Testing a model for the well-posedness of the Cauchy-characteristic problem in Bondi coordinates

Gravity waves reveal colliding black holes, galaxies, the birth of a black hole in a supernova and the growth pains of our universe. Gravitational waves are unambiguous measured only at future null infinity

Well-posedness of Characteristic Evolution in Bondi Coordinates

Gravitational waves carry information about their source, and their detection will uncover facets of our universe, otherwise invisible. Recently, we made publicly available a waveform computation tool, the PITT code, as part of the Einstein Toolkit open software for relativistic astrophysics. The code implements the “characteristic method,” which computes the gravitational waves infinitely far from their source in terms of compactified light cones. We proved that our code produces waveforms that satisfy the demands of next generation detectors. However, the main problem is that the well-posedness of the Einstein equations in characteristic formulation is not proven. Here we present our progress towards developing and testing a new computational evolution algorithm based on the well-posedness of the characteristic evolution. We analyze the well-posedness of the problem for quasi-linear scalar waves propagating on an asymptotically flat curved space background with source, in null Bondi-Sachs coordinates. We design a new numerical boundary and evolution algorithm, and proved that is stable both numerically and analytically. We built and run numerical tests to confirm the well-posedness and stability properties of the new algorithm. The knowledge gained from the model problems considered here should be of benefit to a better understanding of the gravitational case. A new characteristic code based upon well-posedness would be of great value

A New Algorithm for the Numerical Computation of Gravitational Waves

With gravitational waves, Gravitational Wave Astronomy can “see” colliding back holes and galaxies, the birth of a black hole in a supernova, the growth pains of our universe and the structure of spacetime

A Hyperbolic Solver for Black Hole Initial Data in Numerical Relativity

Initial data in numerical relativity. The constraints are formulated as elliptic equations, parabolic equations and strongly hyperbolic equations. This presentation is about a different approach to initial data for black holes, the strongly hyperbolic method

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

GRB Light Curves in the Relativistic Turbulence Model

Randomly oriented relativistic emitters in a relativistically expanding shell provides an alternative to internal shocks as a mechanism for producing GRBs' variable light curves with efficient conversion of energy to radiation. In this model the relativistic outflow is broken into small emitters moving relativistically in the outflow's rest frame. Variability arises because an observer sees an emitter only when its velocity points towards him so that only a small fraction of the emitters are seen by a given observer. Models with significant relativistic random motions require converting and maintaining a large fraction of the overall energy into these motions. While it is not clear how this is achieved, we explore here, using two toy models, the constraints on parameters required to produce light curves comparable to the observations. We find that a tight relation between the size of the emitters and the bulk and random Lorentz factors is needed and that the random Lorentz factor determines the variability. While both models successfully produce the observed variability there are several inconsistencies with other properties of the light curves. Most of which, but not all, might be resolved if the central engine is active for a long time producing a number of shells, resembling to some extent the internal shocks model.Comment: Significantly revised with a discussion of additional models. Accepted for publication in APJ