Badri Krishnan

Isolated and Dynamical Horizons and Their Applications

Over the past three decades, black holes have played an important role in quantum gravity, mathematical physics, numerical relativity and gravitational wave phenomenology. However, conceptual settings and mathematical models used to discuss them have varied considerably from one area to another. Over the last five years a new, quasi-local framework was introduced to analyze diverse facets of black holes in a unified manner. In this framework, evolving black holes are modelled by dynamical horizons and black holes in equilibrium by isolated horizons. We review basic properties of these horizons and summarize applications to mathematical physics, numerical relativity, and quantum gravity. This paradigm has led to significant generalizations of several results in black hole physics. Specifically, it has introduced a more physical setting for black hole thermodynamics and for black hole entropy calculations in quantum gravity, suggested a phenomenological model for hairy black holes, provided novel techniques to extract physics from numerical simulations, and led to new laws governing the dynamics of black holes in exact general relativity.

Dynamical Horizons and their Properties

A detailed description of how black holes grow in full, non-linear general relativity is presented. The starting point is the notion of dynamical horizons. Expressions of fluxes of energy and angular momentum carried by gravitational waves across these horizons are obtained. Fluxes are local and the energy flux is positive. Change in the horizon area is related to these fluxes. A notion of angular momentum and energy is associated with cross-sections of the horizon and balance equations, analogous to those obtained by Bondi and Sachs at null infinity, are derived. These in turn lead to generalizations of the first and second laws of black hole mechanics. The relation between dynamical horizons and their asymptotic states —the isolated horizons— is discussed briefly. The framework has potential applications to numerical, mathematical, astrophysical and quantum general relativity.

Dynamical horizons: Energy, angular momentum, fluxes and balance laws

Dynamical horizons are considered in full, nonlinear 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 formulas 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.

Matching post-Newtonian and numerical relativity waveforms: Systematic errors and a new phenomenological model for nonprecessing black hole binaries

We present a new phenomenological gravitational waveform model for the inspiral and coalescence of nonprecessing spinning black hole binaries. Our approach is based on a frequency-domain matching of post-Newtonian inspiral waveforms with numerical relativity based binary black hole coalescence waveforms. We quantify the various possible sources of systematic errors that arise in matching post-Newtonian and numerical relativity waveforms, and we use a matching criteria based on minimizing these errors; we find that the dominant source of errors are those in the post-Newtonian waveforms near the merger. An analytical formula for the dominant mode of the gravitational radiation of nonprecessing black hole binaries is presented that captures the phenomenology of the hybrid waveforms. Its implementation in the current searches for gravitational waves should allow cross-checks of other inspiral-merger-ringdown waveform families and improve the reach of gravitational-wave searches.

Detecting gravitational wave emission from the known accreting neutron stars

Detection of gravitational waves from accreting neutron stars (NSs) in our Galaxy, due to ellipticity or internal oscillation, would be a breakthrough in our understanding of compact objects and explain the absence of NSs rotating near the break-up limit. Direct detection, however, poses a formidable challenge. Using the current data available on the properties of the accreting NSs in low-mass X-ray binaries (LMXBs), we quantify the detectability for the known accreting NSs, considering various emission scenarios and taking into account the negative impact of parameter uncertainty on the data analysis process. Only a few of the persistently bright NSs accreting at rates near the Eddington limit are detectable by Advanced LIGO if they are emitting gravitational waves at a rate matching the torque from accretion. A larger fraction of the known population is detectable if the spin and orbital parameters are known in advance, especially with the narrow-band Advanced LIGO. We identify the most promising targets, and list specific actions that would lead to significant improvements in detection probability. These include astronomical observations (especially for unknown orbital periods), improvements in data analysis algorithms and capabilities, and further detector development.

Introduction to isolated horizons in numerical relativity

We present a coordinate-independent method for extracting mass (M�) and angular momentum (J�) of a black hole in numerical simulations. This method, based on the isolated horizon framework, is applicable both at late times when the black hole has reached equilibrium, and at early times when the black holes are widely separated. Assuming that the spatial hypersurfaces used in a given numerical simulation are such that apparent horizons exist and have been located on these ˜ �

Gravitational waves from neutron stars: promises and challenges

We discuss different ways that neutron stars can generate gravitational waves, describe recent improvements in modelling the relevant scenarios in the context of improving detector sensitivity, and show how observations are beginning to test our understanding of fundamental physics. The main purpose of the discussion is to establish promising science goals for third-generation ground-based detectors, like the Einstein Telescope, and identify the various challenges that need to be met if we want to use gravitational-wave data to probe neutron star physics.

A phenomenological template family for black-hole coalescence waveforms

Recent progress in numerical relativity has enabled us to model the non-perturbative merger phase of the binary black-hole coalescence problem. Based on these results, we propose a phenomenological family of waveforms which can model the inspiral, merger and ring-down stages of black-hole coalescence. We also construct a template bank using this family of waveforms and discuss its implementation in the search for signatures of gravitational waves produced by black-hole coalescences in the data of ground-based interferometers. This template bank might enable us to extend the present inspiral searches to higher-mass binary black-hole systems, i.e., systems with total mass greater than about 80 solar masses, thereby increasing the reach of the current generation of ground-based detectors.

Status of the GEO600 detector

Of all the large interferometric gravitational-wave detectors, the German/British project GEO600 is the only one which uses dual recycling. During the four weeks of the international S4 data-taking run it reached an instrumental duty cycle of 97% with a peak sensitivity of 7 × 10−22 Hz−1/2 at 1 kHz. This paper describes the status during S4 and improvements thereafter.

The PyCBC search for gravitational waves from compact binary coalescence

We describe the PyCBC search for gravitational waves from compactobject binary coalescences in advanced gravitational-wave detector data. The search was used in the first Advanced LIGO observing run and unambiguously identified two black hole binary mergers, GW150914 and GW151226. At its core, the PyCBC search performs a matched-filter search for binary merger signals using a bank of gravitational-wave template waveforms. We provide a complete description of the search pipeline including the steps used to mitigate the effects of noise transients in the data, identify candidate events and measure their statistical significance. The analysis is able to measure false-alarm rates as low as one per million years, required for confident detection of signals. Using data from initial LIGO’s sixth science run, we show that the new analysis reduces the background noise in the search, giving a 30% increase in sensitive volume for binary neutron star systems over previous searches.