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For an uncharged test particle in the Kerr-Bertotti-Robinson spacetime, solutions of two major types of orbits are presented, both in exact forms. First, for both prograde and retrograde motions, the radii of innermost stable circular…

We explore the classical stability of topological black holes in d-dimensional anti-de Sitter spacetime, where the horizon is an Einstein manifold of negative curvature. According to the gauge invariant formalism of Ishibashi and Kodama,…

I will discuss some recent results on marginally outer trapped surfaces, apparent horizons, and the trapped region. A couple of applications of the results developed for marginally outer trapped surfaces to coalescence of black holes and to…

We track the evolution of entropy and black holes in a cyclic universe that undergoes repeated intervals of expansion followed by slow contraction and a smooth (non-singular) bounce. In this kind of cyclic scenario, there is no big crunch…

We consider spherically-symmetric black holes in semiclassical gravity. For a collapsing radiating thin shell we derive a sufficient condition on the exterior geometry that ensures that a black hole is not formed. This is also a sufficient…

We consider the motion of massive and massless particles in a five-dimensional spacetime with a compactified extra-dimensional space where a black hole is localized, i.e., a caged black hole spacetime. We show the existence of circular…

Quasisymmetry and omnigeneity of an equilibrium magnetic field are two distinct properties proposed to ensure radial localization of collisionless trapped particles in any stellarator. These constraints are incompletely explored, but have…

We consider scalar-tensor gravity with nonminimal derivative coupling and Born-Infeld electromagnetic field which is minimally coupled to gravity. Since cosmological constant is taken into account it allowed us not only derive static black…

Working in a semi-classical setting, we consider solutions of the Einstein equations that exhibit light trapping in finite time according to distant observers. In spherical symmetry, we construct near-horizon quantities from the assumption…

We consider two proposals for defining black hole entropy in spherical symmetry, where the horizon is defined locally as a trapping horizon. The first case, boundary terms in a dual-null form of the reduced action in two dimensions, gives a…

We argue that black holes admit vortex structure. This is based both on a graviton-condensate description of a black hole as well as on a correspondence between black holes and generic objects with maximal entropy compatible with unitarity,…

This thesis is dedicated to the study of symmetries in reduced models of gravity, with some frozen degrees of freedom. We focus on the minisuperspace reduction whith a finite number of degrees of freedom. Minisuperspaces are treated as…

Physical arguments related with the existence of black hole solutions having a non trapping interior are discussed. Massive scalar fields interacting with gravity are considered. Interior asymptotic solutions showing a scalar field…

Based on perturbation theory, we present the exact first-order solution to the Einstein equations for the exterior static gravitational field of an isolated non-rotating star in a spatially finite universe having the topology of a flat…

Bounds for the area of general closed marginally trapped surfaces (MTSs) are presented. They do not require any stability condition, and are determined by a constant that depends on a particular component of the Einstein tensor on the…

The existence of black holes is a central prediction of general relativity and thus serves as a basic consistency test for modified theories of gravity. In spherical symmetry, only two classes of dynamic solutions are compatible with the…

The properties of universes are explored that are entirely in the interior of black holes in another universe, a `mother universe'. It is argued that these models offer a paradigm that may shed a new light on old cosmological problems. The…

We consider generic rotating axially symmetric "dirty" (surrounded by matter) black holes. Near-horizon circular equatorial orbits are examined in two different cases of near-extremal (small surface gravity $\kappa $) and exactly extremal…

We consider generic, or "dirty" (surrounded by matter), stationary rotating black holes with axial symmetry. The restrictions are found on the asymptotic form of metric in the vicinity of non-extremal, extremal and ultra-extremal horizons,…

We present analytical solutions describing a family of both inwardly and outwardly spiralling orbits in the Kerr spacetime. The solutions are exact, and remarkable for their simplicity. These orbits all have the angular momentum and energy…