Geodesic Deviation in Regge Calculus

Geodesic deviation is the most basic manifestation of the influence of gravitational fields on matter. We investigate geodesic deviation within the framework of Regge calculus, and compare the results with the continuous formulation of general relativity on two different levels. We show that the continuum and simplicial descriptions coincide when the cumulative effect of the Regge contributions over an infinitesimal element of area is considered. This comparison provides a quantitative relation between the curvature of the continuous description and the deficit angles of Regge calculus. The results presented might also be of help in developing generic ways of including matter terms in the Regge equations.Comment: 9 pages. Latex 2e with 5 EPS figures. Submitted to CQ

Synchrotron Self-Compton Model for Rapid Nonthermal Flares in Blazars with Frequency-Dependent Time Lags

We model rapid variability of multifrequency emission from blazars occurring across the electromagnetic spectrum (from radio to gamma-rays). Lower energy emission is produced by the synchrotron mechanism, whereas higher energy emission is due to inverse Compton scattering of the synchrotron emission. We take into account energy stratification established by particle acceleration at shock fronts and energy losses due to synchrotron emission. We also consider the effect of light travel delays for the synchrotron emission that supplies the seed photons for inverse Compton scattering. The production of a flare is caused by the collision between a relativistic shock wave and a stationary feature in the jet (e.g., a Mach disk). The collision leads to the formation of forward and reverse shocks, which confine two contiguous emission regions resulting in complex profiles of simulated flares. Simulations of multifrequency flares indicate that relative delays between the inverse Compton flares and their synchrotron counterparts are dominated by energy stratification and geometry of the emitting regions, resulting in both negative and positive time delays depending on the frequency of observation. Light travel effects of the seed photons may lead to a noticeable delay of the inverse Compton emission with respect to synchrotron variability if the line of sight is almost perfectly aligned with the jet. We apply the model to a flare in 3C 273 and derive the properties of shocked plasma responsible for the flare. We show that the pronounced negative time delay between the X-ray and IR light curves (X-rays peak after the maximum in the synchrotron emission) can be accounted for if both forward and reverse shocks are considered.Comment: 48 pages, 18 figures, accepted for publication in The Astrophysical Journa

Topological Lattice Gravity Using Self-Dual Variables

Topological gravity is the reduction of general relativity to flat space-times. A lattice model describing topological gravity is developed starting from a Hamiltonian lattice version of B\w F theory. The extra symmetries not present in gravity that kill the local degrees of freedom in $B\wedge F$ theory are removed. The remaining symmetries preserve the geometrical character of the lattice. Using self-dual variables, the conditions that guarantee the geometricity of the lattice become reality conditions. The local part of the remaining symmetry generators, that respect the geometricity-reality conditions, has the form of Ashtekar's constraints for GR. Only after constraining the initial data to flat lattices and considering the non-local (plus local) part of the constraints does the algebra of the symmetry generators close. A strategy to extend the model for non-flat connections and quantization are discussed.Comment: 22 pages, revtex, no figure

Cauchy-characteristic Evolution of Einstein-Klein-Gordon Systems: The Black Hole Regime

The Cauchy+characteristic matching (CCM) problem for the scalar wave equation is investigated in the background geometry of a Schwarzschild black hole. Previously reported work developed the CCM framework for the coupled Einstein-Klein-Gordon system of equations, assuming a regular center of symmetry. Here, the time evolution after the formation of a black hole is pursued, using a CCM formulation of the governing equations perturbed around the Schwarzschild background. An extension of the matching scheme allows for arbitrary matching boundary motion across the coordinate grid. As a proof of concept, the late time behavior of the dynamics of the scalar field is explored. The power-law tails in both the time-like and null infinity limits are verified.Comment: To appear in Phys. Rev. D, 9 pages, revtex, 5 figures available at http://www.astro.psu.edu/users/nr/preprints.htm

Cauchy-characteristic Evolution of Einstein-Klein-Gordon Systems

A Cauchy-characteristic initial value problem for the Einstein-Klein-Gordon system with spherical symmetry is presented. Initial data are specified on the union of a space-like and null hypersurface. The development of the data is obtained with the combination of a constrained Cauchy evolution in the interior domain and a characteristic evolution in the exterior, asymptotically flat region. The matching interface between the space-like and characteristic foliations is constructed by imposing continuity conditions on metric, extrinsic curvature and scalar field variables, ensuring smoothness across the matching surface. The accuracy of the method is established for all ranges of $M/R$, most notably, with a detailed comparison of invariant observables against reference solutions obtained with a calibrated, global, null algorithm.Comment: Submitted to Phys. Rev. D, 16 pages, revtex, 7 figures available at http://nr.astro.psu.edu:8080/preprints.htm

Apparent horizons in simplicial Brill wave initial data

We construct initial data for a particular class of Brill wave metrics using Regge calculus, and compare the results to a corresponding continuum solution, finding excellent agreement. We then search for trapped surfaces in both sets of initial data, and provide an independent verification of the existence of an apparent horizon once a critical gravitational wave amplitude is passed. Our estimate of this critical value, using both the Regge and continuum solutions, supports other recent findings.Comment: 7 pages, 6 EPS figures, LaTeX 2e. Submitted to Class. Quant. Gra

A fully (3+1)-D Regge calculus model of the Kasner cosmology

We describe the first discrete-time 4-dimensional numerical application of Regge calculus. The spacetime is represented as a complex of 4-dimensional simplices, and the geometry interior to each 4-simplex is flat Minkowski spacetime. This simplicial spacetime is constructed so as to be foliated with a one parameter family of spacelike hypersurfaces built of tetrahedra. We implement a novel two-surface initial-data prescription for Regge calculus, and provide the first fully 4-dimensional application of an implicit decoupled evolution scheme (the ``Sorkin evolution scheme''). We benchmark this code on the Kasner cosmology --- a cosmology which embodies generic features of the collapse of many cosmological models. We (1) reproduce the continuum solution with a fractional error in the 3-volume of 10^{-5} after 10000 evolution steps, (2) demonstrate stable evolution, (3) preserve the standard deviation of spatial homogeneity to less than 10^{-10} and (4) explicitly display the existence of diffeomorphism freedom in Regge calculus. We also present the second-order convergence properties of the solution to the continuum.Comment: 22 pages, 5 eps figures, LaTeX. Updated and expanded versio

Stable characteristic evolution of generic 3-dimensional single-black-hole spacetimes

We report new results which establish that the accurate 3-dimensional numerical simulation of generic single-black-hole spacetimes has been achieved by characteristic evolution with unlimited long term stability. Our results cover a selection of distorted, moving and spinning single black holes, with evolution times up to 60,000M.Comment: 4 pages, 3 figure

Relativistic hydrodynamics on spacelike and null surfaces: Formalism and computations of spherically symmetric spacetimes

We introduce a formulation of Eulerian general relativistic hydrodynamics which is applicable for (perfect) fluid data prescribed on either spacelike or null hypersurfaces. Simple explicit expressions for the characteristic speeds and fields are derived in the general case. A complete implementation of the formalism is developed in the case of spherical symmetry. The algorithm is tested in a number of different situations, predisposing for a range of possible applications. We consider the Riemann problem for a polytropic gas, with initial data given on a retarded/advanced time slice of Minkowski spacetime. We compute perfect fluid accretion onto a Schwarzschild black hole spacetime using ingoing null Eddington-Finkelstein coordinates. Tests of fluid evolution on dynamic background include constant density and TOV stars sliced along the radial null cones. Finally, we consider the accretion of self-gravitating matter onto a central black hole and the ensuing increase in the mass of the black hole horizon.Comment: 23 pages, 13 figures, submitted to Phys. Rev.

Proton--induced deuteron breakup at GeV energies with forward emission of a fast proton pair

A study of the deuteron breakup reaction $pd \to (pp)n$ with forward emission of a fast proton pair with small excitation energy $E_{pp}<$ 3 MeV has been performed at the ANKE spectrometer at COSY--J\"ulich. An exclusive measurement was carried out at six proton--beam energies $T_p=$~0.6,~0.7,~0.8,~0.95,~1.35, and 1.9 GeV by reconstructing the momenta of the two protons. The differential cross section of the breakup reaction, averaged up to $8^{\circ}$ over the cm polar angle of the total momentum of the $pp$ pairs, has been obtained. Since the kinematics of this process is quite similar to that of backward elastic $pd \to dp$ scattering, the results are compared to calculations based on a theoretical model previously applied to the $pd \to dp$ process.Comment: 17 pages including 6 figures and 1 table v2: minor changes; v3: minor change of author list; v4: changes in accordance with referee remark