Head-on collision of two black holes: Comparison of different approaches.
A benchmark problem for numerical relativity has been the head-on collision of two black holes starting from the ``Misner initial data,'' a closed form momentarily stationary solution to the constraint equations with an adjustable closeness parameter ${\mathrm{\ensuremath{\mu}}}_{0}$. We show here how an electric mixture of approximation methods can provide both an efficient means of determining the time development of the initial data and a good understanding of the physics of the problem. When the Misner data are chosen to correspond to holes initially very close together, a common horizon surrounds both holes and the geometry exterior to the horizon can be treated as a nonspherical perturbation of a single Schwarzschild hole. When the holes are initially well separated the problem can be treated with a different approximation scheme, ``the particle-membrane method.'' For all initial separations, numerical relativity is in principle applicable, but is costly and of uncertain accuracy. We present here a comparison of the different approaches. We compare waveforms, for l=2 and l=4 radiation, for different values of ${\mathrm{\ensuremath{\mu}}}_{0}$, from the three different approaches to the problem.

title: Colliding Black Holes: How Far Can the Close Approximation Go?
abstract: We study the head-on collision of two equal-mass momentarily stationary black holes, using black hole perturbation theory up to second order. Compared to first-order results, this significantly improves agreement with numerically computed waveforms and energy. Much more important, second-order results correctly indicate the range of validity of perturbation theory. This use of second-order, to provide ``error bars,'' makes perturbation theory a viable tool for providing benchmarks for numerical relativity in more generic collisions and, in some range of collision parameters, for supplying waveform templates for gravitational wave detection.

title: Analytic approximations to the spacetime of a critical gravitational collapse.
abstract: We present analytic expressions that approximate the behavior of the spacetime of a collapsing spherically symmetric scalar field in the critical regime first discovered by Choptuik. We find that the critical region of spacetime can usefully be divided into a ``quiescent'' region and an ``oscillatory'' region, and a moving ``transition edge'' that separates the two regions. We find that in each region the critical solution can be well approximated by a flat spacetime scalar field solution. A qualitative nonlinear matching of the solutions across the edge yields the right order of magnitude for the oscillations of the discretely self-similar critical solution found by Choptuik.

title: Role of Constraining Forces for Ultrarelativistic Particle Motion as a Source of Gravitational Radiation
abstract: A study is made of gravitational radiation from the constraining forces, idealized as stresses in a thin rod, necessary to hold a particle in an ultrarelativistic circular orbit. Both the particle and the constraining forces generate radiation spectra which fall off in frequency as ${\ensuremath{\omega}}^{\ensuremath{-}(\frac{1}{3})}$ up to a critical frequency, ${\ensuremath{\omega}}_{\mathrm{crit}}=3{[1\ensuremath{-}{(\frac{{v}_{\mathrm{particle}}}{v})}^{2}]}^{\ensuremath{-}(\frac{3}{2})}\ifmmode\times\else\texttimes\fi{}\mathrm{frequency}\mathrm{of}\mathrm{rotation}$, but the power generated by the constraining forces is much smaller than that due to the particle's mass.

title: The Future of space-time

title: Inspiralling Black holes: The close limit
abstract: We calculate an estimate of the gravitational radiation emitted when two equal mass black holes coalesce at the end of their binary inspiral, using several approximations based on considering the holes close to each other. A shortcoming of our method is that it is limited to models forming final holes with slow rotation, but our results clearly suggest a trend for larger angular momenta. We find that about 1% of the mass energy of the pair will emerge as gravitational waves during the final stages of the collision and that a negligible fraction of the angular momentum will be radiated. PACS numbers: 04.30.Db, 04.25.Dm, 04.70.Bw, 97.80.Fk An international network of interferometric gravitational wave (GW) observatories (the LIGO project in the U.S., the VIRGO and GEO projects in Europe, and the TAMA project in Japan ) will be capable of detecting gravitational waves in the next few years. This could have revolutionary implications for astronomy since it constitutes a new form of “light” with which to observe the Universe, a form that is better correlated with the bulk motions of matter and is very hard to shield or distort. Gravitational waves were originally predicted by Einstein in 1915 but their theoretical existence was not completely understood until the 1960’s  and their direct experimental detection has remained a daunting challenge . One of the most promising sources for detection is the collision of two black holes to form a single, final hole. Such a collision is expected to be the end point of the decaying inspiral for a binary pair of holes. Just how promising such collisions are depends very much on the masses of the colliding holes and is connected with the characteristics of detectors. The sensitivity of the laser interferometric detectors, like LIGO, peaks around 100 Hz. The major determinant of the frequency of GWs produced in a black hole inspiral/collision is M, the mass of the system (and of the final black hole formed). The frequency scales as 1M and is around 10 4 Hz for a 1MO system. The usual black hole candidates are stellar mass holes and supermassive holes (10 6 MO) in the centers of many galaxies. The frequency of GWs from the former candidates would be too high except for the weak radiation from the early inspiral. GWs from supermassive holes would be too low in frequency for Earth based systems but well suited to space based detection. Black holes of 100MO would be ideal as sources and black holes of any mass can in principle exist. But the astrophysical motivation for such “middleweight” holes was weak. Recent observations  of x-ray emission from galaxies suggest that some galaxies may contain middleweight holes, perhaps as an evolutionary stage in the formation of supermassive holes. Should such a middleweight hole exist it will produce GWs near the optimal 100 Hz frequency when it collides with compact objects of equal or smaller masses. For two different reasons, we focus here on the collision of roughly equal mass holes. The first is that the power radiated from the collision of holes of masses m1 # m2 scales as m1m2 2 , at least in the case that m1

title: eta meson photoproduction on hydrogen near threshold.
abstract: The total cross section for {gamma}{ital p}{r_arrow}{eta}{ital p} near threshold has been measured using the PHOENICS tagging system at the ELSA electron facility of the Physikalisches Institut der Universitaet Bonn. The photons are created by bremsstrahlung, and are tagged by measuring the momentum of each electron after the photon has been emitted. The recoil proton from {gamma}{ital p}{r_arrow}{eta}{ital p} is detected by the AMADEUS counter setup in coincidence with the tagging system. Data were taken with AMADEUS at 3.3{degree} in the laboratory, where the large Jacobian increases our event rate so that we obtain the cross section from threshold ({ital E}{sub {gamma}}=707.2 MeV) to {ital E}{sub {gamma}}{congruent}720 MeV with adequate statistics. The {gamma}{ital p}{r_arrow}{eta}{ital p} events are identified by kinematics, {ital dE}/{ital dx}, and timing information. We find that in our energy region the production cross section is consistent with {ital S}-wave production.