Dynamics of Scalar Fields in the Background of Rotating Black Holes

A numerical study of the evolution of a massless scalar field in the background of rotating black holes is presented. First, solutions to the wave equation are obtained for slowly rotating black holes. In this approximation, the background geometry is treated as a perturbed Schwarzschild spacetime with the angular momentum per unit mass playing the role of a perturbative parameter. To first order in the angular momentum of the black hole, the scalar wave equation yields two coupled one-dimensional evolution equations for a function representing the scalar field in the Schwarzschild background and a second field that accounts for the rotation. Solutions to the wave equation are also obtained for rapidly rotating black holes. In this case, the wave equation does not admit complete separation of variables and yields a two-dimensional evolution equation. The study shows that, for rotating black holes, the late time dynamics of a massless scalar field exhibit the same power-law behavior as in the case of a Schwarzschild background independently of the angular momentum of the black hole.Comment: 14 pages, RevTex, 6 Figure

Transvaginal-laparoscopic anterior rectum resection in a hysterectomized woman with deep-infiltrating endometriosis: Description of a gynecologic natural orifice transendoluminal surgery approach

Deep-infiltrating endometriosis may affect the vagina, the rectum, and the cervicoisthmic part of the uterus, resulting in severe pain, particularly dyschezia, dysmenorrhea, dyspareunia, and diminished quality of life. Advanced surgical techniques, such as laparoscopic-assisted anterior rectum resection, are recognized as safe and effective therapeutic approaches. In some cases, a laparotomy or minilaparotomy has to be performed for technical reasons. This can be avoided in some cases by transvaginal-laparoscopic low anterior rectum resection. The technique is a 4-step procedure, which can be described as follows: step 1 (vaginal) - rectovaginal examination, preparation of the rectovaginal septum, opening of the pouch of Douglas, mobilization of the endometriotic nodule and the rectum, temporary vaginal closure; step 2 (laparoscopic) - removal of additional endometriotic lesions, adhesiolysis, final mobilization of the rectum, mobilization of the rectosigmoid, endoscopic resection using an endoscopic stapler step 3 (vaginal) - transvaginal resection of the lesion, preparation of the oral anvil, closure of the vagina; and step 4 (laparoscopic) - endoscopic transanal stapler anastomosis and underwater rectoscopy, prophylaxis of adhesions, drainage. We used this procedure to treat a 46-year-old woman (gravida 2, para 2) who was admitted to our hospital for severe lower abdominal pain, constipation, dyspareunia, dyschezia, and cyclic rectal bleedings. The symptoms were caused by an endometriotic nodule accompanied by a palpable rectum stenosis. In addition, she reported a past abdominal hysterectomy with complications caused by symptomatic myomatous uterus. As a gynecologic natural orifice surgery approach, the transvaginal-laparoscopic anterior rectum resection may be an additional useful surgical technique that could be offered by surgical gynecologists to some women with deep-infiltrating endometriosis

Supergravities with Minkowski x Sphere Vacua

Recently the authors have introduced a new gauged supergravity theory with a positive definite potential in D=6, obtained through a generalised Kaluza-Klein reduction from D=7. Of particular interest is the fact that this theory admits certain Minkowski x Sphere vacua. In this paper we extend the previous results by constructing gauged supergravities with positive definitive potentials in diverse dimensions, together with their vacuum solutions. In addition, we prove the supersymmetry of the generalised reduction ansatz. We obtain a supersymmetric solution with no form-field fluxes in the new gauged theory in D=9. This solution may be lifted to D=10, where it acquires an interpretation as a time-dependent supersymmetric cosmological solution supported purely by the dilaton. A further uplift to D=11 yields a solution describing a pp-wave.Comment: Latex, 26 pages, typos correcte

Axisymmetric core collapse simulations using characteristic numerical relativity

We present results from axisymmetric stellar core collapse simulations in general relativity. Our hydrodynamics code has proved robust and accurate enough to allow for a detailed analysis of the global dynamics of the collapse. Contrary to traditional approaches based on the 3+1 formulation of the gravitational field equations, our framework uses a foliation based on a family of outgoing light cones, emanating from a regular center, and terminating at future null infinity. Such a coordinate system is well adapted to the study of interesting dynamical spacetimes in relativistic astrophysics such as stellar core collapse and neutron star formation. Perhaps most importantly this procedure allows for the unambiguous extraction of gravitational waves at future null infinity without any approximation, along with the commonly used quadrupole formalism for the gravitational wave extraction. Our results concerning the gravitational wave signals show noticeable disagreement when those are extracted by computing the Bondi news at future null infinity on the one hand and by using the quadrupole formula on the other hand. We have strong indication that for our setup the quadrupole formula on the null cone does not lead to physical gravitational wave signals. The Bondi gravitational wave signals extracted at infinity show typical oscillation frequencies of about 0.5 kHz.Comment: 17 pages, 18 figures, submitted to Phys. Rev.

The spinorial geometry of supersymmetric heterotic string backgrounds

We determine the geometry of supersymmetric heterotic string backgrounds for which all parallel spinors with respect to the connection $\hat\nabla$ with torsion $H$, the NS$\otimes$NS three-form field strength, are Killing. We find that there are two classes of such backgrounds, the null and the timelike. The Killing spinors of the null backgrounds have stability subgroups K\ltimes\bR^8 in $Spin(9,1)$, for $K=Spin(7)$, SU(4), $Sp(2)$, $SU(2)\times SU(2)$ and $\{1\}$, and the Killing spinors of the timelike backgrounds have stability subgroups $G_2$, SU(3), SU(2) and $\{1\}$. The former admit a single null $\hat\nabla$-parallel vector field while the latter admit a timelike and two, three, five and nine spacelike $\hat\nabla$-parallel vector fields, respectively. The spacetime of the null backgrounds is a Lorentzian two-parameter family of Riemannian manifolds $B$ with skew-symmetric torsion. If the rotation of the null vector field vanishes, the holonomy of the connection with torsion of $B$ is contained in $K$. The spacetime of time-like backgrounds is a principal bundle $P$ with fibre a Lorentzian Lie group and base space a suitable Riemannian manifold with skew-symmetric torsion. The principal bundle is equipped with a connection $\lambda$ which determines the non-horizontal part of the spacetime metric and of $H$. The curvature of $\lambda$ takes values in an appropriate Lie algebra constructed from that of $K$. In addition $dH$ has only horizontal components and contains the Pontrjagin class of $P$. We have computed in all cases the Killing spinor bilinears, expressed the fluxes in terms of the geometry and determine the field equations that are implied by the Killing spinor equations.Comment: 73pp. v2: minor change

Plasma waves driven by gravitational waves in an expanding universe

In a Friedmann-Robertson-Walker (FRW) cosmological model with zero spatial curvature, we consider the interaction of the gravitational waves with the plasma in the presence of a weak magnetic field. Using the relativistic hydromagnetic equations it is verified that large amplitude magnetosonic waves are excited, assuming that both, the gravitational field and the weak magnetic field do not break the homogeneity and isotropy of the considered FRW spacetime.Comment: 14 page

Criteria of efficiency for conformal prediction

We study optimal conformity measures for various criteria of efficiency of classification in an idealised setting. This leads to an important class of criteria of efficiency that we call probabilistic; it turns out that the most standard criteria of efficiency used in literature on conformal prediction are not probabilistic unless the problem of classification is binary. We consider both unconditional and label-conditional conformal prediction.Comment: 31 page

Spherical collapse of supermassive stars: neutrino emission and gamma-ray bursts

We present the results of numerical simulations of the spherically symmetric gravitational collapse of supermassive stars (SMS). The collapse is studied using a general relativistic hydrodynamics code. The coupled system of Einstein and fluid equations is solved employing observer time coordinates, by foliating the spacetime by means of outgoing null hypersurfaces. The code contains an equation of state which includes effects due to radiation, electrons and baryons, and detailed microphysics to account for electron-positron pairs. In addition energy losses by thermal neutrino emission are included. We are able to follow the collapse of SMS from the onset of instability up to the point of black hole formation. Several SMS with masses in the range $5\times 10^5 M_{\odot}- 10^9 M_{\odot}$ are simulated. In all models an apparent horizon forms initially, enclosing the innermost 25% of the stellar mass. From the computed neutrino luminosities, estimates of the energy deposition by $\nu\bar{\nu}$-annihilation are obtained. Only a small fraction of this energy is deposited near the surface of the star, where, as proposed recently by Fuller & Shi (1998), it could cause the ultrarelativistic flow believed to be responsible for $\gamma$-ray bursts. Our simulations show that for collapsing SMS with masses larger than $5\times 10^5 M_{\odot}$ the energy deposition is at least two orders of magnitude too small to explain the energetics of observed long-duration bursts at cosmological redshifts. In addition, in the absence of rotational effects the energy is deposited in a region containing most of the stellar mass. Therefore relativistic ejection of matter is impossible.Comment: 13 pages, 11 figures, submitted to A&

Composite p-Branes in Diverse Dimensions

We use a simple algebraic method to find a special class of composite p-brane solutions of higher dimensional gravity coupled with matter. These solutions are composed of n constituent p-branes corresponding n independent harmonic functions. A simple algebraic criteria of existence of such solutions is presented. Relations with D=11,10 known solutions are discussed.Comment: 11 pages, latex, emlines2.sty; corrections in Sect.