The present status of the quasi-local mass, energy-momentum and angular-momentum
constructions in general relativity is reviewed. First, the general ideas, concepts, and …

Any spacetime containing a degenerate Killing horizon, such as an extremal black hole,
possesses a well-defined notion of a near-horizon geometry. We review such near-horizon …

We review the first modern singularity theorem, published by Penrose in 1965. This is the
first genuine post-Einsteinian result in general relativity, where the fundamental and fruitful …

At the beginning of the 20th century, only two physical fields were known, the
electromagnetic and gravitational ones. Einstein's theory of special relativity (SR), created in …

Area products for multihorizon stationary black holes often have intriguing properties, and
are often (though not always) independent of the mass of the black hole itself (depending …

We detail the construction of the most general asymptotically flat, stationary, rotating,
nonextremal, dyonic black hole of the four-dimensional N= 2 supergravity coupled to 3 …

The spin angular momentum S of an isolated Kerr black hole is bounded by the surface area
A of its apparent horizon: $8\pi S\leqslant A $, with equality for extremal black holes. In this …

We study the near-horizon spacetime for isolated and dynamical trapping horizons
(equivalently marginally outer trapped tubes). The metric is expanded relative to an ingoing …

Geometrical inequalities show how certain parameters of a physical system set restrictions
on other parameters. For instance, a black hole of given mass can not rotate too fast, or an …

Even though extended gravity theories have come up with different healthy measures of
complexity for spherical and non‐spherical systems, the study of complexity factors for …