2,636 research outputs found

### Quantum geometry and black hole entropy: inclusion of distortion and rotation

Equilibrium states of black holes can be modelled by isolated horizons. If
the intrinsic geometry is spherical, they are called type I while if it is
axi-symmetric, they are called type II. The detailed theory of geometry of
quantum type I horizons and the calculation of their entropy can be generalized
to type II, thereby including arbitrary distortions and rotations. The leading
term in entropy of large horizons is again given by 1/4th of the horizon area
for the same value of the Barbero-Immirzi parameter as in the type I case.
Ideas and constructions underlying this extension are summarized.Comment: Text based on parallel talk given at the VI Mexican School on
Gravitation and Mathematical Physics: ``Approaches to Quantum Gravity'', held
in Playa del Carmen, Mexico, in November of 2004; IGPG preprint number added;
metadata abstract correcte

### Mechanics of Rotating Isolated Horizons

Black hole mechanics was recently extended by replacing the more commonly
used event horizons in stationary space-times with isolated horizons in more
general space-times (which may admit radiation arbitrarily close to black
holes). However, so far the detailed analysis has been restricted to
non-rotating black holes (although it incorporated arbitrary distortion, as
well as electromagnetic, Yang-Mills and dilatonic charges). We now fill this
gap by first introducing the notion of isolated horizon angular momentum and
then extending the first law to the rotating case.Comment: 31 pages REVTeX, 1 eps figure; Minor typos corrected and a footnote
adde

### Photon inner product and the Gauss linking number

It is shown that there is an interesting interplay between self-duality, loop
representation and knots invariants in the quantum theory of Maxwell fields in
Minkowski space-time. Specifically, in the loop representation based on
self-dual connections, the measure that dictates the inner product can be
expressed as the Gauss linking number of thickened loops.Comment: 18 pages, Revtex. No figures. To appear in Class. Quantum Gra

### 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

### Constructing Hamiltonian quantum theories from path integrals in a diffeomorphism invariant context

Osterwalder and Schrader introduced a procedure to obtain a (Lorentzian)
Hamiltonian quantum theory starting from a measure on the space of (Euclidean)
histories of a scalar quantum field. In this paper, we extend that construction
to more general theories which do not refer to any background, space-time
metric (and in which the space of histories does not admit a natural linear
structure). Examples include certain gauge theories, topological field theories
and relativistic gravitational theories. The treatment is self-contained in the
sense that an a priori knowledge of the Osterwalder-Schrader theorem is not
assumed.Comment: Plain Latex, 25 p., references added, abstract and title changed
(originally :``Osterwalder Schrader Reconstruction and Diffeomorphism
Invariance''), introduction extended, one appendix with illustrative model
added, accepted by Class. Quantum Gra

### Non-minimal couplings, quantum geometry and black hole entropy

The black hole entropy calculation for type I isolated horizons, based on
loop quantum gravity, is extended to include non-minimally coupled scalar
fields. Although the non-minimal coupling significantly modifies quantum
geometry, the highly non-trivial consistency checks for the emergence of a
coherent description of the quantum horizon continue to be met. The resulting
expression of black hole entropy now depends also on the scalar field precisely
in the fashion predicted by the first law in the classical theory (with the
same value of the Barbero-Immirzi parameter as in the case of minimal
coupling).Comment: 14 pages, no figures, revtex4. Section III expanded and typos
correcte

### Quantum horizons and black hole entropy: Inclusion of distortion and rotation

Equilibrium states of black holes can be modelled by isolated horizons. If
the intrinsic geometry is spherical, they are called type I while if it is
axi-symmetric, they are called type II. The detailed theory of geometry of
\emph{quantum} type I horizons and the calculation of their entropy can be
generalized to type II, thereby including arbitrary distortions and rotations.
The leading term in entropy of large horizons is again given by 1/4th of the
horizon area for the \emph{same} value of the Barbero-Immirzi parameter as in
the type I case. Ideas and constructions underlying this extension are
summarized.Comment: 9 page

### 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

### 2+1 Gravity without dynamics

A three dimensional generally covariant theory is described that has a 2+1
canonical decomposition in which the Hamiltonian constraint, which generates
the dynamics, is absent. Physical observables for the theory are described and
the classical and quantum theories are compared with ordinary 2+1 gravity.Comment: 9 page

### Spherically Symmetric Quantum Horizons

Isolated horizon conditions specialized to spherical symmetry can be imposed
directly at the quantum level. This answers several questions concerning
horizon degrees of freedom, which are seen to be related to orientation, and
its fluctuations at the kinematical as well as dynamical level. In particular,
in the absence of scalar or fermionic matter the horizon area is an approximate
quantum observable. Including different kinds of matter fields allows to probe
several aspects of the Hamiltonian constraint of quantum geometry that are
important in inhomogeneous situations.Comment: 4 pages, RevTeX

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