Apparent Horizons with Nontrivial Topology and the Hyperhoop Conjecture in Six-Dimensional Space-Times

We investigate the validity of the hyperhoop conjecture, which claims to determine a necessary and sufficient condition for the formation of black hole horizons in higher-dimensional space-times. Here we consider momentarily static, conformally flat initial data sets each describing a gravitational field of uniform massive k-sphere sources, for k=1,2, on the five-dimensional Cauchy surface. The numerical result shows the validity of the hyperhoop conjecture for a wide range of model parameters. We also confirm for the first time the existence of an apparent horizon homeomorphism to S**2 x S**2 or S**1 x S**3, which is a higher-dimensional generalization of the black ring.Comment: 17 pages, 12 figures. to appear in Phys. Rev.

Electromagnetic radiation due to naked singularity formation in self-similar gravitational collapse

Dynamical evolution of test fields in background geometry with a naked singularity is an important problem relevant to the Cauchy horizon instability and the observational signatures different from black hole formation. In this paper we study electromagnetic perturbations generated by a given current distribution in collapsing matter under a spherically symmetric self-similar background. Using the Green's function method, we construct the formula to evaluate the outgoing energy flux observed at the future null infinity. The contributions from "quasi-normal" modes of the self-similar system as well as "high-frequency" waves are clarified. We find a characteristic power-law time evolution of the outgoing energy flux which appears just before naked singularity formation, and give the criteria as to whether or not the outgoing energy flux diverges at the future Cauchy horizon.Comment: 20 pages, 7 figures, references added to match the published versio

Black ring formation in particle systems

It is known that the formation of apparent horizons with non-spherical topology is possible in higher-dimensional spacetimes. One of these is the black ring horizon with $S^1\times S^{D-3}$ topology where $D$ is the spacetime dimension number. In this paper, we investigate the black ring horizon formation in systems with $n$-particles. We analyze two kinds of system: the high-energy $n$-particle system and the momentarily-static $n$-black-hole initial data. In the high-energy particle system, we prove that the black ring horizon does not exist at the instant of collision for any $n$. But there remains a possibility that the black ring forms after the collision and this result is not sufficient. Because calculating the metric of this system after the collision is difficult, we consider the momentarily-static $n$-black-hole initial data that can be regarded as a simplified $n$-particle model and numerically solve the black ring horizon that surrounds all the particles. Our results show that there is the minimum particle number that is necessary for the black ring formation and this number depends on $D$. Although many particle number is required in five-dimensions, $n=4$ is sufficient for the black ring formation in the $D\ge 7$ cases. The black ring formation becomes easier for larger $D$. We provide a plausible physical interpretation of our results and discuss the validity of Ida and Nakao's conjecture for the horizon formation in higher-dimensions. Finally we briefly discuss the probable methods of producing the black rings in accelerators.Comment: 26 pages, 7 figure

Improved analysis of black hole formation in high-energy particle collisions

We investigate formation of an apparent horizon (AH) in high-energy particle collisions in four- and higher-dimensional general relativity, motivated by TeV-scale gravity scenarios. The goal is to estimate the prefactor in the geometric cross section formula for the black hole production. We numerically construct AHs on the future light cone of the collision plane. Since this slice lies to the future of the slice used previously by Eardley and Giddings (gr-qc/0201034) and by one of us and Nambu (gr-qc/0209003), we are able to improve the prefactor estimates. The black hole production cross section increases by 40-70% in the higher-dimensional cases, indicating larger black hole production rates in future-planned accelerators than previously estimated. We also determine the mass and the angular momentum of the final black hole state, as allowed by the area theorem.Comment: 28 pages, 14 figures, references and minor comments adde

Nonaxisymmetric instability of rapidly rotating black hole in five dimensions

We present results from numerical solution of Einstein's equation in five dimensions describing evolution of rapidly rotating black holes. We show, for the first time, that the rapidly rotating black holes in higher dimensions are unstable against nonaxisymmetric deformation; for the five-dimensional case, the critical value of spin parameter for onset of the instability is $\approx 0.87$.Comment: 4 pages, 3 figures, accepted for publication in PRD(R

Black hole initial data in Gauss-Bonnet gravity: Momentarily static case

We study the method for generating the initial data of black hole systems in Gauss-Bonnet (GB) gravity. The initial data are assumed to be momentarily static and conformally flat. Although the equation for the conformal factor is highly nonlinear, it is successfully solved by numerical relaxation for one-black-hole and two-black-hole systems. The common apparent horizon is studied in the two-black-hole initial data, and the result suggests that the Penrose inequalities are satisfied in this system. This is the first step for simulating black hole collisions in higher-curvature theories.Comment: 30 pages, 10 figures, submitted to PR

Detecting gravitational waves from inspiraling binaries with a network of detectors : coherent strategies by correlated detectors

We discuss the coherent search strategy to detect gravitational waves from inspiraling compact binaries by a network of correlated laser interferometric detectors. From the maximum likelihood ratio statistic, we obtain a coherent statistic which is slightly different from and generally better than what we obtained in our previous work. In the special case when the cross spectrum of two detectors normalized by the power spectrum density is constant, the new statistic agrees with the old one. The quantitative difference of the detection probability for a given false alarm rate is also evaluated in a simple case.Comment: 4 pages, 1 Postscript figures, uses revtex4.st

Highly distorted apparent horizons and the hoop conjecture

By analyzing the apparent horizon (AH) formation in the collision of two pp-waves with rectangular sources in four dimensions, we study to what extent the AH can be distorted without violating the energy conditions. It is shown that the highly distorted AH can form in this system although it cannot be arbitrarily long. The hoop conjecture is examined for the formation of such highly distorted AHs, and our result gives a strong support to the hoop conjecture. We also point out the possible relation between the AH topology theorem and the hoop conjecture.Comment: 10 pages, 5 figures, submitted to PRD(R

High-energy head-on collisions of particles and hoop conjecture

We investigate the apparent horizon formation for high-energy head-on collisions of particles in multi-dimensional spacetime. The apparent horizons formed before the instance of particle collision are obtained analytically. Using these solutions, we discuss the feature of the apparent horizon formation in the multi-dimensional spacetime from the viewpoint of the hoop conjecture.Comment: 4pages, 4figure

On Detection of Black Hole Quasi-Normal Ringdowns: Detection Efficiency and Waveform Parameter Determination in Matched Filtering

Gravitational radiation from a slightly distorted black hole with ringdown waveform is well understood in general relativity. It provides a probe for direct observation of black holes and determination of their physical parameters, masses and angular momenta (Kerr parameters). For ringdown searches using data of gravitational wave detectors, matched filtering technique is useful. In this paper, we describe studies on problems in matched filtering analysis in realistic gravitational wave searches using observational data. Above all, we focus on template constructions, matches or signal-to-noise ratios (SNRs), detection probabilities for Galactic events, and accuracies in evaluation of waveform parameters or black hole hairs. We have performed matched filtering analysis for artificial ringdown signals which are generated with Monte-Carlo technique and injected into the TAMA300 observational data. It is shown that with TAMA300 sensitivity, the detection probability for Galactic ringdown events is about 50% for black holes of masses greater than $20 M_{\odot}$ with SNR $> 10$. The accuracies in waveform parameter estimations are found to be consistent with the template spacings, and resolutions for black hole masses and the Kerr parameters are evaluated as a few % and $\sim 40$, respectively. They can be improved up to $< 0.9$ and $< 24$ for events of ${\rm SNR} \ge 10$ by using fine-meshed template bank in the hierarchical search strategy.Comment: 10 pages, 10 figure