# Section 7: Gravitational Waves

Gravitational waves are the gravitational analogues to electromagnetic waves—electric and magnetic fields that oscillate in the plane perpendicular to the direction that the wave travels. Similarly, gravitational waves are gravitational fields that oscillate perpendicular to the direction of travel. Unlike electromagnetic waves, which can be produced by a single oscillating electric charge, conservation of linear momentum requires at least two masses moving in opposition to produce gravitational waves. In the theory of special relativity, the constant c, called the speed of light, connects space with time and is the speed at which all massless particles travel. Like electromagnetic waves, gravitational waves are believed to propagate at the speed c.

General relativity predicts the existence of gravitational waves. In matter-free regions of spacetime where gravity is weak, the field equations of general relativity simplify to wave equations for spacetime itself. The solutions to these equations are transverse ripples in spacetime, propagating at the speed of light, which we identify as gravitational waves. The distortion of spacetime caused by a gravitational wave is distinctive: In the plane perpendicular to the direction the wave is travelling, space is stretched along one axis and compressed along the orthogonal axis, and vice versa one half-wave cycle later.

Figure 20: Distortion of space from a gravitational wave.

What are the similarities and differences between electromagnetic and gravitational waves? Both waves travel at speed c and carry with them energy and momentum. For electromagnetic waves, spacetime is the background medium in which the waves travel, while for gravitational waves, spacetime itself constitutes the waves. Electromagnetic waves are produced by accelerating or oscillating electric charges, while gravitational waves are produced by accelerating or oscillating mass distributions.

The frequencies of both waves reflect the oscillation frequencies of the sources that produce them. Electronic, vibrational, and rotational transitions (that is, oscillations) in atoms and molecules provide the most common source of electromagnetic waves, producing wave frequencies between roughly 107 and 1017 Hertz (Hz, or cycles per second). The most efficient sources for gravitational waves are massive objects undergoing rapid acceleration, such as pairs of neutron stars and/or black holes orbiting closely about one another. Considerations of orbital speeds and masses lead us to expect that the strongest gravitational radiation will have frequencies less than 10,000 Hz. Electromagnetic waves interact strongly with matter through absorption or scattering. Gravitational waves, by contrast, interact extremely weakly with matter; they travel essentially unimpeded through spacetime.

## Indirect detection of gravitational waves

The most obvious difference between gravitational and electromagnetic waves is the fact that no one has yet directly detected gravitational waves—although this situation should change soon, given the significant progress in the technologies necessary for detection. In the meantime, we have strong indirect evidence that gravitational radiation exists. Astronomers have monitored the orbital frequency of the binary neutron star system PSR1913+16 since 1974, the year that Russell Hulse and Joseph Taylor discovered the system. One of the neutron stars is a pulsar that beams radio waves to the Earth as the neutron star rotates about its axis. Astrophysicists use the arrival times of the radio pulses to reconstruct the orbit of the binary system. The oscillating mass distribution of this binary system should generate gravitational waves and lose orbital energy as the waves radiate outward. A loss in orbital energy moves the neutron stars closer together and decreases the orbital period. The observed decrease of the orbital period over the past 35 years agrees with the energy loss through gravitational radiation predicted by general relativity to better than 1 percent accuracy.

Figure 21: Orbital period of the binary neutron star system PSR 1913+15 measured from 1975 to 2000.

Radio pulses from pulsars arrive at such a regular rate as to provide hope that pulsars may provide a means to detect very low frequency gravitational waves. Waves with frequencies around 10-9 Hz (equivalent to wavelengths of around 10 light-years) may persist from mass motions early in the history of the universe. When such a wave passes a pulsar, it slightly alters the arrival time of the radio beam from the pulsar. By comparing the arrival times of signals from perhaps 100 pulsars spread across the sky for many years, astronomers might possibly detect the tell-tale distortion of spacetime that is the signature of a passing gravitational wave.

Researchers believe that even lower frequency (that is, longer wavelength) gravitational waves were created in the early moments of the universe. We have evidence for events around 380,000 years after the Big Bang in the form of extraordinarily precise measurements of the cosmic microwave background (CMB), which is electromagnetic radiation left over from the early universe. Primordial gravitational waves would leave their imprint on the CMB as a distinctive polarization pattern as one compares the polarization of CMB radiation from different regions across the sky. Intense efforts are under way to mount instruments with enough polarization sensitivity to search for the primordial gravitational waves. Both ground-based observations (CLOVER, EBEX, Polarbear, QUIET, SPIDER, and SPUD instruments, to name a few) and space-based measurements from the Planck satellite launched in 2009 promise rapid progress toward the detection of primordial gravitational waves.

## Direct detection of gravitational waves

The earliest attempts to detect gravitational waves directly used resonant mass detectors, also called "bar detectors," first developed by Joseph Weber. A typical bar detector might be a 5000 kg cylinder, two meters long, suspended in vacuum, and made from a low mechanical loss material such as certain alloys of aluminum. A burst of gravitational radiation could stretch and compress the bar, exciting the roughly one kilohertz lowest frequency vibrational mode of the cylinder. Sensors at the ends of the cylinder would detect the vibrations. A low-loss material would ring for many vibrational cycles, enhancing the ability to identify the excess vibration from a gravitational wave in the presence of background noise. Modern versions of the bar detectors (for example, the NAUTILUS and AURIGA detectors in Italy, miniGRAIL in the Netherlands, and the EXPLORER bar in Switzerland) are cooled to liquid helium temperatures or even lower to reduce the mechanical losses and thermal vibrations, and to reduce the noise inherent in the motion sensors.

Figure 22: Nautilus cryogenic antenna at the Laboratori Nazionali di Frascati, Italy.

The most developed technology for the detection of gravitational waves involves long baseline laser interferometers. These instruments use laser light as a "meter stick" to compare the distances between a central object and distant objects along perpendicular axes. A passing gravitational wave will compress spacetime along one axis while stretching it along a perpendicular axis. An interferometer provides a precise measurement of the relative distance that light travels along different paths.

The long baseline gravitational wave interferometers are refined versions of the Michelson interferometer that, when it failed to detect the ether late in the 19th century, helped to set the scene for the theory of special relativity. But instead of being mounted rigidly on a table, the end mirrors of the gravitational wave instruments are suspended, like pendulums, from thin wires. In addition, the entire laser path occurs within a vacuum chamber. In the horizontal plane, the end mirrors are essentially objects in freefall, able to follow the stretching and compressing of spacetime from a gravitational wave. (In the classical picture of gravitational waves, the waves produce horizontal forces on the end mirrors; suspended mirrors can move in response to the wave forces.) However, even the strongest gravitational waves that one might hope to detect on Earth stretch space by an extremely small amount: The strain (change in distance divided by the distance) between two objects is expected to be less than 10-18. To make the change in distance large enough for an interferometer to detect, designers must make the baseline as long as possible.

## Gravitational wave discovery on Earth and in space

Figure 23: Aerial view of the LIGO Observatory at Hanford, Washington.