103 research outputs found
Inonu-Wigner Contractions of Kac-Moody Algebras
We discuss In\"on\"u-Wigner contractions of affine Kac-Moody algebras. We
show that the Sugawara construction for the contracted affine algebra exists
only for a fixed value of the level , which is determined in terms of the
dimension of the uncontracted part of the starting Lie algebra, and the
quadratic Casimir in the adjoint representation. Further, we discuss
contractions of coset spaces, and obtain an affine {\it translation}
algebra, which yields a Virasoro algebra (via a GKO construction) with a
central charge given by .Comment: 11 pages, IMSc/92-2
Black Hole Entropy and Quantum Gravity
An elementary introduction is given to the problem of black hole entropy as
formulated by Bekenstein and Hawking. The information theoretic basis of
Bekenstein's formulation is briefly reviewed and compared with Hawking's
approach. The issue of calculating the entropy by actual counting of
microstates is taken up next within two currently popular approaches to quantum
gravity, viz., string theory and canonical quantum gravity. The treatment of
the former assay is confined to a few remarks, mainly of a critical nature,
while some of the computational techniques of the latter approach are
elaborated. We conclude by trying to find commonalities between these two
rather disparate directions of work.Comment: 13 pages, Revtex, 5 eps figures. Invited talk at National Symposium
on Trends and Perspectives in Theoretical Physics, IACS, Calcutta, India,
April, 1998. One reference adde
Thermal stability of radiant black holes
Beginning with a brief sketch of the derivation of Hawking's theorem of
horizon area increase, based on the Raychaudhuri equation, we go on to discuss
the issue as to whether generic black holes, undergoing Hawking radiation, can
ever remain in stable thermal equilibrium with that radiation. We derive a
universal criterion for such a stability, which relates the black hole mass and
microcanonical entropy, both of which are well-defined within the context of
the Isolated Horizon, and in principle calculable within Loop Quantum Gravity.
The criterion is argued to hold even when thermal fluctuations of electric
charge are considered, within a {\it grand} canonical ensemble.Comment: Latex2e, 13 pages, 2 eps figures. Contribution to the volume to be
published by the Indian Association for the Cultivation of Science, Kolkata,
India in revered memory of Prof. A. K. Raychaudhur
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