69 research outputs found
An algorithm to obtain global solutions of the double confluent Heun equation
A procedure is proposed to construct solutions of the double confluent Heun
equation with a determinate behaviour at the singular points. The connection
factors are expressed as quotients of Wronskians of the involved solutions.
Asymptotic expansions are used in the computation of those Wronskians. The
feasibility of the method is shown in an example, namely, the Schroedinger
equation with a quasi-exactly-solvable potential
Black Hole Scattering from Monodromy
We study scattering coefficients in black hole spacetimes using analytic
properties of complexified wave equations. For a concrete example, we analyze
the singularities of the Teukolsky equation and relate the corresponding
monodromies to scattering data. These techniques, valid in full generality,
provide insights into complex-analytic properties of greybody factors and
quasinormal modes. This leads to new perturbative and numerical methods which
are in good agreement with previous results.Comment: 28 pages + appendices, 2 figures. For Mathematica calculation of
Stokes multipliers, download "StokesNotebook" from
https://sites.google.com/site/justblackholes/techy-zon
Kerr-de Sitter Quasinormal Modes via Accessory Parameter Expansion
Quasinormal modes are characteristic oscillatory modes that control the
relaxation of a perturbed physical system back to its equilibrium state. In
this work, we calculate QNM frequencies and angular eigenvalues of Kerr--de
Sitter black holes using a novel method based on conformal field theory. The
spin-field perturbation equations of this background spacetime essentially
reduce to two Heun's equations, one for the radial part and one for the angular
part. We use the accessory parameter expansion of Heun's equation, obtained via
the isomonodromic -function, in order to find analytic expansions for the
QNM frequencies and angular eigenvalues. The expansion for the frequencies is
given as a double series in the rotation parameter and the extremality
parameter , where is the de Sitter radius and
and are the radii of, respectively, the cosmological and event
horizons. Specifically, we give the frequency expansion up to order
for general , and up to order with the
coefficients expanded up to . Similarly, the expansion for the
angular eigenvalues is given as a series up to with
coefficients expanded for small . We verify the new expansion for the
frequencies via a numerical analysis and that the expansion for the angular
eigenvalues agrees with results in the literature.Comment: 38+19 pages, 8 figures. v3: minor changes, matches published versio
NumGfun: a Package for Numerical and Analytic Computation with D-finite Functions
This article describes the implementation in the software package NumGfun of
classical algorithms that operate on solutions of linear differential equations
or recurrence relations with polynomial coefficients, including what seems to
be the first general implementation of the fast high-precision numerical
evaluation algorithms of Chudnovsky & Chudnovsky. In some cases, our
descriptions contain improvements over existing algorithms. We also provide
references to relevant ideas not currently used in NumGfun
The black hole behind the cut
We study the analytic structure of the heavy-heavy-light-light holographic
correlators in the supergravity approximation of the AdS/CFT
duality. As an explicit example, we derive the correlator where the heavy
operator is a classical microstate of the 5D supersymmetric black hole and its
dual geometry interpolates as a function of a continuous parameter between
global AdS and the extremal BTZ black hole. The simplest perturbation of
this interpolating geometry by a light field is described by the Heun equation
and we exploit the relation of its connection coefficients to the Liouville CFT
to analytically compute the correlator in the two limits, focusing in
particular on the black hole regime. In this limit we find that the real poles
of the correlator become dense and can be approximated by a cut. We show that,
when the charges of the heavy state are in the black hole regime, the
discontinuity across the cut has complex poles corresponding to the
quasi-normal modes of BTZ. This behaviour is qualitatively similar to what is
expected for the large central charge limit of a typical black hole microstateComment: 59 pages, 1 figur
The black hole behind the cut
We study the analytic structure of the heavy-heavy-light-light holographic correlators in the supergravity approximation of the AdS3 × S 3/CFT2 duality. As an explicit example, we derive the correlator where the heavy operator is a classical microstate of the 5D supersymmetric black hole and its dual geometry interpolates as a function of a continuous parameter between global AdS3 and the extremal BTZ black hole. The simplest perturbation of this interpolating geometry by a light field is described by the Heun equation and we exploit the relation of its connection coefficients to the Liouville CFT to analytically compute the correlator in the two limits, focusing in particular on the black hole regime. In this limit we find that the real poles of the correlator become dense and can be approximated by a cut. We show that, when the charges of the heavy state are in the black hole regime, the discontinuity across the cut has complex poles corresponding to the quasi-normal modes of BTZ. This behaviour is qualitatively similar to what is expected for the large central charge limit of a typical black hole microstate
Monodromy Approach to Pair Production of Charged Black Holes and Electric Fields
To find the pair production, absorption cross section and quasi-normal modes
in background fields, we advance the monodromy method that makes use of the
regular singular points of wave equations. We find the mean number of pairs
produced in background fields whose mode equations belong to the Riemann
differential equation and apply the method to the three particular cases: (i)
charges near the horizon of near-extremal black holes, (ii) charges with
minimal energy under the static balance in nonextremal charged black holes, and
(iii) charges in the Sauter-type electric fields. We then compare the results
from the monodromy with those from the exact wave functions in terms of the
hypergeometric functions with three regular singular points. The explicit
elaboration of monodromy and the model calculations worked out here seem to
reveal evidences that the monodromy may provide a practical technique to study
the spontaneous pair production in general black holes and electromagnetic
fields.Comment: version to appear in Chinese Journal of Physic
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