134 research outputs found
Holography and Stiff-matter on the Brane
Recently, Verlinde noted a surprising similarity between Friedmann equation
governing radiation dominated universe and Cardy's entropy formula in conformal
field theory. In this note, we study a brane-universe filled with radiation and
stiff-matter. We analyze Friedmann equation in this context and compare our
results with Cardy's entropy formula.Comment: 6 pages, Latex, references added to match with published versio
On the geometry of the symmetrized bidisc
We study the action of the automorphism group of the complex dimensional
manifold symmetrized bidisc on itself. The automorphism group is 3
real dimensional. It foliates into leaves all of which are 3 real
dimensional hypersurfaces except one, viz., the royal variety. This leads us to
investigate Isaev's classification of all Kobayashi-hyperbolic 2 complex
dimensional manifolds for which the group of holomorphic automorphisms has real
dimension 3 studied by Isaev. Indeed, we produce a biholomorphism between the
symmetrized bidisc and the domain
in Isaev's list. Isaev calls it . The road to the biholomorphism is paved with various geometric insights
about . Several consequences of the biholomorphism follow including
two new characterizations of the symmetrized bidisc and several new
characterizations of . Among the results on , of
particular interest is the fact that is a "symmetrization". When
we symmetrize (appropriately defined in the context in the last section) either
or (Isaev's notation), we get .
These two domains and are in Isaev's list and
he mentioned that these are biholomorphic to . We
produce explicit biholomorphisms between these domains and .Comment: 22 pages, Accepted in Indiana University Mathematics Journa
Pick interpolation and invariant distances
In this article, we study the role of invariant distances in the Pick
interpolation problem. Given a Carath\'eodory hyperbolic domain in
some , we have introduced a notion of an invariant object that
gives a necessary and sufficient condition for any Pick interpolation problem
to be solvable on . This invariant object plays the same role as that
of Carath\'eodory pseudodistance in the two-point Pick interpolation problem.
Furthermore, a full description of the invariant object is given when
is the open unit disc.Comment: 10 pages, comments are welcom
Black Holes in AdS Einstein Gauss Bonnet Gravity With Power- Yang Mills Field
In this paper we construct an exact spherically symmetric black hole solution
with a power Yang-Mills (YM) source in the context of Einstein
Gauss-Bonnet gravity ( EGB). We choose our source as
, where is an arbitrary positive real
number. Thereafter we study the horizon structure, thermodynamic issues like
thermal stability and black hole phase transition of this black hole solution.
Our focus here is to analyse the black hole space-time under the net non-linear
effect coming both from the gravitational sector (due to Gauss-Bonnet term) as
well as from the gauge fields (the power of Yang-Mills field invariant) in
-dimensions. We evaluate some extended thermodynamic quantities such as
pressure, temperature, entropy in order to establish the form of the Smarr
formula and the first law of thermodynamics. The behaviour of heat capacity as
a function of horizon radius is thoroughly studied to understand the thermal
stability of the black hole solution. An interesting phenomena of existence/
absence of thermal phase transition occur due to the nonlinearity of YM source.
For some values of the parameters, we find that the solution exhibits a
first-order phase transition, like a van der Waals fluid. In addition, we also
verify Maxwell's equal area law numerically by crucial analysis of Gibbs free
energy as a function of temperature. Moreover, the critical exponents are
derived and showed the universality class of the scaling behaviour of
thermodynamic quantities near criticality.Comment: 20 Pages, 16 figures, typos corrected, references added, minor
change
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