454 research outputs found
Conformal scattering for a nonlinear wave equation on a curved background
The purpose of this paper is to establish a geometric scattering result for a
conformally invariant nonlinear wave equation on an asymptotically simple
spacetime. The scattering operator is obtained via trace operators at null
infinities. The proof is achieved in three steps. A priori linear estimates are
obtained via an adaptation of the Morawetz vector field in the Schwarzschild
spacetime and a method used by H\"ormander for the Goursat problem. A
well-posedness result for the characteristic Cauchy problem on a light cone at
infinity is then obtained. This requires a control of the nonlinearity uniform
in time which comes from an estimates of the Sobolev constant and a decay
assumption on the nonlinearity of the equation. Finally, the trace operators on
conformal infinities are built and used to define the conformal scattering
operator
Recovering the mass and the charge of a Reissner-Nordstr\"om black hole by an inverse scattering experiment
In this paper, we study inverse scattering of massless Dirac fields that
propagate in the exterior region of a Reissner-Nordstr\"om black hole. Using a
stationary approach we determine precisely the leading terms of the high-energy
asymptotic expansion of the scattering matrix that, in turn, permit us to
recover uniquely the mass of the black hole and its charge up to a sign
Scattering of massive Dirac fields on the Schwarzschild black hole spacetime
With a generally covariant equation of Dirac fields outside a black hole, we
develop a scattering theory for massive Dirac fields. The existence of modified
wave operators at infinity is shown by implementing a time-dependent
logarithmic phase shift from the free dynamics to offset a long-range mass
term. The phase shift we obtain is a matrix operator due to the existence of
both positive and negative energy wave components.Comment: LaTex, 17 page
Universal Bound on Dynamical Relaxation Times and Black-Hole Quasinormal Ringing
From information theory and thermodynamic considerations a universal bound on
the relaxation time of a perturbed system is inferred, , where is the system's temperature. We prove that black holes
comply with the bound; in fact they actually {\it saturate} it. Thus, when
judged by their relaxation properties, black holes are the most extreme objects
in nature, having the maximum relaxation rate which is allowed by quantum
theory.Comment: 4 page
Local energy decay of massive Dirac fields in the 5D Myers-Perry metric
We consider massive Dirac fields evolving in the exterior region of a
5-dimensional Myers-Perry black hole and study their propagation properties.
Our main result states that the local energy of such fields decays in a weak
sense at late times. We obtain this result in two steps: first, using the
separability of the Dirac equation, we prove the absence of a pure point
spectrum for the corresponding Dirac operator; second, using a new form of the
equation adapted to the local rotations of the black hole, we show by a Mourre
theory argument that the spectrum is absolutely continuous. This leads directly
to our main result.Comment: 40 page
Asymptotic distribution of quasi-normal modes for Kerr-de Sitter black holes
We establish a Bohr-Sommerfeld type condition for quasi-normal modes of a
slowly rotating Kerr-de Sitter black hole, providing their full asymptotic
description in any strip of fixed width. In particular, we observe a
Zeeman-like splitting of the high multiplicity modes at a=0 (Schwarzschild-de
Sitter), once spherical symmetry is broken. The numerical results presented in
Appendix B show that the asymptotics are in fact accurate at very low energies
and agree with the numerical results established by other methods in the
physics literature. We also prove that solutions of the wave equation can be
asymptotically expanded in terms of quasi-normal modes; this confirms the
validity of the interpretation of their real parts as frequencies of
oscillations, and imaginary parts as decay rates of gravitational waves.Comment: 66 pages, 6 figures; journal version (to appear in Annales Henri
Poincar\'e
Factors of interrupting chemotherapy in patients with Advanced Non-Small-Cell Lung Cancer
<p>Abstract</p> <p>Background</p> <p>Little is known about prognosis of metastatic patients after receiving a first-line treatment and failure. Our group already showed in pre-treated patients enrolled in phase I clinical trials that a performance status (PS) > 2 and an LDH > 600 UI/L were independent prognostic factors. In this prospective study, which included 45 patients, we identified clinical and biological variables as outcome predictors in metastatic Non-Small Cell lung cancer after first line chemotherapy were identified.</p> <p>Findings</p> <p>Forty-five patients that were previously treated for metastatic disease from 12/2000 to 11/2005 in the comprehensive cancer centre (Centre Léon Bérard). Clinical assessment and blood parameters were recorded and considered. Patient prognostic factors for overall survival (OS) with a 0.05-significance level in univariate analysis were entered in a multivariate Cox model for further analysis.</p> <p>Patients' median age was 58.5 years (range: 37 - 76). Sixty two percent of the patients were PS = 0 or 1. After inclusion, nine patients received second-line (22.5%), and two received third-line chemotherapy (5%). Univariate analysis showed that the factors associated with reduced OS were: PS > 2, weight loss >10%, more than one line of chemotherapy treatment and abnormal blood parameters (hemoglobin (Hb), platelet and neutrophils counts). Multiple regression analysis confirmed that PS > 2 and abnormal hemoglobin were independent predictors for low overall survival. According to the presence of none (33%), 1 (37%) and 2 (30%) prognostic factors, median OS were 12, 5 and 2 months respectively.</p> <p>Conclusion</p> <p>From this prospective study, both PS and anemia were found as independent determinants of survival, we found that both PS and anemia were independent determinants of survival. The combination of poor PS and anemia is an effective strategy to predict survival in the case of patients with metastatic NSCLC receiving further treatment after the first line.</p
Kerr black hole quasinormal frequencies
Black-hole quasinormal modes (QNM) have been the subject of much recent
attention, with the hope that these oscillation frequencies may shed some light
on the elusive theory of quantum gravity. We compare numerical results for the
QNM spectrum of the (rotating) Kerr black hole with an {\it exact} formula
Re, which is based on Bohr's correspondence
principle. We find a close agreement between the two. Possible implications of
this result to the area spectrum of quantum black holes are discussed.Comment: 3 pages, 2 figure
Dirty black holes: Quasinormal modes for "squeezed" horizons
We consider the quasinormal modes for a class of black hole spacetimes that,
informally speaking, contain a closely ``squeezed'' pair of horizons. (This
scenario, where the relevant observer is presumed to be ``trapped'' between the
horizons, is operationally distinct from near-extremal black holes with an
external observer.) It is shown, by analytical means, that the spacing of the
quasinormal frequencies equals the surface gravity at the squeezed horizons.
Moreover, we can calculate the real part of these frequencies provided that the
horizons are sufficiently close together (but not necessarily degenerate or
even ``nearly degenerate''). The novelty of our analysis (which extends a
model-specific treatment by Cardoso and Lemos) is that we consider ``dirty''
black holes; that is, the observable portion of the (static and spherically
symmetric) spacetime is allowed to contain an arbitrary distribution of matter.Comment: 15 pages, uses iopart.cls and setstack.sty V2: Two references added.
Also, the appendix now relates our computation of the Regge-Wheeler potential
for gravity in a generic "dirty" black hole to the results of Karlovini
[gr-qc/0111066
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