A Hamiltonian Approach to the Mass of Isolated Black Holes

Boundary conditions defining a non-rotating isolated horizon are given in Einstein-Maxwell theory. A spacetime representing a black hole which itself is in equilibrium but whose exterior contains radiation admits such a horizon. Inspired by Hamiltonian mechanics, a (quasi-)local definition of isolated horizon mass is formulated. Although its definition does not refer to infinity, this mass takes the standard value in a Reissner-Nordstrom solution. Furthermore, under certain technical assumptions, the mass of an isolated horizon is shown to equal the future limit of the Bondi energy.Comment: 5 pages, LaTeX 2.09, 1 eps figure. To appear in the proceedings of the Eighth Canadian Conference on General Relativity and Relativistic Astrophysic

Canonical Phase Space Formulation of Quasilocal General Relativity

We construct a Hamiltonian formulation of quasilocal general relativity using an extended phase space that includes boundary coordinates as configuration variables. This allows us to use Hamiltonian methods to derive an expression for the energy of a non-isolated region of space-time that interacts with its neighbourhood. This expression is found to be very similar to the Brown-York quasilocal energy that was originally derived by Hamilton-Jacobi methods. We examine the connection between the two formalisms and find that when the boundary conditions for the two are harmonized, the resulting quasilocal energies are identical.Comment: 31 pages, 2 figures, references added, typos corrected, section 3 revised for clarity, to appear in Classical and Quantum Gravit

Isolated Horizons: A Generalization of Black Hole Mechanics

A set of boundary conditions defining a non-rotating isolated horizon are given in Einstein-Maxwell theory. A space-time representing a black hole which itself is in equilibrium but whose exterior contains radiation admits such a horizon . Physically motivated, (quasi-)local definitions of the mass and surface gravity of an isolated horizon are introduced. Although these definitions do not refer to infinity, the quantities assume their standard values in Reissner-Nordstrom solutions. Finally, using these definitions, the zeroth and first laws of black hole mechanics are established for isolated horizons.Comment: 9 pages, LaTeX2e, 3 eps figure

Distinguishing compact binary population synthesis models using gravitational-wave observations of coalescing binary black holes

The coalescence of compact binaries containing neutron stars or black holes is one of the most promising signals for advanced ground-based laser interferometer gravitational-wave detectors, with the first direct detections expected over the next few years. The rate of binary coalescences and the distribution of component masses is highly uncertain, and population synthesis models predict a wide range of plausible values. Poorly constrained parameters in population synthesis models correspond to poorly understood astrophysics at various stages in the evolution of massive binary stars, the progenitors of binary neutron star and binary black hole systems. These include effects such as supernova kick velocities, parameters governing the energetics of common envelope evolution and the strength of stellar winds. Observing multiple binary black hole systems through gravitational waves will allow us to infer details of the astrophysical mechanisms that lead to their formation. Here we simulate gravitational-wave observations from a series of population synthesis models including the effects of known selection biases, measurement errors and cosmology. We compare the predictions arising from different models and show that we will be able to distinguish between them with observations (or the lack of them) from the early runs of the advanced LIGO and Virgo detectors. This will allow us to narrow down the large parameter space for binary evolution models.Comment: 16 pages, 8 figures, updated to match version published in Ap

The first law for slowly evolving horizons

We study the mechanics of Hayward's trapping horizons, taking isolated horizons as equilibrium states. Zeroth and second laws of dynamic horizon mechanics come from the isolated and trapping horizon formalisms respectively. We derive a dynamical first law by introducing a new perturbative formulation for dynamic horizons in which "slowly evolving" trapping horizons may be viewed as perturbatively non-isolated.Comment: 4 pages, typos fixed, minor changes in wording for clarity, to appear in PR

Constraining black-hole spins with gravitational wave observations

The observation of gravitational-wave signals from merging black-hole binaries enables direct measurement of the properties of the black holes. An individual observation allows measurement of the black-hole masses, but only limited information about either the magnitude or orientation of the black hole spins is available, primarily due to the degeneracy between measurements of spin and binary mass ratio. Using the first six black-hole merger observations, we are able to constrain the distribution of black-hole spins. We perform model selection between a set of models with different spin population models combined with a power-law mass distribution to make inferences about the spin distribution. We assume a fixed power-law mass distribution on the black holes, which is supported by the data and provides a realistic distribution of binary mass-ratio. This allows us to accurately account for selection effects due to variations in the signal amplitude with spin magnitude, and provides an improved inference on the spin distribution. We conclude that the first six LIGO and Virgo observations (Abbott et al. 2016a, 2017a,b,c) disfavour highly spinning black holes against low spins by an odds-ratio of 15:1; thus providing strong constraints on spin magnitudes from gravitational-wave observations. Furthermore, we are able to rule out a population of binaries with completely aligned spins, even when the spins of the individual black holes are low, at an odds ratio of 22,000:1, significantly strengthening earlier evidence against aligned spins (Farr et al. 2017). These results provide important information that will aid in our understanding on the formation processes of black-holes

Localization of transient gravitational wave sources: beyond triangulation

Rapid, accurate localization of gravitational wave transient events has proved critical to successful electromagnetic followup. In previous papers we have shown that localization estimates can be obtained through triangulation based on timing information at the detector sites. In practice, detailed parameter estimation routines use additional information and provide better localization than is possible based on timing information alone. In this paper, we extend the timing based localization approximation to incorporate consistency of observed signals with two gravitational wave polarizations, and an astrophysically motivated distribution of sources. Both of these provide significant improvements to source localization, allowing many sources to be restricted to a single sky region, with an area 40% smaller than predicted by timing information alone. Furthermore, we show that the vast majority of sources will be reconstructed to be circularly polarized or, equivalently, indistinguishable from face-on.Comment: 27 pages, 7 figure

Searching for binary coalescences with inspiral templates: Detection and parameter estimation

There has been remarkable progress in numerical relativity recently. This has led to the generation of gravitational waveform signals covering what has been traditionally termed the three phases of the coalescence of a compact binary - the inspiral, merger and ringdown. In this paper, we examine the usefulness of inspiral only templates for both detection and parameter estimation of the full coalescence waveforms generated by numerical relativity simulations. To this end, we deploy as search templates waveforms based on the effective one-body waveforms terminated at the light-ring as well as standard post-Newtonian waveforms. We find that both of these are good for detection of signals. Parameter estimation is good at low masses, but degrades as the mass of the binary system increases.Comment: 14 pages, submitted to proceedings of the NRDA08 meeting, Syracuse, Aug. 11-14, 200

Degeneracy between mass and spin in black-hole-binary waveforms

We explore the degeneracy between mass and spin in gravitational waveforms emitted by black-hole binary coalescences. We focus on spin-aligned waveforms and obtain our results using phenomenological models that were tuned to numerical-relativity simulations. A degeneracy is known for low-mass binaries (particularly neutron-star binaries), where gravitational-wave detectors are sensitive to only the inspiral phase, and the waveform can be modelled by post-Newtonian theory. Here, we consider black-hole binaries, where detectors will also be sensitive to the merger and ringdown, and demonstrate that the degeneracy persists across a broad mass range. At low masses, the degeneracy is between mass ratio and total spin, with chirp mass accurately determined. At higher masses, the degeneracy persists but is not so clearly characterised by constant chirp mass as the merger and ringdown become more significant. We consider the importance of this degeneracy both for performing searches (including searches where only non-spinning templates are used) and in parameter extraction from observed systems. We compare observational capabilities between the early (~2015) and final (2018 onwards) versions of the Advanced LIGO detector.Comment: 11 pages, 9 figure