Testing a Simplified Version of Einstein's Equations for Numerical Relativity

Solving dynamical problems in general relativity requires the full machinery of numerical relativity. Wilson has proposed a simpler but approximate scheme for systems near equilibrium, like binary neutron stars. We test the scheme on isolated, rapidly rotating, relativistic stars. Since these objects are in equilibrium, it is crucial that the approximation work well if we are to believe its predictions for more complicated systems like binaries. Our results are very encouraging.Comment: 9 pages (RevTeX 3.0 with 6 uuencoded figures), CRSR-107

Quasi-circular Orbits for Spinning Binary Black Holes

Using an effective potential method we examine binary black holes where the individual holes carry spin. We trace out sequences of quasi-circular orbits and locate the innermost stable circular orbit as a function of spin. At large separations, the sequences of quasi-circular orbits match well with post-Newtonian expansions, although a clear signature of the simplifying assumption of conformal flatness is seen. The position of the ISCO is found to be strongly dependent on the magnitude of the spin on each black hole. At close separations of the holes, the effective potential method breaks down. In all cases where an ISCO could be determined, we found that an apparent horizon encompassing both holes forms for separations well inside the ISCO. Nevertheless, we argue that the formation of a common horizon is still associated with the breakdown of the effective potential method.Comment: 13 pages, 10 figures, submitted to PR

Spatial variation in the MRE throughout the Scottish Post-Roman to late Medieval period: North Sea values (500-1350 BP)

The marine radiocarbon reservoir effect (MRE) occurs as a spatially and temporally dependent variable owing to localized changes in oceanic water composition. This study investigates ΔR values (deviations from the global average MRE whose ΔR = 0) during the period 500–1350 BP for the east coast of Scotland, where a complex estuarine system exists that drains into the semi-enclosed North Sea basin. Due to the availability of suitable archaeological samples, the data set has a distinct Medieval focus that spans the area from Aberdeen in the north to East Lothian in the south. Many of the ΔR values are not significantly different from 0 (the global average), but there are occasional excursions to negative values (max –172 ± 20) indicating the presence of younger water. These values show greater variability compared to other published data for this general region, suggesting that considerable care must be taken when dating marine derived samples from archaeological sites on the east coast of Scotland

Inner boundary conditions for black hole Initial Data derived from Isolated Horizons

We present a set of boundary conditions for solving the elliptic equations in the Initial Data Problem for space-times containing a black hole, together with a number of constraints to be satisfied by the otherwise freely specifiable standard parameters of the Conformal Thin Sandwich formulation. These conditions altogether are sufficient for the construction of a horizon that is instantaneously in equilibrium in the sense of the Isolated Horizons formalism. We then investigate the application of these conditions to the Initial Data Problem of binary black holes and discuss the relation of our analysis with other proposals that exist in the literature.Comment: 13 pages. Major general revision. Section V comparing with previous approaches restructured; discussion on the lapse boundary condition extended. Appendix with some technical details added. Version accepted for publication in Phys.Rev.

Low Frequency Gravitational Waves from Black Hole MACHO Binaries

Nakamura, Sasaki, Tanaka, and Thorne have recently estimated the initial distribution of binary MACHOs in the galactic halo assuming that the MACHOs are primordial half solar mass black holes, and considered their coalescence as a possible source for ground-based interferometer gravitational wave detectors such as LIGO. Evolving their binary distribution forward in time to the present, the low-frequency (10^{-5} < f < 10^{-1} Hz) spectrum of gravitational waves associated with such a population of compact binaries is calculated. The resulting gravitational waves would form a strong stochastic background in proposed space interferometers such as LISA and OMEGA. Low frequency gravitational waves are likely to become a key tool for determining the properties of binaries within the dark MACHO population.Comment: 8 pages + 2 ps figures; AASTe

The two-phase approximation for black hole collisions: Is it robust?

Recently Abrahams and Cook devised a method of estimating the total radiated energy resulting from collisions of distant black holes by applying Newtonian evolution to the holes up to the point where a common apparent horizon forms around the two black holes and subsequently applying Schwarzschild perturbation techniques . Despite the crudeness of their method, their results for the case of head-on collisions were surprisingly accurate. Here we take advantage of the simple radiated energy formula devised in the close-slow approximation for black hole collisions to test how strongly the Abrahams-Cook result depends on the choice of moment when the method of evolution switches over from Newtonian to general relativistic evolution. We find that their result is robust, not depending strongly on this choice.Comment: 4 pages, 3 figures, submitted to Classical and Quantum Gravit

Real time flight simulation methodology

An example sensitivity study is presented to demonstrate how a digital autopilot designer could make a decision on minimum sampling rate for computer specification. It consists of comparing the simulated step response of an existing analog autopilot and its associated aircraft dynamics to the digital version operating at various sampling frequencies and specifying a sampling frequency that results in an acceptable change in relative stability. In general, the zero order hold introduces phase lag which will increase overshoot and settling time. It should be noted that this solution is for substituting a digital autopilot for a continuous autopilot. A complete redesign could result in results which more closely resemble the continuous results or which conform better to original design goals

Evolution of Binary Black Hole Spacetimes

We describe early success in the evolution of binary black hole spacetimes with a numerical code based on a generalization of harmonic coordinates. Indications are that with sufficient resolution this scheme is capable of evolving binary systems for enough time to extract information about the orbit, merger and gravitational waves emitted during the event. As an example we show results from the evolution of a binary composed of two equal mass, non-spinning black holes, through a single plunge-orbit, merger and ring down. The resultant black hole is estimated to be a Kerr black hole with angular momentum parameter a~0.70. At present, lack of resolution far from the binary prevents an accurate estimate of the energy emitted, though a rough calculation suggests on the order of 5% of the initial rest mass of the system is radiated as gravitational waves during the final orbit and ringdown.Comment: 4 pages, 3 figure

Fragmentation of Nuclei at Intermediate and High Energies in Modified Cascade Model

The process of nuclear multifragmentation has been implemented, together with evaporation and fission channels of the disintegration of excited remnants in nucleus-nucleus collisions using percolation theory and the intranuclear cascade model. Colliding nuclei are treated as face--centered--cubic lattices with nucleons occupying the nodes of the lattice. The site--bond percolation model is used. The code can be applied for calculation of the fragmentation of nuclei in spallation and multifragmentation reactions.Comment: 19 pages, 10 figure