Physics, Astrophysics and Cosmology with Gravitational Waves

TL;DR

This review outlines gravitational waves as a new observational window complementary to electromagnetic astronomy, detailing the observable quantities ($h_+$, $h_\times$, direction, frequency, and luminosity) and the TT-gauge formalism that underpins waveform analysis. It surveys compact-source populations (binaries, collapses, pulsars, SMBHs, EMRIs) and stochastic backgrounds, and links these to detector technologies (bars, ground-based and space-based interferometers) and data-analysis techniques (matched filtering, networks, and Bayesian methods). The authors highlight key “standard siren” amplitude–phase measurements enabling distance estimates and cosmography, tests of general relativity in strong fields (BH spectroscopy, PN consistency, Kerr geometry), and multimessenger synergies via electromagnetic triggers. Overall, GW astronomy promises profound insights into gravity, compact-object astrophysics, and the history of the universe, with LIGO/Virgo/KAGRA and LISA as pivotal instruments for the coming decades.

Abstract

Gravitational wave detectors are already operating at interesting sensitivity levels, and they have an upgrade path that should result in secure detections by 2014. We review the physics of gravitational waves, how they interact with detectors (bars and interferometers), and how these detectors operate. We study the most likely sources of gravitational waves and review the data analysis methods that are used to extract their signals from detector noise. Then we consider the consequences of gravitational wave detections and observations for physics, astrophysics, and cosmology.

Figures (16)

• Figure 1: In Einstein's theory, gravitational waves have two independent polarizations. The effect on proper separations of particles in a circular ring in the $(x,y)$-plane due to a plus-polarized wave traveling in the $z$-direction is shown in (a) and due to a cross-polarized wave is shown in (b). The ring continuously gets deformed into one of the ellipses and back during the first half of a gravitational wave period and gets deformed into the other ellipse and back during the next half.
• Figure 2: Mass-radius plot for gravitational wave sources. The horizontal axis is the total mass of a radiating system, and the vertical axis is its size. Typical values from various sources for ground-based and space-based detectors are shown. Lines give order-of-magnitude constraints and relations. Characteristic frequencies are estimated from $f \sim (G\rho/4\pi)^{1/2}$. The black-hole and binary lines are described in the text.
• Figure 3: The relative orientation of the sky and detector frames (left panel) and the effect of a rotation by the angle $\psi$ in the sky frame (left panel).
• Figure 4: The antenna pattern of an interferometric detector (left panel) with the arms in the $x$-$y$ plane and oriented along the two axes. The response $F$ for waves coming from a certain direction is proportional to the distance to the point on the antenna pattern in that direction. Also shown is the fractional area in the sky over which the response exceeds a fraction $\epsilon$ of the maximum (right panel).
• Figure 5: The right panel plots the noise amplitude spectrum, $\sqrt{fS_h(f)}$, in three generations of ground-based interferometers. For the sake of clarity, we have only plotted initial and advanced LIGO and a possible third generation detector sensitivities. VIRGO has similar sensitivity to LIGO at the initial and advanced stages, and may surpass it at lower frequencies. Also shown are the expected amplitude spectrum of various narrow and broad-band astrophysical sources. The left panel is the same as the right except for the LISA detector. The SMBH sources are assumed to lie at a redshift of $z=1$, but LISA can detect these sources with a good SNR practically anywhere in the universe. The curve labelled "Galactic WDBs" is the confusion background from the unresolvable Galactic population of white dwarf binaries.