184 research outputs found
Topological Measure and Graph-Differential Geometry on the Quotient Space of Connections
(This is a report for the Proceedings of ``Journees Relativistes 1993''
written in September 1993. Containes a short description of the results
published elsewhere in the joint paper with A. Ashtekar) Integral calculus on
the space of gauge equivalent connections is developed. By carring out a
non-linear generalization of the theory of cylindrical measures on topological
vector spaces, a faithfull, diffeomorphism invariant measure is introduced on a
suitable completion of the quotient space. The strip (i.e. momentum) operators
are densely-defined in the resulting Hilbert space and interact with the
measure correctly, to become essentially self adjoint operators.Comment: 3 pp., Proceedings of ``Journees Relativistes 1993'
Black hole entropy from Quantum Geometry
Quantum Geometry (the modern Loop Quantum Gravity using graphs and
spin-networks instead of the loops) provides microscopic degrees of freedom
that account for the black-hole entropy. However, the procedure for state
counting used in the literature contains an error and the number of the
relevant horizon states is underestimated. In our paper a correct method of
counting is presented. Our results lead to a revision of the literature of the
subject. It turns out that the contribution of spins greater then 1/2 to the
entropy is not negligible. Hence, the value of the Barbero-Immirzi parameter
involved in the spectra of all the geometric and physical operators in this
theory is different than previously derived. Also, the conjectured relation
between Quantum Geometry and the black hole quasi-normal modes should be
understood again.Comment: a new section ``The spin probability distribution'' adde
Geometric Characterizations of the Kerr Isolated Horizon
We formulate conditions on the geometry of a non-expanding horizon
which are sufficient for the space-time metric to coincide on with the
Kerr metric. We introduce an invariant which can be used as a measure of how
different the geometry of a given non-expanding horizon is from the geometry of
the Kerr horizon. Directly, our results concern the space-time metric at \IH
at the zeroth and the first orders. Combained with the results of Ashtekar,
Beetle and Lewandowski, our conditions can be used to compare the space-time
geometry at the non-expanding horizon with that of Kerr to every order. The
results should be useful to numerical relativity in analyzing the sense in
which the final black hole horizon produced by a collapse or a merger
approaches the Kerr horizon.Comment: 11 pages, relevance of the results for the numerical relativity
explained, mistakes correcte
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