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For over 25 years, a solution has existed to Einstein's vacuum equation that describes a space-time with two Kerr black holes. First formulated by Kramer and Neugebauer (KN) in 1980 [1], this solution has been extensively researched by…

Black holes are extreme spacetime deformations where even light is imprisoned. There is an extensive astrophysical evidence for the real and abundant existence of these prisons of matter and light in the Universe. Mathematically, black…

Classical black holes are solutions of the field equations of General Relativity. Many astronomical observations suggest that black holes really exist in nature. However, an unambiguous proof for their existence is still lacking. Neither…

We briefly review the recent novel solution of General Relativity, we call the cosmological black hole, firstly discovered in [Roupas, Z. Eur. Phys. J. C 82, 255 (2022)]. A dark energy universe and a Schwartzschild black hole are matched on…

Since the full General Theory of Relativity has been unveiled to the scientific community in 1915, many solutions to the vacuum Einstein field equations have been found and studied. This paper aims at documenting exhaustively the derivation…

It is thought that the final product of the gravitational collapse is a Kerr black hole and astronomers have discovered several good astrophysical candidates. While there is some indirect evidence suggesting that the latter have an event…

The notion of black-hole entropy was introduced by Jacob Bekenstein in 1972. During past 45 years this subject was in the center of interests of the modern theoretical physics. In this paper we briefly discuss "puzzles" of the black-hole…

We trace the origins and development of black hole thermodynamics across the past half-century, emphasizing the framework's relation to classical thermodynamics, and the vital role played by the notions of equilibrium, stationarity, and…

Although implicit in the discovery of the Schwarzschild solution 40 years earlier, the issues raised by the theory of what are now known as black holes were so unsettling to physicists of Einstein's generation that the subject remained in a…

Black hole solutions in general relativity come with pathologies such as singularity and mass inflation instability, which are believed to be cured by a yet-to-be-found quantum theory of gravity. Without such consistent description, one may…

We study the quantum creation of black hole pairs in the (anti-)de Sitter space background. These black hole pairs in the Kerr-Newman family are created from constrained instantons. At the $WKB$ level, for the chargeless and nonrotating…

Creation of a black hole in quantum cosmology is the third way of black hole formation. In contrast to the gravitational collapse from a massive body in astrophysics or from the quantum fluctuation of matter fields in the very early…

We prove the existence of a family of initial data for the Einstein vacuum equation which can be interpreted as the data for two Kerr-like black holes in arbitrary location and with spin in arbitrary direction. When the mass parameter of…

Because of the very definition of black holes --- no light escapes them and falling objects get infinitely faint when approaching --- it is impossible to ever prove that they exist. However, electromagnetic and gravitational-wave…

The possible existence of black holes has fascinated scientists at least since Michell and Laplace's proposal that a gravitating object could exist from which light could not escape. In the 20th century, in light of the general theory of…

The dark energy issue is focusing the attention of an incresing number of physicists all over the world. Among the possible alternatives in order to explain what as been named the "Mystery of the Millennium" are the so-called Modified…

We investigate the physics of black holes in the light of the quantum theoretical framework proposed in [1]. It is argued that black holes are completely non-local objects, and that the only one which really exists is the universe itself.

The Kerr-Newman metric is the unique vacuum solution of the General Relativistic field equations, in which any singularities or spacetime pathologies are hidden behind horizons. They are believed to describe the spacetimes of massive…

The problem of stability of rotating black holes is the subject of a long standing research program since the 1960s and remains an unresolved problem in general relativity. A major obstacle in the black hole stability problem is that the…

There is no proof that black holes contain singularities when they are generated by real physical bodies. Roger Penrose claimed sixty years ago that trapped surfaces inevitably lead to light rays of finite affine length (FALL's). Penrose…