An Overview of Gravitational Waves

The following sections are included:

• Preface
• Contents

The existence of gravitational radiation is a natural prediction of any relativistic description of the gravitational interaction. In this chapter, we focus on gravitational waves, as predicted by Einstein’s general theory of relativity. First, we introduce those mathematical concepts that are necessary to properly formulate the physical theory, such as the notions of manifold, vector, tensor, metric, connection and curvature. Second, we motivate, formulate and then discuss Einstein’s equation, which relates the geometry of spacetime to its matter content. Gravitational waves are later introduced as solutions of the linearized Einstein equation around flat spacetime. These waves are shown to propagate at the speed of light and to possess two polarization states. Gravitational waves can interact with matter, allowing for their direct detection by means of laser interferometers. Finally, Einstein’s quadrupole formulas are derived and used to show that nonspherical compact objects moving at relativistic speeds are powerful gravitational wave sources.

The focus of this chapter is on describing the prospective sources of the gravitational wave universe accessible to present and future observations, from kHz, to mHz down to nano-Hz frequencies. The multi-frequency gravitational wave universe gives a deep view into the cosmos, inaccessible otherwise. It has as main actors core-collapsing massive stars, neutron stars, coalescing compact object binaries of different flavours, massive black hole binaries, extreme mass ratio inspirals, and possibly the very early universe itself. Here, we highlight the science aims and describe the gravitational wave signals expected from the sources and the information gathered in it. We show that the observation of gravitational wave sources will play a transformative role in our understanding of the processes ruling stellar evolution, galaxy assembly, the nature of the strong forces in neutron star interiors, and the most mysterious interaction of Nature: gravity.

We describe the way gravitational waves interact with matter and with test light beams. We pay attention to the case of ground-based detectors, then to space-borne. We develop a formalism allowing to treat complex optical systems such as the large scale inteferometric detectors presently operating or nearly operating in the USA or in Europe.

In this chapter, we first briefly review the early history of gravitational wave detection, and how the research turned towards the large scale interferometers that proved to be the most effective devices for gravitational wave astronomy. We provide an overview of what is generically defined as the “first generation” of interferometric detectors, a number of instruments built around the globe at the end of the last century, differing in size, technology and scope. A more detailed description is dedicated to the “second generation”, or “advanced detectors”, and their main subsystems, which represent the state of the art of the science and technology in the field. In the final section, we give a glimpse of what the next generation of detectors may look like. Given the many similitudes between different projects, throughout the chapter we will use LIGO as the leading example, and highlight how the other projects compared to it both technologically and strategically. This choice is mainly due to the size of the LIGO project and of the LIGO Scientific Collaboration, and to the pivotal role they played in the history of the field and eventually in the first detection of gravitational waves. It is important to note, however, that the comparatively small amount of space and detail dedicated to other endeavors is not indicative of the importance of the role they have played and still play in the field.

Similar to the electromagnetic band, the gravitational wave band of interest stretches over many decades of frequencies searching for signals from a large range of masses. Maybe the signal-richest frequency range spans from a few μHz to a few hundred mHz. It includes many hundred thousand compact galactic binaries and merger signals involving 10⁴ to 10⁸ solar mass black holes; probably the most common black holes in the centers of galaxies throughout the history of the universe. This is the motivation behind plans for a space-based laser interferometric gravitational wave observatories which float around since the ’70s. These plans culminated in the late ’90s into plans for the well known Laser Interferometric Space Antenna (LISA) which, after being cancelled in 2011, is now reemerging as one of the most likely next large space missions. LISA and LISA-like missions use three spacecraft separated by a few million kilometers in a heliocentric orbit. Free floating proof masses inside each spacecraft define the end points of laser interferometer arms in a Michelson-like configuration. This chapter briefly reviews the sources and the history before it focuses on the design of a LISA-like mission.

The following sections are included:

• Introduction
• Performance Limits of a “Link” of the Interferometry Measurement System
• LISA Pathfinder: Concept and Strategy
• LISA Pathfinder Instrument
• The Stray Forces Model and the LISA Pathfinder Performances
• The LISA Pathfinder On-Orbit Investigations
• First Results of the LISA Pathfinder On-Orbit Experiment
• References

The following sections are included:

• Introduction
• GW Sources in the Nanohertz Band
• Monitoring of Pulsars
• Modeling of GW Signal
• Data Analysis
• Latest Results
• References

We present the perspective of using atom interferometry for gravitational wave (GW) detection in the mHz to about 10 Hz frequency band. We focus on light-pulse atom interferometers which have been subject to intense developments in the past 25 years. We calculate the effect of the GW on the atom interferometer and present in details the atomic gradiometer configuration which has retained more attention recently. The principle of such a detector is to use free-falling atoms to measure the phase of a laser, which is modified by the GW. We highlight the potential benefits of using atom interferometry compared to optical interferometry as well as the challenges which remain for the realization of an atom-interferometry-based GW detector. We present some of the important noise sources which are expected in such detectors and strategies to cirucumvent them. Experimental techniques related to cold atom interferometers are briefly explained. We finally present the current progress and projects in this rapidly evolving field.

The following section is included:

• Index