Initial data for fluid bodies in general relativity

We show that there exist asymptotically flat almost-smooth initial data for Einstein-perfect fluid's equation that represent an isolated liquid-type body. By liquid-type body we mean that the fluid energy density has compact support and takes a strictly positive constant value at its boundary. By almost-smooth we mean that all initial data fields are smooth everywhere on the initial hypersurface except at the body boundary, where tangential derivatives of any order are continuous at that boundary. PACS: 04.20.Ex, 04.40.Nr, 02.30.JrComment: 38 pages, LaTeX 2e, no figures. Accepted for publication in Phys. Rev.

De l'\'equation de prescription de courbure scalaire aux \'equations de contrainte en relativit\'e g\'en\'erale sur une vari\'et\'e asymptotiquement hyperbolique

Two problems concerning asymptotically hyperbolic manifolds with an inner boundary are studied. First, we study scalar curvature presciption with either Dirichlet or mean curvature prescription interior boundary condition. Then we apply those results to the Lichnerowicz equation with (future or past) apparent horizon interior boundary condition. In the last part we show how to construct TT-tensors. Thus we obtain Cauchy data with constant mean curvature for Einstein vacuum equations.Comment: Added reference

On the existence of initial data containing isolated black holes

We present a general construction of initial data for Einstein's equations containing an arbitrary number of black holes, each of which is instantaneously in equilibrium. Each black hole is taken to be a marginally trapped surface and plays the role of the inner boundary of the Cauchy surface. The black hole is taken to be instantaneously isolated if its outgoing null rays are shear-free. Starting from the choice of a conformal metric and the freely specifiable part of the extrinsic curvature in the bulk, we give a prescription for choosing the shape of the inner boundaries and the boundary conditions that must be imposed there. We show rigorously that with these choices, the resulting non-linear elliptic system always admits solutions.Comment: 11 pages, 2 figures, RevTeX

Is general relativity `essentially understood' ?

The content of Einstein's theory of gravitation is encoded in the properties of the solutions to his field equations. There has been obtained a wealth of information about these solutions in the ninety years the theory has been around. It led to the prediction and the observation of physical phenomena which confirm the important role of general relativity in physics. The understanding of the domain of highly dynamical, strong field configurations is, however, still quite limited. The gravitational wave experiments are likely to provide soon observational data on phenomena which are not accessible by other means. Further theoretical progress will require, however, new methods for the analysis and the numerical calculation of the solutions to Einstein's field equations on large scales and under general assumptions. We discuss some of the problems involved, describe the status of the field and recent results, and point out some open problems.Comment: Extended version of a talk which was to be delivered at the DPG Fruehjahrstagung in Berlin, 5 March 200

Predictions of polarized dust emission from interstellar clouds: spatial variations in the efficiency of radiative torque alignment

Polarization carries information about the magnetic fields in interstellar clouds. The observations of polarized dust emission are used to study the role of magnetic fields in the evolution of molecular clouds and the initial phases of star-formation. We study the grain alignment with realistic simulations, assuming the radiative torques to be the main mechanism that spins the grains up. The aim is to study the efficiency of the grain alignment as a function of cloud position and to study the observable consequences of these spatial variations. Our results are based on the analysis of model clouds derived from MHD simulations. The continuum radiative transfer problem is solved with Monte Carlo methods to estimate the 3D distribution of dust emission and the radiation field strength affecting the grain alignment. We also examine the effect of grain growth in cores. We are able to reproduce the results of Cho & Lazarian using their assumptions. However, the anisotropy factor even in the 1D case is lower than their assumption of $\gamma = 0.7$, and thus we get less efficient radiative torques. Compared with our previous paper, the polarization degree vs. intensity relation is steeper because of less efficient grain alignment within dense cores. Without grain growth, the magnetic field of the cores is poorly recovered above a few $A_{\rm V}$. If grain size is doubled in the cores, the polarization of dust emission can trace the magnetic field lines possibly up to $A_{\rm V} \sim 10$ magnitudes. However, many of the prestellar cores may be too young for grain coagulation to play a major role. The inclusion of direction dependent radiative torque efficiency weakens the alignment. Even with doubled grain size, we would not expect to probe the magnetic field past a few magnitudes in $A_{\rm V}$.Comment: 12 pages, 15 figures, submitted to A&A 19.12.2008; 09.01.2009: Corrected the name of Juvela; 24.04.2009: revised, added content, 13 pages, 16 figures; 18.06.2009: Language edited, print versio

Conformal structures of static vacuum data

In the Cauchy problem for asymptotically flat vacuum data the solution-jets along the cylinder at space-like infinity develop in general logarithmic singularities at the critical sets at which the cylinder touches future/past null infinity. The tendency of these singularities to spread along the null generators of null infinity obstructs the development of a smooth conformal structure at null infinity. For the solution-jets arising from time reflection symmetric data to extend smoothly to the critical sets it is necessary that the Cotton tensor of the initial three-metric h satisfies a certain conformally invariant condition (*) at space-like infinity, it is sufficient that h be asymptotically static at space-like infinity. The purpose of this article is to characterize the gap between these conditions. We show that with the class of metrics which satisfy condition (*) on the Cotton tensor and a certain non-degeneracy requirement is associated a one-form $\kappa$ with conformally invariant differential $d\kappa$. We provide two criteria: If $h$ is real analytic, $\kappa$ is closed, and one of it integrals satisfies a certain equation then h is conformal to static data near space-like infinity. If h is smooth, $\kappa$ is asymptotically closed, and one of it integrals satisfies a certain equation asymptotically then h is asymptotically conformal to static data at space-like infinity.Comment: 68 pages, typos corrected, references and details adde

On the horizon instability of an extreme Reissner-Nordstrom black hole

Aretakis has proved that a massless scalar field has an instability at the horizon of an extreme Reissner-Nordstr\"om black hole. We show that a similar instability occurs also for a massive scalar field and for coupled linearized gravitational and electromagnetic perturbations. We present numerical results for the late time behaviour of massless and massive scalar fields in the extreme RN background and show that instabilities are present for initial perturbations supported outside the horizon, e.g.\ an ingoing wavepacket. For a massless scalar we show that the numerical results for the late time behaviour are reproduced by an analytic calculation in the near-horizon geometry. We relate Aretakis' conserved quantities at the future horizon to the Newman-Penrose conserved quantities at future null infinity.Comment: 44 pages, 19 figure

Original Article Morusin induces cell death through inactivating STAT3 signaling in prostate cancer cells

Abstract: STAT3 has been recognized as an efficacious drug target for prostate cancer because of its constitutive activation in this fatal disease. We recently identified the root bark of Morus alba Linn. as a potential STAT3 inhibitor among 33 phytomedicines traditionally used in Korea. Morusin, an active compound isolated from the root bark of Morus alba, has shown anti-oxidant and anti-inflammatory effects. In the present study, we examined whether morusin has a potential as an anti-cancer agent in prostate cancer. We found that morusin suppressed viability of prostate cancer cells, but little effect in normal human prostate epithelial cells. Morusin also reduced STAT3 activity by inhibiting its phosphorylation, nuclear accumulation, and DNA binding activity. In addition, morusin down-regulated expression of STAT3 target genes encoding Bcl-xL, Bcl-2, Survivin, c-Myc and Cyclin D1, which are involved in regulation of apoptosis and cell cycle. Furthermore, morusin induced apoptosis in human prostate cancer cells by reducing STAT3 activity. Taken together, these results suggest that morusin could be a potentially therapeutic agent for prostate cancer by reducing STAT3 activity and inducing apoptosis

Theorems on existence and global dynamics for the Einstein equations

This article is a guide to theorems on existence and global dynamics of solutions of the Einstein equations. It draws attention to open questions in the field. The local-in-time Cauchy problem, which is relatively well understood, is surveyed. Global results for solutions with various types of symmetry are discussed. A selection of results from Newtonian theory and special relativity that offer useful comparisons is presented. Treatments of global results in the case of small data and results on constructing spacetimes with prescribed singularity structure or late-time asymptotics are given. A conjectural picture of the asymptotic behaviour of general cosmological solutions of the Einstein equations is built up. Some miscellaneous topics connected with the main theme are collected in a separate section.Comment: Submitted to Living Reviews in Relativity, major update of Living Rev. Rel. 5 (2002)

Stationary Black Holes: Uniqueness and Beyond

The spectrum of known black-hole solutions to the stationary Einstein equations has been steadily increasing, sometimes in unexpected ways. In particular, it has turned out that not all black-hole-equilibrium configurations are characterized by their mass, angular momentum and global charges. Moreover, the high degree of symmetry displayed by vacuum and electro-vacuum black-hole spacetimes ceases to exist in self-gravitating non-linear field theories. This text aims to review some developments in the subject and to discuss them in light of the uniqueness theorem for the Einstein-Maxwell system.Comment: Major update of the original version by Markus Heusler from 1998. Piotr T. Chru\'sciel and Jo\~ao Lopes Costa succeeded to this review's authorship. Significantly restructured and updated all sections; changes are too numerous to be usefully described here. The number of references increased from 186 to 32