23 research outputs found
Generic master equations for quasi-normal frequencies
Generic master equations governing the highly-damped quasi-normal frequencies
[QNFs] of one-horizon, two-horizon, and even three-horizon spacetimes can be
obtained through either semi-analytic or monodromy techniques. While many
technical details differ, both between the semi-analytic and monodromy
approaches, and quite often among various authors seeking to apply the
monodromy technique, there is nevertheless widespread agreement regarding the
the general form of the QNF master equations. Within this class of generic
master equations we can establish some rather general results, relating the
existence of "families" of QNFs of the form omega_{a,n} = (offset)_a + i n
(gap) to the question of whether or not certain ratios of parameters are
rational or irrational.Comment: 23 pages; V2: Minor additions, typos fixed. Matches published versio
Semi-analytic results for quasi-normal frequencies
The last decade has seen considerable interest in the quasi-normal
frequencies [QNFs] of black holes (and even wormholes), both asymptotically
flat and with cosmological horizons. There is wide agreement that the QNFs are
often of the form omega_n = (offset) + i n (gap), though some authors have
encountered situations where this behaviour seems to fail. To get a better
understanding of the general situation we consider a semi-analytic model based
on a piecewise Eckart (Poeschl-Teller) potential, allowing for different
heights and different rates of exponential falloff in the two asymptotic
directions. This model is sufficiently general to capture and display key
features of the black hole QNFs while simultaneously being analytically
tractable, at least for asymptotically large imaginary parts of the QNFs. We
shall derive an appropriate "quantization condition" for the asymptotic QNFs,
and extract as much analytic information as possible. In particular, we shall
explicitly verify that the (offset)+ i n (gap) behaviour is common but not
universal, with this behaviour failing unless the ratio of rates of exponential
falloff on the two sides of the potential is a rational number. (This is
"common but not universal" in the sense that the rational numbers are dense in
the reals.) We argue that this behaviour is likely to persist for black holes
with cosmological horizons.Comment: V1: 28 pages, no figures. V2: 3 references added, no physics changes.
V3: 29 pages, 9 references added, no physics changes; V4: reformatted, now 27
pages. Some clarifications, comparison with results obtained by monodromy
techniques. This version accepted for publication in JHEP. V5: Minor typos
fixed. Compatible with published versio
Patient morbidity and management patterns of community-based primary health care services in Hong Kong
published_or_final_versio
A scalar field condensation instability of rotating anti-de Sitter black holes
Near-extreme Reissner-Nordstrom-anti-de Sitter black holes are unstable
against the condensation of an uncharged scalar field with mass close to the
Breitenlohner-Freedman bound. It is shown that a similar instability afflicts
near-extreme large rotating AdS black holes, and near-extreme hyperbolic
Schwarzschild-AdS black holes. The resulting nonlinear hairy black hole
solutions are determined numerically. Some stability results for (possibly
charged) scalar fields in black hole backgrounds are proved. For most of the
extreme black holes we consider, these demonstrate stability if the ``effective
mass" respects the near-horizon BF bound. Small spherical
Reissner-Nordstrom-AdS black holes are an interesting exception to this result.Comment: 34 pages; 13 figure