^{1}

^{2}

^{3}

^{1}

^{1}

^{2}

^{3}

^{3}.

The study of black holes has been a central feature of general relativity since its birth in 1915. Shortly after Einstein wrote down the field equations of general relativity, Karl Schwarzschild discovered the first and simplest solutions which represented the gravitational field of a massive body with spherical symmetry, but without any other features like angular momentum or charge. It was noticed that this Schwarzschild solution had a place where the metric apparently became singular, the Schwarzschild radius, which for a spherical body of mass ^{2}. It was initially hoped that “realistic” objects could never be compressed to the extent that the material of the body would be less than this Schwarzschild radius. In the late 1930s starting with the work of Oppenheimer and Snyder, it became clear that it was possible for a material object to be compressed past its Schwarzschild radius and become a black hole. But what of the apparent singularity at the Schwarzschild radius? In the early 1960s, Kruskal and Szekeres were able to find a coordinate system which showed that the Schwarzschild singularity at ^{2} was an artifact of the coordinates that had been used by Schwarzschild and others. The only real singularity in the Schwarzschild solution was the one at the origin, namely,

In the mid-1970s, research led by Bekenstein, Hawking, and others showed that there was a deep connection between black hole physics and quantum mechanics and thermodynamics. Bekenstein was the first to argue that a black hole should have an entropy associated with it and that this entropy should be proportional to the surface area of the event horizon as defined by the Schwarzschild radius. Following on this work, Hawking showed, by applying quantum field theory in the background of a black hole, that black holes emitted thermal radiation and had a temperature now known as the Hawking temperature. These seminal works have led to researchers viewing black holes as a theoretical laboratory to giving hints as to the proper path toward a formulation of the as yet undiscovered theory of quantum gravity. This has led to the concepts like black hole information paradox, the holographic principle and the firewall puzzle, and a host of other interesting conjectures and puzzles.

Finally, with the advent of more powerful telescopes and observing equipment, both on the ground and in space, researchers have begun to gather observational evidence for the existence of black holes, including finding that in the heart of most galaxies there are enormous black holes of million plus solar masses. In our galaxy this “center of the galaxy” black hole is called Sagittarius

This special issue is devoted to works which carry on the tradition of studying various aspects of black holes to understand the workings of gravity as well as other branches of physics.

In the paper by D.-Q. Sun et al. entitled “Hawking Radiation-Quasinormal Modes Correspondence for Large AdS Black Holes” the authors investigate the not exactly thermal nature of the Hawking radiation emitted by a black hole. They find a connection between Hawking radiation and the quasi-normal modes of black holes. They apply their analysis to Schwarzschild, Kerr, and nonextremal Reissner-Nordstrom black holes. They pay particular attention to these black holes in anti-de Sitter spacetime.

In the paper “P-V Criticality of a Specific Black Hole in

In the paper by S. Chakraborty, entitled “Field Equations for Lovelock Gravity: An Alternative Route,” the author studies an alternative derivation of the gravitational field equations for Lovelock gravity starting from Newton’s law, which is closer in spirit to the thermodynamic description of gravity. Projecting the Riemann curvature tensor appropriately and taking a cue from Poisson’s equation, the generalized Einstein’s equations in the Lanczos-Lovelock theories of gravity are derived.

In the paper by W. Zhang and X.-M. Kuang, entitled “The Quantum Effect on Friedmann Equation in FRW Universe,” the quantum mechanically modified Friedmann equation for the Friedmann-Robertson-Walker universe is derived. The authors also analyze the modified Friedmann equations using the conjecture by Padmanabhan of a modified entropy-area relation.

In the paper by M. He et al.

The present volume collects together works which use black holes as a theoretical laboratory for understanding how gravity works and how gravity might fit in with the other theories of modern physics and in particular quantum mechanics.