Chaos and Fractals around Black Holes

Fractal basin boundaries provide an important means of characterizing chaotic systems. We apply these ideas to general relativity, where other properties such as Lyapunov exponents are difficult to define in an observer independent manner. Here we discuss the difficulties in describing chaotic systems in general relativity and investigate the motion of particles in two- and three-black-hole spacetimes. We show that the dynamics is chaotic by exhibiting the basins of attraction of the black holes which have fractal boundaries. Overcoming problems of principle as well as numerical difficulties, we evaluate Lyapunov exponents numerically and find that some trajectories have a positive exponent.Comment: To appear in "Fractals" March issue (World Scientific), 20 figures available by request, also available from SLAC's gr-qc postscript archiv

Mapping the gravitational wave background

The gravitational wave sky is expected to have isolated bright sources superimposed on a diffuse gravitational wave background. The background radiation has two components: a confusion limited background from unresolved astrophysical sources; and a cosmological component formed during the birth of the universe. A map of the gravitational wave background can be made by sweeping a gravitational wave detector across the sky. The detector output is a complicated convolution of the sky luminosity distribution, the detector response function and the scan pattern. Here we study the general de-convolution problem, and show how LIGO (Laser Interferometric Gravitational Observatory) and LISA (Laser Interferometer Space Antenna) can be used to detect anisotropies in the gravitational wave background.Comment: 16 pages, 6 figures. Submitted to CQ

Searching for Massive Black Hole Binaries in the first Mock LISA Data Challenge

The Mock LISA Data Challenge is a worldwide effort to solve the LISA data analysis problem. We present here our results for the Massive Black Hole Binary (BBH) section of Round 1. Our results cover Challenge 1.2.1, where the coalescence of the binary is seen, and Challenge 1.2.2, where the coalescence occurs after the simulated observational period. The data stream is composed of Gaussian instrumental noise plus an unknown BBH waveform. Our search algorithm is based on a variant of the Markov Chain Monte Carlo method that uses Metropolis-Hastings sampling and thermostated frequency annealing. We present results from the training data sets and the blind data sets. We demonstrate that our algorithm is able to rapidly locate the sources, accurately recover the source parameters, and provide error estimates for the recovered parameters.Comment: 11 pages, 6 figures, Submitted to CQG proceedings of GWDAW 11, AEI, Germany, Dec 200

Detecting the Cosmic Gravitational Wave Background with the Big Bang Observer

The detection of the Cosmic Microwave Background Radiation (CMB) was one of the most important cosmological discoveries of the last century. With the development of interferometric gravitational wave detectors, we may be in a position to detect the gravitational equivalent of the CMB in this century. The Cosmic Gravitational Background (CGB) is likely to be isotropic and stochastic, making it difficult to distinguish from instrument noise. The contribution from the CGB can be isolated by cross-correlating the signals from two or more independent detectors. Here we extend previous studies that considered the cross-correlation of two Michelson channels by calculating the optimal signal to noise ratio that can be achieved by combining the full set of interferometry variables that are available with a six link triangular interferometer. In contrast to the two channel case, we find that the relative orientation of a pair of coplanar detectors does not affect the signal to noise ratio. We apply our results to the detector design described in the Big Bang Observer (BBO) mission concept study and find that BBO could detect a background with $\Omega_{gw} > 2.2 \times 10^{-17}$.Comment: 15 pages, 12 Figure

Non-Singular Gravity Without Black Holes

A non-singular, static spherically symmetric solution to the nonsymmetric gravitational and electromagnetic theory field equations is derived, which depends on the four parameters m, l^2, Q and s, where m is the mass, Q is the electric charge, l^2 is the NGT charge of a body and s is a dimensionless constant. The electromagnetic field invariants are also singularity-free, so that it is possible to construct regular particle-like solutions in the theory. All the curvature invariants are finite, there are no null surfaces in the spacetime and there are no black holes. A new stable, superdense object (SDO) replaces black holes.Comment: 26 pages, UTPT-94-0

Comment on the formation of black holes in nonsymmetric gravity

We critically examine the claim made by Burko and Ori that black holes are expected to form in nonsymmetric gravity and find their analysis to be inconclusive. Their conclusion is a result of the approximations they make, and not a consequence of the true dynamics of the theory. The approximation they use fails to capture the crucial equivalence principle violations which enable the full nonsymmetric field equations to detect and tame would-be horizons. An examination of the dynamics of the full theory reveals no indication that black holes should form. For these reasons, one cannot conclude from their analysis that nonsymmetric gravity has black holes. A definitive answers awaits a comprehensive study of gravitational collapse, using the full field equations.Comment: 6 pages, RevTe

Facing the LISA Data Analysis Challenge

By being the first observatory to survey the source rich low frequency region of the gravitational wave spectrum, the Laser Interferometer Space Antenna (LISA) will revolutionize our understanding of the Cosmos. For the first time we will be able to detect the gravitational radiation from millions of galactic binaries, the coalescence of two massive black holes, and the inspirals of compact objects into massive black holes. The signals from multiple sources in each class, and possibly others as well, will be simultaneously present in the data. To achieve the enormous scientific return possible with LISA, sophisticated data analysis techniques must be developed which can mine the complex data in an effort to isolate and characterize individual signals. This proceedings paper very briefly summarizes the challenges associated with analyzing the LISA data, the current state of affairs, and the necessary next steps to move forward in addressing the imminent challenges.Comment: 4 pages, no figures, Proceedings paper for the TeV Particle Astrophysics II conference held Aug 28-31 at the Univ. of Wisconsi