was recently generalized by replacing
the static event horizons used in standard treatments with `isolated horizons.'
This framework is extended to incorporate dilaton couplings. Since there can be
gravitational and matter radiation outside isolated horizons, now the
fundamental parameters of the horizon, used in mechanics, must be defined using
only the local structure of the horizon, without reference to infinity. This
task is accomplished and the zeroth and first laws are established. To
complement the previous work, the entire discussion is formulated tensorially,
without any reference to spinors.Comment: Some typos corrected, references updated. Some minor clarifications
added. 20 pages, 1 figure, Revtex fil
Conformal entropy for generalised gravity theories as a consequence of horizon properties
We show that microscopic entropy formula based on Virasoro algebra follows
from properties of stationary Killing horizons for Lagrangians with arbitrary
dependence on Riemann tensor. The properties used are consequence of regularity
of invariants of Riemann tensor on the horizon. Eventual generalisation of
these results to Lagrangians with derivatives of Riemann tensor, as suggested
by an example treated in the paper, relies on assuming regularity of invariants
involving derivatives of Riemann tensor. This assumption however leads also to
new interesting restrictions on metric functions near horizon.Comment: 9 pages, appendix adde
Production and decay of evolving horizons
We consider a simple physical model for an evolving horizon that is strongly
interacting with its environment, exchanging arbitrarily large quantities of
matter with its environment in the form of both infalling material and outgoing
Hawking radiation. We permit fluxes of both lightlike and timelike particles to
cross the horizon, and ask how the horizon grows and shrinks in response to
such flows. We place a premium on providing a clear and straightforward
exposition with simple formulae.
To be able to handle such a highly dynamical situation in a simple manner we
make one significant physical restriction, that of spherical symmetry, and two
technical mathematical restrictions: (1) We choose to slice the spacetime in
such a way that the space-time foliations (and hence the horizons) are always
spherically symmetric. (2) Furthermore we adopt Painleve-Gullstrand coordinates
(which are well suited to the problem because they are nonsingular at the
horizon) in order to simplify the relevant calculations.
We find particularly simple forms for surface gravity, and for the first and
second law of black hole thermodynamics, in this general evolving horizon
situation. Furthermore we relate our results to Hawking's apparent horizon,
Ashtekar et al's isolated and dynamical horizons, and Hayward's trapping
horizons. The evolving black hole model discussed here will be of interest,
both from an astrophysical viewpoint in terms of discussing growing black
holes, and from a purely theoretical viewpoint in discussing black hole
evaporation via Hawking radiation.Comment: 25 pages, uses iopart.cls V2: 5 references added; minor typos; V3:
some additional clarifications, additional references, additional appendix on
the Viadya spacetime. This version published in Classical and Quiantum
Gravit
From the Einstein-Cartan to the Ashtekar-Barbero canonical constraints, passing through the Nieh-Yan functional
The Ashtekar-Barbero constraints for General Relativity with fermions are
derived from the Einstein-Cartan canonical theory rescaling the state
functional of the gravity-spinor coupled system by the exponential of the
Nieh-Yan functional. A one parameter quantization ambiguity naturally appears
and can be associated with the Immirzi parameter.Comment: Minor changes, two references added, accepted for publication in
Phys. Rev.
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