119298185
BSSN in spherical symmetry
The BSSN (Baumgarte?Shapiro?Shibata?Nakamura) formulation of the Einstein evolution equations is written in spherical symmetry. These equations can be used to address a number of technical and conceptual issues in numerical relativity in the context of a single Schwarzschild black hole. One of the benefits of spherical symmetry is that the numerical grid points can be tracked on a Kruskal?Szekeres diagram. Boundary conditions suitable for puncture evolution of a Schwarzschild black hole are presented. Several results are shown for puncture evolution using a fourth-order finite difference implementation of the equations.
119986427
On the Poisson brackets of differentiable generators in classical field theory
The canonical formulation of field theory on open spaces is considered. It is proved, under appropriate assumptions, that the Poisson bracket of two differentiable generators is also a differentiable generator.
119005465
Modifying the Einstein equations off the constraint hypersurface
A new technique is presented for modifying the Einstein evolution equations off the constraint hypersurface. With this approach the evolution equations for the constraints can be specified freely. The equations of motion for the gravitational field variables are modified by the addition of terms that are linear and nonlocal in the constraints. These terms are obtained from solutions of the linearized Einstein constraints.
16432578
Dust as a standard of space and time in canonical quantum gravity.
The coupling of the metric to an incoherent dust introduces into spacetime a privileged dynamical reference frame and time foliation. The comoving coordinates of the dust particles and the proper time along the dust worldlines become canonical coordinates in the phase space of the system. The Hamiltonian constraint can be resolved with respect to the momentum that is canonically conjugate to the dust time. Formal imposition of the resolved constraint as an operator restriction on the quantum states yields a functional Schr\"odinger equation. The ensuing Hamiltonian density has an extraordinary feature: it depends only on the geometric variables, not on the dust coordinates or time. This has three important consequences. First, the functional Schr\"odinger equation can be solved by separating the dust time from the geometric variables. Second, disregarding the standard factor-ordering difficulties, the Hamiltonian densities strongly commute and therefore can be simultaneously defined by spectral analysis. Third, the standard constraint system of vacuum gravity is cast into a form in which it generates a true Lie algebra. The particles of dust introduce into space a privileged system of coordinates that allows the supermomentum constraint to be solved explicitly. The Schr\"odinger equation yields a formally conserved inner product that can be written in terms of either the instantaneous state functionals or the solutions of constraints. Gravitational observables admit a similar dual representation. Examples of observables are given, though neither the intrinsic metric nor the extrinsic curvature are observables. This comes as close as one can reasonably expect to a satisfactory phenomenological quantization scheme that is free of most of the problems of time.
16734842
Black Hole Thermodynamics in a Box
Simple calculations indicate that the partition function for a black hole is defined only if the temperature is fixed on a finite boundary. Consequences of this result are discussed. (Contribution to the Proceedings of the Lanczos Centenary Conference.)
6269112
Action functionals for relativistic perfect fluids
Action functionals describing relativistic perfect fluids are presented. Two of these actions apply to fluids whose equations of state are specified by giving the fluid energy density as a function of particle number density and entropy per particle. Other actions apply to fluids whose equations of state are specified in terms of other choices of dependent and independent fluid variables. Particular cases include actions for isentropic fluids and pressureless dust. The canonical Hamiltonian forms of these actions are derived, symmetries and conserved charges are identified, and the boundary value and initial value problems are discussed. As in previous works on perfect fluid actions, the action functionals considered depend on certain Lagrange multipliers and Lagrangian coordinate fields. Particular attention is paid to the interpretations of these variables and to their relationships to the physical properties of the fluid.
42670702
Accuracy of gravitational waveform models for observing neutron-star–black-hole binaries in Advanced LIGO
Gravitational waves radiated by the coalescence of compact-object binaries containing a neutron star and a black hole are one of the most interesting sources for the ground-based gravitational-wave observatories Advanced LIGO and Advanced Virgo. Advanced LIGO will be sensitive to the inspiral of a 1.4M⊙ neutron star into a 10M⊙ black hole to a maximum distance of ∼900  Mpc. Achieving this sensitivity and extracting the physics imprinted in observed signals requires accurate modeling of the binary to construct template waveforms. In a neutron-star–black-hole binary, the black hole may have significant angular momentum (spin), which affects the phase evolution of the emitted gravitational waves. We investigate the ability of currently available post-Newtonian templates to model the gravitational waves emitted during the inspiral phase of neutron-star–black-hole binaries. We restrict to the case where the spin of the black hole is aligned with the orbital angular momentum and compare several post-Newtonian approximants. We examine restricted amplitude post-Newtonian waveforms that are accurate to third-and-a-half post-Newtonian order in the orbital dynamics and complete to second-and-a-half post-Newtonian order in the spin dynamics. We also consider post-Newtonian waveforms that include the recently derived third-and-a-half post-Newtonian order spin-orbit correction and the third post-Newtonian order spin-orbit tail correction. We compare these post-Newtonian approximants to the effective-one-body waveforms for spin-aligned binaries. For all of these waveform families, we find that there is a large disagreement between different waveform approximants, starting at low to moderate black hole spins, particularly for binaries where the spin is antialigned with the orbital angular momentum. The match between the TaylorT4 and TaylorF2 approximants is ∼0.8 for a binary with m_BH/m_NS∼4 and χ_BH = cJ_BH/Gm^(2)_(BH)∼0.4. We show that the divergence between the gravitational waveforms begins in the early inspiral at v∼0.2 for χ_BH∼0.4. Post-Newtonian spin corrections beyond those currently known will be required for optimal detection searches and to measure the parameters of neutron-star–black-hole binaries. The strong dependence of the gravitational-wave signal on the spin dynamics will make it possible to extract significant astrophysical information from detected systems with Advanced LIGO and Advanced Virgo.
8392884
High-accuracy comparison of numerical relativity simulations with post-Newtonian expansions
Numerical simulations of 15 orbits of an equal-mass binary black-hole system are presented. Gravitational waveforms from these simulations, covering more than 30 cycles and ending about 1.5 cycles before merger, are compared with those from quasicircular zero-spin post-Newtonian (PN) formulae. The cumulative phase uncertainty of these comparisons is about 0.05 radians, dominated by effects arising from the small residual spins of the black holes and the small residual orbital eccentricity in the simulations. Matching numerical results to PN waveforms early in the run yields excellent agreement (within 0.05 radians) over the first ~15 cycles, thus validating the numerical simulation and establishing a regime where PN theory is accurate. In the last 15 cycles to merger, however, generic time-domain Taylor approximants build up phase differences of several radians. But, apparently by coincidence, one specific post-Newtonian approximant, TaylorT4 at 3.5PN order, agrees much better with the numerical simulations, with accumulated phase differences of less than 0.05 radians over the 30-cycle waveform. Gravitational-wave amplitude comparisons are also done between numerical simulations and post-Newtonian, and the agreement depends on the post-Newtonian order of the amplitude expansion: the amplitude difference is about 6%–7% for zeroth order and becomes smaller for increasing order. A newly derived 3.0PN amplitude correction improves agreement significantly (<1% amplitude difference throughout most of the run, increasing to 4% near merger) over the previously known 2.5PN amplitude terms.
119488847
Scintillating fiber hodoscope for a bremsstrahlung luminosity monitor at an electron–positron collider
The performance of a scintillating fiber (2 mm diameter) position sensitive detector (4.8×4.8 cm2 active area) for the single bremsstrahlung luminosity monitor at the VEPP‐2M electron‐positron collider in Novosibirsk, Russia is described. Custom electronics is triggered by coincident hits in the Y and Y planes of 24 fibers each, and reduces 64 photomultiplier signals to a 10‐bit (X,Y) address. Hits are accumulated (10 kHz) in memory and display (few Hz) the VEPP‐2M collision vertex. Fitting the strongly peaked distribution (∼3–4 mm at 1.6 m from the collision vertex of VEPP‐2M) to the expected QED angular distribution yields a background in agreement with an independent determination of the VEPP‐2M luminosity.
110973
Searching for gravitational waves from binary coalescence
We describe the implementation of a search for gravitational waves from compact binary coalescences in LIGO and Virgo data. This all-sky, all-time, multidetector search for binary coalescence has been used to search data taken in recent LIGO and Virgo runs. The search is built around a matched filter analysis of the data, augmented by numerous signal consistency tests designed to distinguish artifacts of non-Gaussian detector noise from potential detections. We demonstrate the search performance using Gaussian noise and data from the fifth LIGO science run and demonstrate that the signal consistency tests are capable of mitigating the effect of non-Gaussian noise and providing a sensitivity comparable to that achieved in Gaussian noise.
7374498
FINDCHIRP: an algorithm for detection of gravitational waves from inspiraling compact binaries
Matched-filter searches for gravitational waves from coalescing compact binaries by the LIGO 
Scientific Collaboration use the FINDCHIRP algorithm: an implementation of the optimal filter with 
innovations to account for unknown signal parameters and to improve performance on detector data 
that has nonstationary and non-Gaussian artifacts. We provide details on the FINDCHIRP algorithm as used 
in the search for subsolar mass binaries, binary neutron stars, neutron starblack hole binaries, and binary 
black holes.