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Glossary accretion: the process by which gas flows around and onto a compact gravitating object. advection-dominated accretion flow (ADAF): an accretion flow in which most of the energy released by viscous action is carried with the gas to the center rather than being radiated. anisotropic: not isotropic (q.v.), that is, not the same in all directions. An anisotropy is a measure of the difference between directions. The cosmic background radiation (q.v.) is approximately isotropic in its temperature in different directions on the sky, but has minute anisotropies in temperature. bending of light: deflection of light (or other electromagnetic radiation) from a straight-line path as it falls in a gravitational field. BeppoSAX satellite: BeppoSAX is an Italian/Dutch mission that can accurately determine the location of x-ray and gamma-ray bursts (for information online, see <http://www.sdc.asi.it>~. big bang: the initial instant of the universe characterized in general relativity by arbitrarily high density, temperature, and curvature. Binary Black Hole Alliance: a multidisciplinary collaboration among relativity theorists and computer scientists at eight institutions to develop algorithms and software for solving Einstein's equations on supercomputers. The alli- ance focused on the coalescence of two black holes in binary orbit about each other. It was funded by the NSF from 1993 to 1998 as one of its Grand Challenge projects in computational science. (Cf. Neutron Star Grand Chal- lenge.) 104

APPENDIX B 105 binary pulsar: a radio pulsar (q.v.) that is gravitationally bound to a companion star and orbits it. The signals from such a system can be used to test some aspects of general relativity to great precision. blackbody spectrum: Every body in thermal equilibrium emits the same kind of light characterized only by the body's temperature. The distribution of in- tensity with wavelength is called the blackbody spectrum, and an object emitting this characteristic spectrum is called a blackbody. black hole: a region of space where the gravitational pull is so strong that classically, nothing can escape. The boundary of this region is called the black hole's event horizon (q.v.~. Black holes can form when a massive star undergoes gravitational collapse (q.v.~. black hole evaporation: the quantum mechanical process whereby a black hole losses mass and becomes smaller due to Hawking radiation (q.v.~. Chandra X-ray satellite (formerly Advanced X-ray Astrophysics Facility): a NASA satellite observatory that was launched on the space shuttle on July 23, 1999. It will image the x-ray sky over the energy range from 0.1 to 10 keV with resolution similar to that of the Hubble Space Telescope (for infor- mation online, see <http://chandra.harvard.edu/index.html>~. classical: a general term meaning non-quantum mechanical. For example, gen- eral relativity is a classical theory with deterministic equations of motion for the geometry of spacetime. In a non-classical quantum theory of gravity only probabilities for spacetime geometries would be predicted. closed universe: a finite-volume universe resulting from the gravitational pull of a high density of matter. It may be visualized as the three-dimensional analog of the surface of a sphere; if one travels straight in any direction, one eventually returns to the same place. COBE: the Cosmic Background Explorer satellite for seeing the details of the light from the big bang (for information online, see <http://www.gsfc.nasa. gov/astro/cobe/cobe_home. html>) . cold dark matter: another name for subatomic particles that interact weakly with ordinary matter and radiation. These subatomic particles can cluster gravita- tionally and form galaxies. Weakly interacting massive particles are a form of cold dark matter. Compton Gamma Ray Observatory (CGRO): Named after American Nobel laureate Arthur Holly Compton, the Gamma Ray Observatory was launched by NASA in 1991 to study the spectrum, location, and nature of gamma-rays and gamma-ray bursts from astronomical sources. For information online, see <http://antwrp.gsfc.nasa.gov/cossc/cossc.html>. cosmic background radiation (CMB): the residual light from the big bang. While nearly uniform, there are tiny variations in its temperature due to fluctuations in the density of the early universe. These tiny density fluctuations grew to form today's galaxies.

106 APPENDIX B cosmic censorship conjecture: the conjecture that the inevitable singularities (q.v) formed in a physically realistic gravitational collapse are formed inside black holes, hidden from the view of a distant observer. cosmic string: a string-like defect in matter fields that is the relic of a phase transition in the early universe. Cosmic strings are one possible seed for the formation of galaxies. cosmological constant: the energy density associated with the vacuum (empty space). Recent astronomical observations suggest that there is a net energy associated with the vacuum. If there is a positive vacuum energy, then the expansion of the universe will eventually accelerate and our descendants will find themselves in a nearly empty universe. cosmology: the study of the origin, evolution, fate, and physical properties of the universe as a whole. critical density to close the universe: the dividing value between a universe with density high enough for its gravitational pull to stop the cosmological expan sion and one with density low enough that the expansion continues forever. curvature: the bending or warping of space and time, predicted by general relativity and theories like it. dark matter: Astronomers can determine the mass of galaxies using a variety of techniques. All of these methods find a mass that exceeds the mass in stars by more than a factor of 10. These observations imply that most of the mass of our Galaxy, and most of the mass of other galaxies, is made up of some kind of non-luminous matter or dark matter. Possible candidates for the dark matter range from subatomic particles to supermassive black holes. (See also "hot dark matter" and "cold dark matter.") density;fluctuations: The universe is not uniform. The density of matter varies from place to place. These variations are called density fluctuations. distribution of galaxies: see large-scale structure. dragging of inertialframes: a general relativistic phenomenon predicted to occur near rotating masses, in which freely falling laboratories would be dragged slightly around the body. One consequence is that a gyroscope in such a laboratory would process with respect to the direction it would point in empty space. Einstein's equation: a mathematical equation written down by Einstein in 1915 to describe how matter and energy curve space and time. This curvature accounts for gravity, superseding Newton's theory of a gravitational force, which remains a good approximation only when gravity is weak. equation of state of nuclear matter: An equation of state describes how the density of a substance increases as the pressure on it is increased. Stars remain in equilibrium by balancing the inward pull of gravity against the outward pressure force, so the equation of state must be known to construct

APPENDIX B 107 theoretical models of stars. Neutron stars are at such high densities and pressures that their atoms have been completely crushed until the nuclei merge, producing "nuclear matter." equivalence principle: a fundamental principle of general relativity one of whose consequences is that all objects (and light) fall in a gravitational field in the same way independent of their internal structure or other properties. This universality of free fall is one of the most accurately verified principles in physics. event horizon: the surface of a black hole. It is a one-way membrane, allowing matter or signals to flow in but not out. Friedmann-Robertson-Walker (FRW) cosmological models: the mathematical description of the simplest possible universe with matter density and ex- pansion rates the same everywhere in space and in all directions (homoge- neous and isotropic). It approximately describes the behavior of our uni- verse on the largest spatial scales. galaxy: a large assemblage of stars and gas with a total mass in the range from 10 million to 100 billion solar masses. The Sun and the solar system are part of the Milky Way Galaxy. gamma-ray: electromagnetic radiation more energetic than x-rays. gamma-ray bursts: bursts of gamma-rays from cosmic sources observed by detectors on satellites. Several hundred are detected per year and range in duration from fractions of a second to several tens of seconds. They are seen distributed uniformly across the sky, suggesting that the sources are at cos- mological distances. general relativity: Einstein's theory of gravity in which the gravity is the curved geometry of space and time. Global Positioning System (GPS): a U.S. navigation system in which 24 Earth- orbiting satellites carrying atomic clocks broadcast precise time and location information. A receiver intercepting signals from four or more GPS satel- lites uses the information to determine its precise absolute location, in some circumstances to better than 15 meters. gravitational collapse: A star remains in equilibrium by balancing the inward pull of gravity against an outward pressure force. If gravity overwhelms the pressure, nothing can hold the star up, and it undergoes gravitational collapse to a black hole. gravitational inverse square law: the prediction, originally due to Newton, that gravitational forces become weaker as the inverse square of the distance between objects. Any quantum force produced by the exchange of massless objects must also satisfy an inverse square law. gravitational lens: an object that deflects the rays of light from a distant astro- nomical source by the gravitational pull of an intermediate mass that may be

108 APPENDIX B a galaxy or a cluster of galaxies. The deflection causes a distortion in the image of the distant source, and sometimes also leads to multiple images. gravitational wave: a ripple in the geometry of spacetime propagating as a wave according to general relativity. gravitational wave background: (1) gravitational waves arriving from so many sources that the individual signals are indistinguishable; (2) gravitational wave "static," akin to the (electromagnetic) cosmic background radiation. gravitational Wilson loops: one-dimensional integrals of the quantum geometric variables around closed paths that are analogous to the similar quantities occurring in gauge theories. Gravity Probe B.: also known as the NASA Relativity Mission. It is expected to make the first measurement of the "frame-dragging" effect predicted by general relativity, i.e., the modification of spacetime produced by Earth's rotation. The satellite contains ultraprecise gyroscopes whose precession with respect to the fixed stars is monitored (for information online, see <http ://einstein. Stanford. educe. Hawking radiation: the approximately thermal radiation emitted by a black hole as a result of quantum effects. hertz: a standard unit of frequency equal to one cycle per second. higher dimensions: String theory predicts that space has more than three dimen- sions, but the extra dimensions can be seen only at very high energies. "holographic" view of space and time: the possibility that physical processes in a region of space can be completely described by quantities defined only on the boundary of that region. homogeneous: a situation in which the basic properties of a system are the same from place to place, at a selected moment of time. When observed at scales so large that the fine details of galaxies and clusters can be ignored, the universe appears to be homogeneous. horizon: see event horizon. hot dark matter: dark matter (q.v.) that is moving today with velocities compa- rable to or equal to the velocity of light. Neutrinos are an example. Hubble constant (Ho) a measure of the expansion rate of the universe (usually in units of kilometers per second of increasing galaxy recession speed per megaparsec [106 parsecs] of galaxy distance). 1/ Ho is a measure of the age of the universe. inflationary universe: The inflationary theory proposes an extremely rapid pe- riod of expansion shortly after the big bang. During this rapid expansion, the energy density of the universe was dominated by vacuum energy. This vacuum energy later was converted into the matter and radiation that fills the universe today.

APPENDIX B 109 infrared: a region of the electromagnetic spectrum with wavelengths longer than those of visible light. Hot objects typically are very bright at infrared wave- lengths. isotropic: a situation in which the basic properties of a system observed from one location are the same in every direction. The cosmic background radiation (q.v.) is isotropic to a few parts in a hundred thousand. LAGEOS (laser-ranged geodynamics satellite): a massive, spherical satellite studded with laser reflectors, in orbit around Earth. Accurate tracking of the two existing LAGEOS satellites yields information about Earth's structure (through its gravity field) and about the motion of the ground on which the tracking stations sit, and can study relativistic effects in gravity (for informa- tion online, see <http://ilrs.gsfc.nasa.gov/ilrs/lageos.html>~. Iarge-scale structure: the arrangements of the positions of the galaxies in the universe. On the largest scales this shows clusters, walls, and voids. laser interferometer: a device that uses laser light to make accurate comparison of the lengths of two perpendicular paths. Lense-Thirring effect: synonymous with "dragging of inertial frames" (q.v.~. The effect is named after Josef Lense and Hans Thirring, Austrian physicists who first calculated the general relativistic predictions for dragging in 1918. LIGO (Laser Interferometer Gravitational-Wave Observatory): an NSF-spon- sored project to build and operate two 4-kilometer laser interferometers to detect gravitational waves (for information online, see <http://www.ligo. caltech.edu/>~. lunar laser ranging: a technique for precise determination of the lunar orbit, in which laser beams are bounced off special reflectors deposited on the Moon by Apollo astronauts and Soviet unmanned landers. The Earth-Moon dis- tance can be effectively monitored to centimeter accuracies. MAP satellite: NASA's Microwave Anisotropy Probe, which is scheduled for launch in fall 2000, will accurately map the microwave sky with an angular resolution of 0.2 degrees. At MAP' s frequencies (22 to 96 GHz), most of the fluctuations in the microwave sky are due to variations in the cosmic micro- wave background (for information online, see <http://map.gsfc.nasa.gov>~. microlensing: the phenomenon in which the deflecting mass of a gravitational lens (q.v.) is a star rather than a galaxy or cluster, with a correspondingly smaller angle of deflection. neutron star: a star at such a high density and pressure that its atoms have been completely crushed until the nuclei merge and most of the electrons have been squeezed onto the protons, forming neutron-rich material.

110 APPENDIX B Neutron Star Grand Challenge: a collaboration funded by NASA to calculate the properties of a binary system of two neutron stars coalescing as they emit gravitational radiation (cf. Binary Black Hole Alliance). Newtonian gravity: Newton's theory of gravity, which states that falling and orbiting of a mass in the vicinity of another mass are caused by an attractive force along a line joining them. This theory is the limit of general relativity when speeds are much less than the speed of light and gravitational fields are weak. Newton's gravitational constant G: the fundamental constant that determines the strength of all gravitational phenomena. In the usual SI system, it is numeri- cally equal to the gravitational force (in Newtons) between two 1-kilogram objects separated by 1 meter. "no hair" theorem for black holes: the surprising result that no matter how complicated the initial physical situation that produces a black hole, the final black hole is described by only a few parameters. The simplest black holes are completely specified by only their mass, charge, and spin. parsec: a unit of distance of roughly 3 light-years or 3 x 10~6 meters. Planck length: the unique length that can be constructed from Newton's gravita- tional constant, the velocity of light, and the quantum of action and that characterizes quantum gravity phenomena. Its value is 1 0-33 cm. There is a corresponding Planck energy (10~9 GeV) and Planck time (10~3 S). Planck satellite: the European Space Agency's Planck surveyor satellite, sched- uled for launch in 2007, will measure the microwave sky over a wide range of wavelengths (22 to 900 GHz) with an angular resolution of 0.1 degree (for information online, see <http://astro.estec.esa.nl/SA-general/Projects/ Planck/>~. polarization: the directional pattern of a wave's effects on test bodies. polymer-like geometry: an intuitive term used to describe geometry of the physi- cal space at the smallest scales in a specific approach to quantum gravity. At a fundamental level, space resembles a one-dimensional polymer, and the three-dimensional continuum arises only as an approximation at scales much larger than 1 0-33 cm. post-Newtonian: General relativity and theories like it reproduce Newton's laws of gravity as a first approximation. The first general relativistic corrections beyond Newtonian theory (called post-Newtonian) are responsible for such phenomena as the bending of light or the advance of Mercury's perihelion. This approximation is not valid in the vicinity of neutron stars or black holes vat the big ban". precession of an orbit: An orbit processes when the long axis of its elliptical shape rotates slowly rather than remaining in a fixed direction. principle of equivalence: see equivalence principle.

APPENDIX B 111 principle of relativity: the statement that there is no absolute rest; given two objects in uniform relative motion, each one can be treated as being at rest and the other as moving with respect to it. pulsar: a spinning neutron star that emits beamed radiation. The radiation is received as series of pulses as the beam sweeps over the observer just like a lighthouse. quadrupole moment: a mathematical quantity that measures non-sphericity of a mass distribution. If this quantity changes in time, the body emits gravita- tional waves. quantum cosmology: the area of physics and astrophysics concerned with a theory of the quantum initial state of the universe (q.v.) and its consequences for observations today. quantum initial state of the universe: sometimes called the wave function of the universe. If quantum mechanics applies to the universe as a whole, then the universe must have been in some particular initial quantum state. That state provides a boundary condition for the big bang and all subsequent epochs of the universe. quantum of area: an elementary unit of area whose existence is predicted by the quantum theory of geometry (q.v.~. quantum theory of geometry: a theory of the microscopic structure of space, derived from the application of the principles of quantum mechanics to the geometry of physical space. quasar: a very compact and extraordinarily luminous source of radiation in the nucleus of a distant galaxy. Quasars are believed to be powered by accretion of gas onto massive black holes. quasi-normal modes: the characteristic vibrations of a disturbed black hole, analogous to the normal modes of vibration of a bell. The black hole' s quasi- normal modes are, however, strongly damped by the emission of gravita- tional waves. quasi-periodic oscillations: rapid not-quite-regular variations in the brightness of the x-rays emitted by matter accreting (q.v.) onto a neutron star or black hole. The almost periodic variations (whose period varies in time) are be- lieved to reflect the dynamics of the inner part of the disk of accreting matter. radio waves: electromagnetic waves with wavelengths very long compared to those of visible light. The radio band is usually considered to include all electromagnetic waves with wavelengths greater than about 1 millimeter. redshift: the shift of a spectral line to longer wavelengths. The radiation emitted from a receding body on Earth, or a receding galaxy in the universe, or a body deep in the gravitational potential of a black hole is all redshifted. Regge calculus: an approximation to general relativity in which geometry is represented by flat units joined together to approximate a four-dimensional

2 APPENDIX B curved spacetime, much in the same way that the two-dimensional curved surface of a geodesic dome is made from flat triangles. ring-down: loss of energy by gravitational waves as a newly formed black hole settles down to equilibrium (cf. quasi-normal modes). scalar-tensor gravitational theory: a theory that modifies general relativity by adding a field known as a "scalar" to the equations for spacetime curvature. This scalar, which ascribes a single number to each point in space and time, can play the role of the gravitational coupling strength (usually denoted G), which thus can vary in space and time. In general relativity, G is strictly constant. Schwarzschild radius: the location of the "surface" of a black hole, from whose interior it is impossible to escape. singularity: a region of the universe where a classical description breaks down because it predicts infinite spacetime curvature or density of matter. General relativity predicts that a singularity is the ultimate result of gravitational collapse. solar mass: the mass of the Sun. spacetime: the four-dimensional continuum in which we live, consisting of the three dimensions of space and one dimension of time. General relativity (q.v.) is concerned with the curvature (q.v.) of spacetime. special relativity: Einstein's theory of spacetime structure, in which Newton's notion of absolute time is abandoned to account for the experimental fact that the speed of light is a universal constant and does not depend on the relative motion between the observer and the light source. string theory: a new physical theory that appears to be both a consistent quantum theory of gravity and a unified theory of all particles and forces. strong gravitational fields: gravitational fields that are so strong that Newton's theory of gravity is inadequate, because the new effects predicted by general relativity are important. structure formation: Galaxies are clustered into filaments, sheets, and clusters. Structure formation describes how gravity forms these structures out of tiny initial density fluctuations. supermassive black holes: The cores of most galaxies appear to contain black holes with masses 1 million to 1 billion times the mass of our Sun. These supermassive black holes are thought to be the engines that power quasars. Our own Galaxy has a 2-million-solar-mass black hole in its center. supernova: a gigantic explosion that signals the death of a massive star. Often, the explosion leaves behind a neutron star; in other cases it may produce a black hole. (Cf. Type IA supernova, Type II supernova.) Supernova 1987A: a supernova that was observed in 1987 in the nearby galaxy called the Large Magellanic Cloud. This is the closest supernova to have been observed since the invention of the telescope.

APPENDIX B 113 supersymmetry: a postulated symmetry relating particles with integer and half- integer spin. This symmetry would relate all of the elementary particles and forces in a grand unified theory. The validity of supersymmetry at high energy is required for string theory (q.v.) to describe our world. thermal radiation: radiation emitted with a blackbody spectrum (q.v.~. topology change: a possible physical phenomenon in which the topology of space (q.v.) changes. Classical general relativity forbids these changes in all physically reasonable circumstances. Whether quantum effects of gravity will enable them is an important open question. topology of space: A two-dimensional surface could be an infinite plane, but might instead have the form of the surface of a sphere, of a donut, or a more complicated shape. The topology of space refers to the analogous attributes of our physical three-dimensional space. Type IA supernova: the sudden burning of the carbon and oxygen in a white dwarf star, producing a powerful explosion. Because they appear to have uniform peak luminosities, supernovae of Type IA are used as standard candles to measure the geometry of the universe. Type II supernova: When a massive star has exhausted all of its nuclear fuel, its core collapses and forms a neutron star. In the process it blows off the outer envelope in a gigantic explosion, releasing a thousand times more energy in a millisecond than our Sun will release in its entire lifetime. Most of this energy is released in the form of neutrinos. While photons carry off less than 1 percent of the total energy of a supernova, a single supernova will outshine an entire galaxy for several weeks. If the collapse is asymmetric, then the supernova explosion will also radiate gravitational waves. unified theory, unification of all forces: a theory that in one conceptual frame- work provides a fundamental theory of the electromagnetic, weak, strong, and (often) the gravitational interaction. String theory is an example. The characteristic features of such a theory are expected to emerge only at very high energies at or near the Planck scale. universality offree fall (UFF): a central prediction of general relativity that the gravitational acceleration of a small object depends only on its location in space, and not on any properties of the object itself. velocity of light c: a very high speed (about 3 x 108 m/s) that is "nature's speed limit." This is the speed at which any massless object (such as light) travels. Objects with mass must always travel more slowly than c. waveform: a wave's strength (amplitude) as a function of time. weakly interacting massive particles: hypothetical candidates for the dark mat- ter. These particles are potentially detectable in underground dark matter searches. Alternatively, they can be produced in particle accelerators. They are a form of cold dark matter.

4 APPENDIX B X-ray binary: a double star in which one of the stars accretes matter from its companion and emits a copious amount of x-rays. The x-ray-emitting star is either a black hole or a neutron star.