Truncated post-Newtonian neutron star model

As a preliminary step towards simulating binary neutron star coalescing problem, we test a post-Newtonian approach by constructing a single neutron star model. We expand the Tolman-Oppenheimer-Volkov equation of hydrostatic equilibrium by the power of $c^{-2}$, where $c$ is the speed of light, and truncate at the various order. We solve the system using the polytropic equation of state with index $\Gamma=5/3, 2$ and 3, and show how this approximation converges together with mass-radius relations. Next, we solve the Hamiltonian constraint equation with these density profiles as trial functions, and examine the differences in the final metric. We conclude the second `post-Newtonian' approximation is close enough to describe general relativistic single star. The result of this report will be useful for further binary studies. (Note to readers) This paper was accepted for publication in Physical Review D. [access code dsj637]. However, since I was strongly suggested that the contents of this paper should be included as a section in our group's future paper, I gave up the publication.Comment: 5 pages, RevTeX, 3 eps figs, epsf.sty, accepted for publication in PRD (Brief Report), but will not appea

Laser Interferometric Detectors of Gravitational Waves

A laser interferometric detector of gravitational waves is studied and a complete solution (to first order in the metric perturbation) of the coupled Einstein-Maxwell equations with appropriate boundary conditions for the light beams is determined. The phase shift, the light deflection and the rotation of the polarization axis induced by gravitational waves are computed. The results are compared with previous literature, and are shown to hold also for detectors which are large in comparison with the gravitational wavelength.Comment: 13 pages, LaTe

Matter flows around black holes and gravitational radiation

We develop and calibrate a new method for estimating the gravitational radiation emitted by complex motions of matter sources in the vicinity of black holes. We compute numerically the linearized curvature perturbations induced by matter fields evolving in fixed black hole backgrounds, whose evolution we obtain using the equations of relativistic hydrodynamics. The current implementation of the proposal concerns non-rotating holes and axisymmetric hydrodynamical motions. As first applications we study i) dust shells falling onto the black hole isotropically from finite distance, ii) initially spherical layers of material falling onto a moving black hole, and iii) anisotropic collapse of shells. We focus on the dependence of the total gravitational wave energy emission on the flow parameters, in particular shell thickness, velocity and degree of anisotropy. The gradual excitation of the black hole quasi-normal mode frequency by sufficiently compact shells is demonstrated and discussed. A new prescription for generating physically reasonable initial data is discussed, along with a range of technical issues relevant to numerical relativity.Comment: 27 pages, 12 encapsulated figures, revtex, amsfonts, submitted to Phys. Rev.

Momentum constraint relaxation

Full relativistic simulations in three dimensions invariably develop runaway modes that grow exponentially and are accompanied by violations of the Hamiltonian and momentum constraints. Recently, we introduced a numerical method (Hamiltonian relaxation) that greatly reduces the Hamiltonian constraint violation and helps improve the quality of the numerical model. We present here a method that controls the violation of the momentum constraint. The method is based on the addition of a longitudinal component to the traceless extrinsic curvature generated by a vector potential w_i, as outlined by York. The components of w_i are relaxed to solve approximately the momentum constraint equations, pushing slowly the evolution toward the space of solutions of the constraint equations. We test this method with simulations of binary neutron stars in circular orbits and show that effectively controls the growth of the aforementioned violations. We also show that a full numerical enforcement of the constraints, as opposed to the gentle correction of the momentum relaxation scheme, results in the development of instabilities that stop the runs shortly.Comment: 17 pages, 10 figures. New numerical tests and references added. More detailed description of the algorithms are provided. Final published versio

The Collision of Two Black Holes

We study the head-on collision of two equal mass, nonrotating black holes. We consider a range of cases from holes surrounded by a common horizon to holes initially separated by about $20M$, where $M$ is the mass of each hole. We determine the waveforms and energies radiated for both the $\ell = 2$ and $\ell=4$ waves resulting from the collision. In all cases studied the normal modes of the final black hole dominate the spectrum. We also estimate analytically the total gravitational radiation emitted, taking into account the tidal heating of horizons using the membrane paradigm, and other effects. For the first time we are able to compare analytic calculations, black hole perturbation theory, and strong field, nonlinear numerical calculations for this problem, and we find excellent agreement.Comment: 14 pages, 93-

Stable Topologies of Event Horizon

In our previous work, it was shown that the topology of an event horizon (EH) is determined by the past endpoints of the EH. A torus EH (the collision of two EH) is caused by the two-dimensional (one-dimensional) set of the endpoints. In the present article, we examine the stability of the topology of the EH. We see that a simple case of a single spherical EH is unstable. Furthermore, in general, an EH with handles (a torus, a double torus, ...) is structurally stable in the sense of catastrophe theory.Comment: 21 pages, revtex, five figures containe

Hamiltonian Relaxation

Due to the complexity of the required numerical codes, many of the new formulations for the evolution of the gravitational fields in numerical relativity are not tested on binary evolutions. We introduce in this paper a new testing ground for numerical methods based on the simulation of binary neutron stars. This numerical setup is used to develop a new technique, the Hamiltonian relaxation (HR), that is benchmarked against the currently most stable simulations based on the BSSN method. We show that, while the length of the HR run is somewhat shorter than the equivalent BSSN simulation, the HR technique improves the overall quality of the simulation, not only regarding the satisfaction of the Hamiltonian constraint, but also the behavior of the total angular momentum of the binary. The latest quantity agrees well with post-Newtonian estimations for point-mass binaries in circular orbits.Comment: More detailed description of the numerical implementation added and some typos corrected. Version accepted for publication in Class. and Quantum Gravit

A method for detecting gravitational waves coincident with gamma ray bursts

The mechanism for gamma ray bursters and the detection of gravitational waves (GWs) are two outstanding problems facing modern physics. Many models of gamma ray bursters predict copious GW emission, so the assumption of an association between GWs and GRBs may be testable with existing bar GW detector data. We consider Weber bar data streams in the vicinity of known GRB times and present calculations of the expected signal after co-addition of 1000 GW/GRBs that have been shifted to a common zero time. Our calculations are based on assumptions concerning the GW spectrum and the redshift distribution of GW/GRB sources which are consistent with current GW/GRB models. We discuss further possibilities of GW detection associated with GRBs in light of future bar detector improvements and suggest that co-addition of data from several improved bar detectors may result in detection of GWs (if the GW/GRB assumption is correct) on a time scale comparable with the LIGO projects.Comment: Accepted by MNRAS. 9 pages, 6 ps figures, MNRAS style. Proof corrections made, accepted versio

Binary Neutron Stars in General Relativity: Quasi-Equilibrium Models

We perform fully relativistic calculations of binary neutron stars in quasi-equilibrium circular orbits. We integrate Einstein's equations together with the relativistic equation of hydrostatic equilibrium to solve the initial value problem for equal-mass binaries of arbitrary separation. We construct sequences of constant rest mass and identify the innermost stable circular orbit and its angular velocity. We find that the quasi-equilibrium maximum allowed mass of a neutron star in a close binary is slightly larger than in isolation.Comment: 4 pages, 3 figures, RevTe

The Head-On Collision of Two Equal Mass Black Holes Peter Anninos

We study the head-on collision of two equal mass, nonrotating black holes. Various initial configurations are investigated, including holes which are initially surrounded by a common apparent horizon to holes that are separated by about $20M$, where $M$ is the mass of a single black hole. We have extracted both $\ell = 2$ and $\ell=4$ gravitational waveforms resulting from the collision. The normal modes of the final black hole dominate the spectrum in all cases studied. The total energy radiated is computed using several independent methods, and is typically less than $0.002 M$. We also discuss an analytic approach to estimate the total gravitational radiation emitted in the collision by generalizing point particle dynamics to account for the finite size and internal dynamics of the two black holes. The effects of the tidal deformations of the horizons are analysed using the membrane paradigm of black holes. We find excellent agreement between the numerical results and the analytic estimates.Comment: 33 pages, NCSA 94-048, WUGRAV-94-