A region of spacetime exerting a gravitational field so strong that neither matter nor radiation can escape. Black holes are extreme cosmic objects predicted by German-born U.S. theoretical physicist Albert Einstein's theory of general relativity. Within a boundary known as the event horizon, the escape velocity needed to overcome the gravitational attraction of the black hole exceeds the speed of light, meaning that nothing that crosses over the event horizon can ever leave. Black holes are therefore by definition invisible, but because of their powerful gravitational fields, they can be indirectly observed through the highly conspicuous effects they have on their cosmic environments. These effects include the gravitational intake of matter through accretion disks, a process that generates tremendous heat and light and is well-observed at scales from binary star systems to the cores of galaxies. In the absence of ongoing accretion, black holes should also theoretically cause severe localized warping of spacetime, gravitationally lensing light from luminous sources and distorting their appearance (Fig. 1). The merging of two black holes each with roughly 30 times the Sun's mass, detected in 2015 by the Laser Interferometer Gravitational-wave Detector (LIGO), opened a new and fruitful way of studying black holes, and revealed a mass range of stellar-mass black holes greater than had been thought to be possible. See also: Astronomy; Escape velocity; Gravitation; Gravitational lens; Gravitational radiation; Heat; Light; LIGO (Laser Interferometer Gravitational-wave Observatory); Relativity

The phenomenon occurring in the special theory of relativity wherein two observers who start together with identical clocks and then undergo different motions can have different total elapsed time on their clocks when they rejoin later. This effect is a well-defined, mathematically consistent prediction of special relativity which has been verified by experiment but, historically, it has been referred to as a paradox because of erroneous reasoning in the manner in which the effect is commonly analyzed. The clock-paradox phenomenon arises because there is no notion of absolute simultaneity in the theory of special relativity.

The change in the frequency of a wave observed at a receiver whenever the wave's source, the receiver, or the carrying medium of the wave is in motion relative to the other. The Doppler effect was predicted in 1842 CE by Austrian physicist Christian Doppler, and first verified for sound waves by Dutch chemist and meteorologist C. H. D. Buys-Ballot in 1845 from experiments conducted on a moving train. The Doppler effect for sound waves is now a commonplace experience: If one is passed by a fast car or a plane, the pitch of its noise is considerably higher during the vehicle's approach than during the receding (Fig. 1). The same phenomenon is observed if the source is at rest and the receiver is passing it. An optical Doppler effect was first observed as a shift of spectral lines by German physicist Johannes Stark in 1905 in experiments involving high-velocity canal rays produced in a cathode-ray tube. See also: Cathode-ray tube; Light; Optics; Pitch; Sound

James Clerk Maxwell and his contemporaries in the nineteenth century found it inconceivable that a wave motion should propagate in empty space. They therefore postulated a medium, which they called the ether, that filled all space and transmitted electromagnetic vibrations.

A massive body producing distorted, magnified, or multiple images of more distant objects when its gravitational fields bend the paths of light rays. Examples of foreground bodies that can act as gravitational lenses of background objects include highly massive galaxy clusters or individual galaxies. When stars or planets act as gravitational lenses, the effect is known as gravitational microlensing. Background objects can be galaxy clusters or standalone galaxies, oftentimes luminous quasars (Fig. 1). In the case of microlensing, the background objects can be anything that emits or reflects electromagnetic radiation, including stars, brown dwarfs, exoplanets, white dwarfs, neutron stars, and black holes (that is, if the black hole's immediate environment is emitting radiation, for instance from an accretion disk). Astronomers use gravitational lenses to study properties of galaxies and quasars, as well as provide information on the universe and its contents, including matter, dark matter, and dark energy. Microlensing is useful for many astrophysical investigations, including the discovery of distant exoplanets that would otherwise be difficult or impossible to detect. See also: Astronomy; Brown dwarf; Dark energy; Dark matter; Exoplanet; Galaxy; Matter; Quasar; Star; Universe

A wave in spacetime generated by the acceleration of mass and that travels at the speed of light. Gravitational waves, which transport energy as gravitational radiation (Fig. 1), are an implicit outcome of the special theory of relativity formulated by German-born U.S. theoretical physicist Albert Einstein in 1905, and which were subsequently put forward explicitly in his theory of general relativity in 1915. Einstein showed that the acceleration of masses generates time-dependent gravitational fields that can carry energy away from their source at the speed of light. Gravitational waves are likened to "ripples" moving through spacetime—the term used for the intertwining of the three dimensions of physical space with a fourth dimension, time, and thus comprising the four-dimensional geometry of the universe described by relativity. See also: Acceleration; Energy; Gravity; Light; Mass; Observation of gravitational waves; Relativity; Spacetime

A shift toward longer wavelengths of spectral lines emitted by atoms in strong gravitational fields. One of three famous predictions of the general theory of relativity, this shift results from the slowing down of all periodic processes in a gravitational field, and as a direct consequence of Einstein's equivalence principle; it can also be seen as a manifestation of the conservation of energy. For weak gravitational fields, the amount of the shift is proportional to the difference in gravitational potential between the source and the receiver. See also: Gravitation; Relativity; Conservation of energy

A theoretically deduced particle postulated as the quantum of the gravitational field. According to Einstein's theory of general relativity, accelerated masses (or other distributions of energy) should emit gravitational waves, just as accelerated charges emit electromagnetic waves. And according to quantum field theory, such a radiation field should be quantized; that is, its energy should appear in discrete quanta, called gravitons, just as the energy of light appears in discrete quanta, namely photons. See also: Photon; Quantum field theory; Relativity

The mutual attraction of all entities with mass or energy in the universe. Gravity, also referred to as gravitation, is one of the four fundamental interactions in nature. We experience gravity in everyday life as the force that holds our feet to the ground and brings a thrown ball back toward the Earth (Fig. 1). More broadly, gravity holds our planet in orbit around the Sun, and our Sun in orbit around the center of the Milky Way Galaxy. At grander scales, gravity holds galaxy clusters together and is the force responsible for building up structure across the expanse of the cosmos. See also: Cosmology; Earth; Earth's gravity field; Fundamental interactions; Galaxy; Milky Way Galaxy; Planet; Solar system; Sun; Universe

The relationship in the special theory of relativity between the sets of coordinates (t, x, y, z) and (t′, x′, y′, z′) used to label events in spacetime by two inertial observers, O and O′, who are moving with respect to each other. Many of the effects predicted by special relativity can be derived in a direct manner from the Lorentz transformation formulas.