1,167 research outputs found
On reducing the Heun equation to the hypergeometric equation
The reductions of the Heun equation to the hypergeometric equation by
polynomial transformations of its independent variable are enumerated and
classified. Heun-to-hypergeometric reductions are similar to classical
hypergeometric identities, but the conditions for the existence of a reduction
involve features of the Heun equation that the hypergeometric equation does not
possess; namely, its cross-ratio and accessory parameters. The reductions
include quadratic and cubic transformations, which may be performed only if the
singular points of the Heun equation form a harmonic or an equianharmonic
quadruple, respectively; and several higher-degree transformations. This result
corrects and extends a theorem in a previous paper, which found only the
quadratic transformations. [See K. Kuiken, "Heun's equation and the
hypergeometric equation", SIAM Journal on Mathematical Analysis 10:3 (1979),
655-657.]Comment: 36 pages, a few additional misprints correcte
Scalar Perturbations of two-dimensional Horava-Lifshitz Black Holes
In this article, we study the stability of black hole solutions found in the
context of dilatonic Horava-Lifshitz gravity in dimensions by means of
the quasinormal modes approach. In order to find the corresponding quasinormal
modes, we consider the perturbations of massive and massless scalar fields
minimally coupled to gravity. In both cases, we found that the quasinormal
modes have a discrete spectrum and are completely imaginary, which leads to
damping modes. For a massive scalar field and a non-vanishing cosmological
constant, our results suggest unstable behaviour for large values of the scalar
field mass.Comment: 18 pages, 1 figure. Accepted version in EPJC. arXiv admin note: text
overlap with arXiv:gr-qc/070109
Acceleration of generalized hypergeometric functions through precise remainder asymptotics
We express the asymptotics of the remainders of the partial sums {s_n} of the
generalized hypergeometric function q+1_F_q through an inverse power series z^n
n^l \sum_k c_k/n^k, where the exponent l and the asymptotic coefficients {c_k}
may be recursively computed to any desired order from the hypergeometric
parameters and argument. From this we derive a new series acceleration
technique that can be applied to any such function, even with complex
parameters and at the branch point z=1. For moderate parameters (up to
approximately ten) a C implementation at fixed precision is very effective at
computing these functions; for larger parameters an implementation in higher
than machine precision would be needed. Even for larger parameters, however,
our C implementation is able to correctly determine whether or not it has
converged; and when it converges, its estimate of its error is accurate.Comment: 36 pages, 6 figures, LaTeX2e. Fixed sign error in Eq. (2.28), added
several references, added comparison to other methods, and added discussion
of recursion stabilit
Integral means spectrum of whole-plane SLE
We complete the mathematical analysis of the fine structure of harmonic
measure on SLE curves that was initiated by Beliaev and Smirnov, as described
by the averaged integral means spectrum. For the unbounded version of
whole-plane SLE as studied by Duplantier, Nguyen, Nguyen and Zinsmeister, and
Loutsenko and Yermolayeva, a phase transition has been shown to occur for high
enough moments from the bulk spectrum towards a novel spectrum related to the
point at infinity. For the bounded version of whole-plane SLE studied here, a
similar transition phenomenon, now associated with the SLE origin, is proved to
exist for low enough moments, but we show that it is superseded by the earlier
occurrence of the transition to the SLE tip spectrum.Comment: 14 pages, 1 figure; final versio
Anisotropic scale invariant cosmology
We study a possibility of anisotropic scale invariant cosmology. It is shown
that within the conventional Einstein gravity, the violation of the null energy
condition is necessary. We construct an example based on a ghost condensation
model that violates the null energy condition. The cosmological solution
necessarily contains at least one contracting spatial direction as in the
Kasner solution. Our cosmology is conjectured to be dual to, if any, a
non-unitary anisotropic scale invariant Euclidean field theory. We investigate
simple correlation functions of the dual theory by using the holographic
computation. After compactification of the contracting direction, our setup may
yield a dual field theory description of the winding tachyon condensation that
might solve the singularity of big bang/crunch of the universe.Comment: 12 pages, v2: reference adde
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