Complete null data for a black hole collision

We present an algorithm for calculating the complete data on an event horizon which constitute the necessary input for characteristic evolution of the exterior spacetime. We apply this algorithm to study the intrinsic and extrinsic geometry of a binary black hole event horizon, constructing a sequence of binary black hole event horizons which approaches a single Schwarzschild black hole horizon as a limiting case. The linear perturbation of the Schwarzschild horizon provides global insight into the close limit for binary black holes, in which the individual holes have joined in the infinite past. In general there is a division of the horizon into interior and exterior regions, analogous to the division of the Schwarzschild horizon by the r=2M bifurcation sphere. In passing from the perturbative to the strongly nonlinear regime there is a transition in which the individual black holes persist in the exterior portion of the horizon. The algorithm is intended to provide the data sets for production of a catalog of nonlinear post-merger wave forms using the PITT null code.Comment: Revised version, to appear in Phys. Rev. D. July 15 (2001), 41 pages, 11 figures, RevTeX/epsf/psfi

Quantum Mechanics of Extended Objects

We propose a quantum mechanics of extended objects that accounts for the finite extent of a particle defined via its Compton wavelength. The Hilbert space representation theory of such a quantum mechanics is presented and this representation is used to demonstrate the quantization of spacetime. The quantum mechanics of extended objects is then applied to two paradigm examples, namely, the fuzzy (extended object) harmonic oscillator and the Yukawa potential. In the second example, we theoretically predict the phenomenological coupling constant of the $\omega$ meson, which mediates the short range and repulsive nucleon force, as well as the repulsive core radius.Comment: RevTex, 24 pages, 1 eps and 5 ps figures, format change

Finding Principal Null Direction for Numerical Relativists

We present a new method for finding principal null directions (PNDs). Because our method assumes as input the intrinsic metric and extrinsic curvature of a spacelike hypersurface, it should be particularly useful to numerical relativists. We illustrate our method by finding the PNDs of the Kastor-Traschen spacetimes, which contain arbitrarily many $Q=M$ black holes in a de Sitter back-ground.Comment: 10 pages, LaTeX style, WU-AP/38/93. Figures are available (hard copies) upon requests [[email protected] (H.Shinkai)

Testable polarization predictions for models of CMB isotropy anomalies

Anomalies in the large-scale CMB temperature sky measured by WMAP have been suggested as possible evidence for a violation of statistical isotropy on large scales. In any physical model for broken isotropy, there are testable consequences for the CMB polarization field. We develop simulation tools for predicting the polarization field in models that break statistical isotropy locally through a modulation field. We study two different models: dipolar modulation, invoked to explain the asymmetry in power between northern and southern ecliptic hemispheres, and quadrupolar modulation, posited to explain the alignments between the quadrupole and octopole. For the dipolar case, we show that predictions for the correlation between the first 10 multipoles of the temperature and polarization fields can typically be tested at better than the 98% CL. For the quadrupolar case, we show that the polarization quadrupole and octopole should be moderately aligned. Such an alignment is a generic prediction of explanations which involve the temperature field at recombination and thus discriminate against explanations involving foregrounds or local secondary anisotropy. Predicted correlations between temperature and polarization multipoles out to l = 5 provide tests at the ~ 99% CL or stronger for quadrupolar models that make the temperature alignment more than a few percent likely. As predictions of anomaly models, polarization statistics move beyond the a posteriori inferences that currently dominate the field.Comment: 17 pages, 15 figures; published in PRD; references adde

Lightcone reference for total gravitational energy

We give an explicit expression for gravitational energy, written solely in terms of physical spacetime geometry, which in suitable limits agrees with the total Arnowitt-Deser-Misner and Trautman-Bondi-Sachs energies for asymptotically flat spacetimes and with the Abbot-Deser energy for asymptotically anti-de Sitter spacetimes. Our expression is a boundary value of the standard gravitational Hamiltonian. Moreover, although it stands alone as such, we derive the expression by picking the zero-point of energy via a ``lightcone reference.''Comment: latex, 7 pages, no figures. Uses an amstex symbo

Isotropic Solutions of the Einstein-Liouville Equations

The gravitational field generated by a gas whose one-particle distribution function obeys the Liouville equation is examined under the following assumptions: First, the distribution is locally isotropic in momentum space with respect to some world-velocity field; second, if the particles have rest-mass zero, the gas is irrotational. It is shown that the model is then either stationary or a Robertson-Walker model. The time dependence of the radius in the Robertson-Walker models is given in terms of integrals containing the distribution function

Gravitational Waves from a Fissioning White Hole

We present a fully nonlinear calculation of the waveform of the gravitational radiation emitted in the fission of a vacuum white hole. At early times, the waveforms agree with close-approximation perturbative calculations but they reveal dramatic time and angular dependence in the nonlinear regime. The results pave the way for a subsequent computation of the radiation emitted after a binary black hole merger.Comment: 11 pages, 6 figures, RevTeX

A Causal Source which Mimics Inflation

How unique are the inflationary predictions for the cosmic microwave anisotropy pattern? In this paper, it is asked whether an arbitrary causal source for perturbations in the standard hot big bang could effectively mimic the predictions of the simplest inflationary models. A surprisingly simple example of a `scaling' causal source is found to closely reproduce the inflationary predictions. This letter extends the work of a previous paper (ref. 6) to a full computation of the anisotropy pattern, including the Sachs Wolfe integral. I speculate on the possible physics behind such a source.Comment: 4 pages, RevTex, 3 figure