Quasi-local black hole horizons

This article introduces the subject of quasi-local horizons at a level suitable for physics graduate students who have taken a first course on general relativity. It reviews properties of trapped surfaces and trapped regions in some simple examples, general properties of trapped surfaces including their stability properties, the definitions and some applications of dynamical-, trapping-, and isolated-horizons.Comment: 41 pages, 12 Figures. To appear in the Springer Handbook of Spacetime, Springer Verlag (2013

Tidal deformations of spinning black holes in Bowen-York initial data

We study the tidal deformations of the shape of a spinning black hole horizon due to a binary companion in the Bowen-York initial data set. We use the framework of quasi-local horizons and identify a black hole by marginally outer trapped surfaces. The intrinsic horizon geometry is specified by a set of mass and angular-momentum multipole moments $\mathcal{M}_n$ and $\mathcal{J}_n$ respectively. The tidal deformations are described by the change in these multipole moments caused by an external perturbation. This leads us to define two sets of dimensionless numbers, the tidal coefficients for $\mathcal{M}_n$ and $\mathcal{J}_n$, which specify the deformations of a black hole with a binary companion. We compute these tidal coefficients in a specific model problem, namely the Bowen-York initial data set for binary black holes. We restrict ourselves to axisymmetric situations and to small spins. Within this approximation, we analytically compute the conformal factor, the location of the marginally trapped surfaces, and finally the multipole moments and the tidal coefficients.Comment: 22 pages, 1 figur

UNDERSTANDING THE MEIOTIC ROLES OF SISTERS UNBOUND IN DROSOPHILA MELANOGASTER

During meiosis, cohesin is required for sister chromatid cohesion and for formation of chromosome cores. Multiple processes including chromosome segregation, recombination and synaptonemal complex (SC) are dependent on cohesin. Cohesin complex consists of two SMC subunits- SMC1, SMC3 and two non-SMC subunits RAD21/REC8 in meiosis and SA. But in Drosophila, non-SMC subunits have not been shown to be required for cohesion. We have identified a gene sisters unbound, which along with previously identified ord and solo, form a group of three genes (sos) which do not have any sequence similarity to cohesins but performs functions demonstrated by cohesins. Proper chromosome segregation requires that homologs are connected by chiasmata during meiosis I and that sister centromeres are mono-oriented at meiosis I and bi-oriented at anaphase II. For both these functions cohesion is necessary. Cohesins are also required for proper assembly axial elements/lateral elements (AE/LE), SC, inhibiting sister chromatid exchange (SCE) and recombination. SUNN is required for all these functions and it localizes to chromosomes in a pattern similar to cohesion proteins ORD, SOLO and cohesin subunit SMC1 and is mutually interdependent on SOLO, SMC1 for localization. Bioinformatics analysis suggests that SUNN is a structural homolog of SA. Based on functional and structural similarity to cohesin complex components we predict that SUNN is a part of the Drosophila meiotic cohesin complex

Dynamical Horizons: Energy, Angular Momentum, Fluxes and Balance Laws

Dynamical horizons are considered in full, non-linear general relativity. Expressions of fluxes of energy and angular momentum carried by gravitational waves across these horizons are obtained. Fluxes are local, the energy flux is positive and change in the horizon area is related to these fluxes. The flux formulae also give rise to balance laws analogous to the ones obtained by Bondi and Sachs at null infinity and provide generalizations of the first and second laws of black hole mechanics.Comment: 4 pages, RevTeX4. Minor typos corrected. To appear in Phys.Rev.Let

Marginalizing the likelihood function for modeled gravitational wave searches

Matched filtering is a commonly used technique in gravitational wave searches for signals from compact binary systems and from rapidly rotating neutron stars. A common issue in these searches is dealing with four extrinsic parameters which do not affect the phase evolution of the system: the overall amplitude, initial phase, and two angles determining the overall orientation of the system. The F-statistic maximizes the likelihood function analytically over these parameters, while the B-statistic marginalizes over them. The B-statistic, while potentially more powerful and capable of incorporating astrophysical priors, is not as widely used because of the computational difficulty of performing the marginalization. In this paper we address this difficulty and show how the marginalization can be done analytically by combining the four parameters into a set of complex amplitudes. The results of this paper are applicable to both transient non-precessing binary coalescence events, and to long lived signals from rapidly rotating neutron stars.Comment: 26 page

Swift Pointing and Gravitational-Wave Bursts from Gamma-Ray Burst Events

The currently accepted model for gamma-ray burst phenomena involves the violent formation of a rapidly rotating solar-mass black hole. Gravitational waves should be associated with the black-hole formation, and their detection would permit this model to be tested. Even upper limits on the gravitational-wave strength associated with gamma-ray bursts could constrain the gamma-ray burst model. This requires joint observations of gamma-ray burst events with gravitational and gamma-ray detectors. Here we examine how the quality of an upper limit on the gravitational-wave strength associated with gamma-ray bursts depends on the relative orientation of the gamma-ray-burst and gravitational-wave detectors, and apply our results to the particular case of the Swift Burst-Alert Telescope (BAT) and the LIGO gravitational-wave detectors. A result of this investigation is a science-based ``figure of merit'' that can be used, together with other mission constraints, to optimize the pointing of the Swift telescope for the detection of gravitational waves associated with gamma-ray bursts.Comment: iop style, 1 figure, 6 pages, presented at GWDAW 200

The slicing dependence of non-spherically symmetric quasi-local horizons in Vaidya Spacetimes

It is well known that quasi-local black hole horizons depend on the choice of a time coordinate in a spacetime. This has implications for notions such as the surface of the black hole and also on quasi-local physical quantities such as horizon measures of mass and angular momentum. In this paper, we compare different horizons on non-spherically symmetric slicings of Vaidya spacetimes. The spacetimes we investigate include both accreting and evaporating black holes. For some simple choices of the Vaidya mass function function corresponding to collapse of a hollow shell, we compare the area for the numerically found axisymmetric trapping horizons with the area of the spherically symmetric trapping horizon and event horizon. We find that as expected, both the location and area are dependent on the choice of foliation. However, the area variation is not large, of order $0.035\%$ for a slowly evolving horizon with $\dot{m}=0.02$. We also calculate analytically the difference in area between the spherically symmetric quasi-local horizon and event horizon for a slowly accreting black hole. We find that the difference can be many orders of magnitude larger than the Planck area for sufficiently large black holes.Comment: 10 pages, 5 figures, corrected minor typo

Distorted Black Holes with Charge

We present new solutions to the Einstein-Maxwell equations representing a class of charged distorted black holes. These solutions are static-axisymmetric and are generalizations of the distorted black hole solutions studied by Geroch and Hartle. Physically, they represent a charged black hole distorted by external matter fields. We discuss the zeroth and first law for these black holes. The first law is proved in two different forms, one motivated by the isolated horizon framework and the other using normalizations at infinity.Comment: 18 pages, LaTe

Painlev\'e-II approach to binary black hole merger dynamics: universality from integrability

The binary black hole merger waveform is both simple and universal. Adopting an effective asymptotic description of the dynamics, we aim at accounting for such universality in terms of underlying (effective) integrable structures. More specifically, under a ``wave-mean flow'' perspective, we propose that fast degrees of freedom corresponding to the observed waveform would be subject to effective linear dynamics, propagating on a slowly evolving background subject to (effective) non-linear integrable dynamics. The Painlev\'e property of the latter would be implemented in terms of the so-called Painlev\'e-II transcendent, providing a structural link between i) orbital (in particular, EMRI) dynamics in the inspiral phase, ii) self-similar solutions of non-linear dispersive Korteweg-de Vries-like equations (namely, the `modified Korteweg-de Vries' equation) through the merger and iii) the matching with the isospectral features of black hole quasi-normal modes in late ringdown dynamics. Moreover, the Painlev\'e-II equation provides also a `non-linear turning point' problem, extending the linear discussion in the recently introduced Airy approach to binary black hole merger waveforms. Under the proposed integrability perspective, the simplicity and universality of the binary black hole merger waveform would be accounted to by the `hidden symmetries' of the underlying integrable (effective) dynamics. In the spirit of asymptotic reasoning, and considering Ward's conjecture linking integrability and self-dual Yang-Mills structures, it is tantalizing to question if such universal patterns would reflect the actual full integrability of a (self-dual) sector of general relativity, ultimately responsible for the binary black hole waveform patterns.Comment: 18 pages, no figures. Preliminary versio

Quasi-Local Linear Momentum in Black-Hole Binaries

We propose a quasi-local formula for the linear momentum of black-hole horizons inspired by the formalism of quasi-local horizons. We test this formula using two complementary configurations: (i) by calculating the large orbital linear momentum of the two black holes in an unequal-mass, zero-spin, quasi-circular binary and (ii) by calculating the very small recoil momentum imparted to the remnant of the head-on collision of an equal-mass, anti-aligned-spin binary. We obtain results consistent with the horizon trajectory in the orbiting case, and consistent with the net radiated linear momentum for the much smaller head-on recoil velocity.Comment: 5 pages, 3 figures, revtex