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This chapter examines the spin of a black hole. The spin is usually described as a nondimensional parameter, which can range from zero (a nonspinning black hole) to one (a situation described as “maximally spinning”). The differences in space-time between a nonspinning Schwarzschild black hole and a Kerr black hole of the same mass have potentially observable effects. The most obvious of these differences is the position of the innermost stable circular orbit (ISCO), which has a significant effect on the inner edge of an accretion disk. It is through determination of the physical size of the ISCO that the spins of black holes are determined.

This chapter discusses the formation and evolution of black holes. Stellar-mass black holes are generally understood to be created in supernova explosions that mark the end of the life of a massive star. However, many supernovae create neutron stars rather than black holes, and the precise conditions under which black holes form are still not fully understood. If the black hole is to be detected, further events are required, such as the formation of a binary star system of a kind that can be observed, and in which the existence of a black hole can be demonstrated. In contrast with stellar-mass black hole formation, there is no obvious route to the creation of a supermassive black hole directly from collapsing interstellar gas. Most discussions of the origin and evolution of supermassive black holes posit an initial “seed” black hole of relatively low mass, which then grows over time.

This chapter explores some of the predicted effects of black holes on people's lives and the possibility that they might someday be explored in fact as well as in fiction. These predicted effects include the Hawking radiation, wormholes, and multiverses. The Hawking radiation—in which the interaction between quantum mechanics and relativity has been explored with some success—is a process through which black holes are expected to emit energy and ultimately evaporate. Meanwhile, one of the most enticing possible effects associated with black holes is that they might form wormholes through which widely separated parts of the Universe can be closely connected. Lastly, one final suggestion that might be contemplated is that a separate universe might exist inside the event horizon of a black hole. This is one version of the multiverse concept, in which a variety of universes with a variety of characteristics exist.

Gravity is the weakest interaction known in the Physics. Nevertheless it plays the leading role in astrophysics and cosmology. We discuss specific properties of gravity, explaining why it happens, and introduce the notion of a black hole. We describe final states of a star evolution and conditions, when a massive star collapses and forms a black hole. The Chapter contains also a brief review of the astrophysical evidences of the black hole existence, and describes methods used for identification of stellar mass and supermassive black holes. At the end of this Chapter we review the status of black holes in the modern theoretical physics, unsolved problems of black hole physics, and new ideas how to use black holes as probes of extra dimensions.

This introductory chapter provides a background of black holes. The term “black hole” is not defined in a technical way and is used in different contexts to mean different things. The phrase itself was popularized by the physicist John Archibald Wheeler to replace the cumbersome description “gravitationally completely collapsed object.” However, black holes are not just useful metaphors or remarkable constructs of theoretical physics; they actually exist. Over the past few decades, black holes have moved from theoretical exotica to a well-known and carefully studied class of astronomical objects. Extensive data archives reveal the properties of systems containing black holes, and many details of their behavior are known. In the current astronomical literature, the seemingly bizarre properties of black holes are now taken for granted and are used as a basis for understanding a wide variety of phenomena.

Gravity is responsible not only for the existence of stars and planets; it also creates the weirdest objects imaginable. A body with mass greater than 1.4 solar masses cannot remain a white dwarf and will collapse into a neutron star. But if the mass is greater than about two and a half solar masses, the collapse will continue until it becomes a black hole. This is the strangest object in the universe. Its gravity is so strong that even light cannot get out of it. Anything near it is sucked in, crushed to a point, and approaches infinite density. The laws of physics as now known do not apply at the centre of a black hole and the very meaning of its existence is in doubt.

This Chapter contains a review of many important aspects of modern black hole theory and its applications. It begins with a general definition of a (not‐necessary stationary) black hole and formulation of the most important results on generic properties of black holes, including the Penrose theorem on the structure of the event horizon, the Hawking theorems on the topology and area of the event horizon and black hole uniqueness theorems. Gravitational radiation from black holes in a binary system and modern status and perspectives of the gravitation waves search from black holes and other compact sources are discussed. We also describe black hole models proposed for the explanation of the gamma‐ray bursts. Modeling of black hole properties, in particular their Hawking radiation, in the laboratory experiments is reviewed. We also discuss recent models with large extra dimensions and possibility of micro black hole creation in the collider experiments. This subject is directly connected with the problem of the higher dimensional black holes. Higher dimensional generalization of the Kerr metric, and a variety of new exact solutions for higher dimensional black objects with the non‐spherical topology of the horizon are discussed. The Chapter ends with remarks on two closely related problems on the wormhole and ‘time machine’ existence. It is shown that in order to create and support macroscopic objects of this type a new exotic form of the matter is requires. It seams that this and possible instabilities make the existence of such objects questionable at least at the present state of our knowledge. These and other fascinating open problems are still wait for their solution.

This chapter considers the different issues associated with the numerical evolution of black hole spacetimes. These issues can be separated into three areas: 1) how to evolve black holes successfully and in particular how to deal with the presence of singularities; 2) how to locate the black hole horizons in a numerically generated spacetime; and 3) how to measure physical quantities such as mass and angular momentum associated with a black hole. Topics covered include isometries and throat adapted coordinates, static puncture evolution, singularity avoidance and slice stretching, black hole excision, moving punctures, apparent horizons, event horizons, and isolated and dynamical horizons.

This chapter examines stellar-mass black holes. The empirical study of black holes began in the 1960s with the discovery of quasars and the advent of X-ray astronomy. X-ray detectors could detect X-rays coming from a particular direction—as the instrument rotated, the detector scanned the sky. It was not expected that X-ray sources from outside the solar system would be detectable. However, it was quickly discovered that there were strong X-ray sources that appeared in the same position in every scan. The inferred luminosity of the sources was hundreds or thousands of times brighter than the Sun. When coincident optical stars were identified, they proved to be relatively faint. Thus, it was clear that a new class of celestial sources must exist whose radiation is predominantly in the form of X-rays, with a total luminosity comparable to or greater than that of ordinary stars.

This chapter focuses on supermassive black holes, which are sometimes abbreviated “SMBHs.” Stellar-mass black holes are clearly common consequences of stellar evolution, but they are not the only kinds of black holes identified by astronomers. Much more massive black holes are located in the center of many, and perhaps all, galaxies. These black holes are referred to as supermassive black holes. They are responsible for a range of phenomena originating from objects described as active galactic nuclei (AGN), which were first observed in the form of quasi-stellar objects (QSOs) or quasars. AGN are among the most luminous objects in the Universe and can be observed at great distances. The distances can be so great that the light travel time from the AGN to Earth is a large fraction of the age of the Universe. They are therefore often used to probe the evolution of the Universe.

Black hole is an object so compact that it is inside its event horizon: a one-way surface through which particle and light can only traverse inward, and an exterior observer cannot receive any signal sent from inside. The Schwarzschild geometry is viewed in the Eddington-Finkelstein coordinates as well as in the Kruskal coordinates. Besides a black hole, the GR field equation also allows the solution of a white hole and a wormhole. The gravitational energy released when a particle falls into a tightly bound orbit around a black hole can be enormous. The physical reality of, and observational evidence for, black holes are briefly discussed. Quantum fluctuation around the event horizon brings about the Hawking radiation. This and the Penrose process in a rotating (Kerr) black hole comes about because of the possibility of negative energy particles falling into a black hole.

The Chapter is devoted to rotating black holes, their properties, global structure, and study particle and light motion in their gravitational field. We introduce and explain notions of the horizon and ergosurface in the Kerr geometry, study the extreme rotating limit of the Kerr black hole. We discuss how the rotation of the black hole affects main characteristics of the particle trajectories, in particular the radius of the innermost stable orbit and the energy of a particle at this orbit. We describe a twin paradox for inertial observers moving along circular orbits induced by the black hole rotation. We describe hidden symmetries that are responsible for the complete integrability of the geodesic equations in the Kerr spacetime. As a result of accretion of matter from the accretion disk the velocity of rotation of the black holeincreases. We discuss this effect in detail. Observable properties of the Kerr black hole, including the shadow effect, are considered. Energy extraction processes, in particular the Penrose process and superradiance, are studied. We discuss also weakly magnetized rotating black hole and a possible role of the magnetic field in the energy extraction.

This chapter explores the ways that accretion onto a black hole produces energy and radiation. As material falls into a gravitational potential well, energy is transformed from gravitational potential energy into other forms of energy, so that total energy is conserved. Observing such accretion energy is one of the primary ways that astrophysicists pinpoint the locations of potential black holes. The spectrum and intensity of this radiation is governed by the geometry of the gas flow, the mass infall rate, and the mass of the accretor. The simplest flow geometry is that of a stationary object accreting mass equally from all directions. Such spherically symmetric accretion is referred to as Bondi-Hoyle accretion. However, accretion flows onto black holes are not thought to be spherically symmetric—the infall is much more frequently in the form of a flattened disk.

This chapter addresses the existence of intermediate-mass black holes. There is powerful empirical evidence for two classes of black holes, namely, the stellar-mass black holes, with masses a few times that of the Sun, and the supermassive black holes at the centers of galaxies. The considerable gap in mass between these two categories naturally prompts the question whether black holes might exist at other mass scales. In recent years, two lines of evidence have been presented in support of the idea that black holes with masses intermediate between stellar mass and supermassive might exist. Such sources are referred to as intermediate-mass black holes. In both cases the results are currently still ambiguous, and much debated.

This chapter looks at the detection of black holes through gravitational waves. While further improvements can be expected in the ability to detect and measure electromagnetic radiation, it is possible that the next great advances in observational astrophysics will come from the detection of other kinds of information altogether. Currently, there is a great excitement about the possibility of directly detecting an entirely new “celestial messenger,” namely, gravitational radiation. The existence of gravitational waves is a prediction of general relativity, and current technology is very close to being able to detect them directly. The strongest sources of gravitational radiation are expected to be merging black holes. Since such mergers are expected to occur, both between stellar-mass and supermassive black holes, the detection of gravitational radiation would provide a new way not only to explore gravitational physics but also to look for and to study celestial black holes.

This chapter presents the proofs of fundamental uniqueness theorems for complete stationary solutions of the vacuum, or electrovac, solutions of the Einstein equations. It studies the properties of the Kerr stationary black hole, of which the Schwarzschild black hole is a particular case. It surveys the history of the research on the uniqueness theorem for 3+1-dimensional stationary black holes which was pictured by J. A. Wheeler using the picturesque phrase ‘black holes have no hair’.

This chapter considers one of the main applications of quantum gravity - the quantization of black holes. Attention is mostly restricted to the simplest case of Schwarzschild black holes. Central concepts are Hawking radiation and Bekenstein-Hawking entropy. After a review of black-hole thermodynamics and Hawking radiation, the canonical quantization of the Schwarzschild black hole is presented and explicit expressions for the quantum states are given. This is followed by a discussion of black-hole spectroscopy and entropy. Further sections are on quantum gravitational collapse and the Lemaitre-Tolman-Bondi (LTB) model. The final sections discuss the information-loss problem and primordial black holes. The latter could provide the key for an observational test of quantum gravity.

This Chapter contains brief review of the theory of classical and quantum fields propagating in the black hole geometry. It includes such subjects as quasinormal modes and ringing radiation, separation of variables in the Kerr spacetime and hidden symmetries, Hawking effect and quantum evaporation of black holes, quantum fields in the Rindler frame and the Unruh effect. We formulate and discuss four laws of the black hole thermodynamics. At the end of the Chapter we briefly discuss higher dimension generalizations.