Past and future gauge in numerical relativity

Numerical relativity describes a discrete initial value problem for general relativity. A choice of gauge involves slicing space-time into space-like hypersurfaces. This introduces past and future gauge relative to the hypersurface of present time. Here, we propose solving the discretized Einstein equations with a choice of gauge in the future and a dynamical gauge in the past. The method is illustrated on a polarized Gowdy wave.Comment: To appear in Class Quantum Grav, Let

Numerical Integration of Nonlinear Wave Equations for General Relativity

A second-order numerical implementation is given for recently derived nonlinear wave equations for general relativity. The Gowdy T$^3$ cosmology is used as a test bed for studying the accuracy and convergence of simulations of one-dimensional nonlinear waves. The complete freedom in space-time slicing in the present formulation is exploited to compute in the Gowdy line-element. Second-order convergence is found by direct comparison of the results with either analytical solutions for polarized waves, or solutions obtained from Gowdy's reduced wave equations for the more general unpolarized waves. Some directions for extensions are discussed.Comment: 19 pages (LaTex), 3 figures (ps

The Chandra X-ray view of the power sources in Cepheus A

The central part of the massive star-forming region Cepheus A contains several radio sources which indicate multiple outflow phenomena, yet the driving sources of the individual outflows have not been identified. We present a high-resolution Chandra observation of this region that shows the presence of bright X-ray sources, consistent with active pre-main sequence stars, while the strong absorption hampers the detection of less luminous objects. A new source has been discovered located on the line connecting H_2 emission regions at the eastern and western parts of Cepheus A. This source could be the driving source of HH 168. We present a scenario relating the observed X-ray and radio emission.Comment: 7 pages, 6 figures, accepted for publication in A&

Topological Black Holes of Einstein-Yang-Mills dilaton Gravity

We present the topological solutions of Einstein-dilaton gravity in the presence of a non-Abelian Yang-Mills field. In 4 dimensions, we consider the $So(3)$ and $So(2,1)$ semisimple group as the Yang-Mills gauge group, and introduce the black hole solutions with spherical and hyperbolic horizons, respectively. The solution in the absence of dilaton potential is asymptotically flat and exists only with spherical horizon. Contrary to the non-extreme Reissner-Nordstrom black hole, which has two horizons with a timelike and avoidable singularity, here the solution may present a black hole with a null and unavoidable singularity with only one horizon. In the presence of dilaton potential, the asymptotic behavior of the solutions is neither flat nor anti-de Sitter. These solutions contain a null and avoidable singularity, and may present a black hole with two horizons, an extreme black hole or a naked singularity. We also calculate the mass of the solutions through the use of a modified version of Brown and York formalism, and consider the first law of thermodynamics.Comment: 13 pages, 3 figure

The evolution of the X-ray emission of HH 2 - Investigating heating and cooling processes

Young stellar objects often drive powerful bipolar outflows which evolve on time scales of a few years. An increasing number of these outflows has been detected in X-rays implying the existence of million degree plasma almost co-spatial with the lower temperature gas observed in the optical and near-IR. The details of the heating and cooling processes of the X-ray emitting part of these so-called Herbig-Haro objects are still ambiguous, e.g., whether the cooling is dominated by expansion, radiation or thermal conduction. We present a second epoch Chandra observation of the first X-ray detected Herbig-Haro object (HH 2) and derive the proper-motion of the X-ray emitting plasma and its cooling history. We argue that the most likely explanation for the constancy of the X-ray luminosity, the alignment with the optical emission and the proper-motion is that the cooling is dominated by radiative losses leading to cooling times exceeding a decade. We explain that a strong shock caused by fast material ramming into slower gas in front of it about ten years ago can explain the X-ray emission while being compatible with the available multi-wavelength data of HH 2.Comment: 5 pages with 4 figures; accepted for publication by Astronomy and Astrophysic

Cluster magnetic fields from active galactic nuclei

Active galactic nuclei (AGN) found at the centers of clusters of galaxies are a possible source for weak cluster-wide magnetic fields. To evaluate this scenario, we present 3D adaptive mesh refinement MHD simulations of a cool-core cluster that include injection of kinetic, thermal, and magnetic energy via an AGN-powered jet. Using the MHD solver in FLASH 2, we compare several sub-resolution approaches that link the estimated accretion rate as measured on the simulation mesh to the accretion rate onto the central black hole and the resulting feedback. We examine the effects of magnetized outflows on the accretion history of the black hole and discuss the ability of these models to magnetize the cluster medium.Comment: 4 pages, 2 figures, submitted to conference proceedings "The Monster's Fiery Breath: Feedback in Groups, Galaxies, and Clusters

Some geometry and combinatorics for the S-invariant of ternary cubics

Given a real cubic form f(x,y,z), there is a pseudo-Riemannian metric given by its Hessian matrix, defined on the open subset of R^3 where the Hessian determinant h is non-zero. We determine the full curvature tensor of this metric in terms of h and the S-invariant of f, obtaining in the process various different characterizations of S. Motivated by the case of intersection forms associated with complete intersection threefolds in the product of three projective spaces, we then study ternary cubic forms which arise as follows: we choose positive integers d1, d2, d3, set r = d1 + d2 + d3 - 3, and consider the coefficient F(x,y,z) of H1^d1 H2^d2 H3^d3 in the product (x H1 + y H2 + z H3)^3 (a_1 H1 + b_1 H2 + c_1 H3) ... (a_r H1 + b_r H2 + c_r H3), the a_j, b_j and c_j denoting non-negative real numbers; we assume also that F is non-degenerate. Previous work of the author on sectional curvatures of Kahler moduli suggests a number of combinatorial conjectures concerning the invariants of F. It is proved here for instance that the Hessian determinant, considered as a polynomial in x,y,z and the a_j, b_j, c_j, has only positive coefficients. The same property is also conjectured to hold for the S-invariant; the evidence and background to this conjecture is explained in detail in the paper.Comment: 23 pages, plain Tex, updated and shortened, final versio

Finite size corrections to the blackbody radiation laws

We investigate the radiation of a blackbody in a cavity of finite size. For a given geometry, we use semiclassical techniques to obtain explicit expressions of the modified Planck's and Stefan-Boltzmann's blackbody radiation laws as a function of the size and shape of the cavity. We determine the range of parameters (temperature, size and shape of the cavity) for which these effects are accessible to experimental verification. Finally we discuss potential applications of our findings in the physics of the cosmic microwave background and sonoluminescence.Comment: 5 pages, 1 figure, journal versio