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A classification of 2-dimensional surfaces imbedded in spacetime is presented, according to the algebraic properties of their shape tensor. The classification has five levels, and provides among other things a refinement of the concepts of…

In this thesis three separate problems relevant to general relativity are considered. Methods for algorithmically producing all the solutions of isotropic fluid spheres have been developed over the last five years. A different and somewhat…

Using a second law of complexity, we prove a black hole singularity theorem. By introducing the notion of trapped extremal surfaces, we show that their existence implies null geodesic incompleteness inside globally hyperbolic black holes.…

In the context of f(R) modified gravity theories we determine that the black holes existence is determined by the sign of a parameter dependent of the mass, the charge, the spin and the scalar curvature. We obtain the different…

The imminent detection of gravitational waves will trigger precision tests of gravity through observations of quasinormal ringing of black holes. While General Relativity predicts just two polarizations of gravitational waves, the so-called…

A marginally trapped surface in the four-dimensional Minkowski space is a spacelike surface whose mean curvature vector is lightlike at each point. We associate a geometrically determined moving frame field to such a surface and using the…

We classify all fundamental electrically charged thin shells in general relativity, i.e., static spherically symmetric perfect fluid thin shells with a Minkowski spacetime interior and a Reissner-Nordstr\"om spacetime exterior,…

The recent observations of neutron star mergers have changed our perspective on scalar- tensor theories of gravity, favouring models where gravitational waves travel at the speed of light. In this work we consider a scalar-tensor set-up…

Kerr-Vaidya metrics are the simplest dynamical axially-symmetric solutions, all of which violate the null energy condition and thus are consistent with the formation of a trapped region in finite time according to distant observers. We…

Special class of surfaces in five-dimensional sphere in $C^3$ is considered. Immersion equations for minimal tori of that class are shown to be reducible to the equation $u_{z\bar z}=e^u-e^{-2u}$ which is integrable by means of inverse…

A significant range of geometric structures whose rigidity is explored for both practical and theoretical purposes are formed by modifying generically isostatic triangulated spheres. In the block and hole structures (P, p), some edges are…

In this paper, we consider a charged particle moves around a Weakly Magnetized Kerr-Newman black hole. We first study its circular motion with a detailed analysis in the innermost stable circular orbits(ISCO). Then the dynamics of a…

We present new results concerning the existence of static, electrically charged, perfect fluid spheres that have a regular interior and are arbitrarily close to a maximally charged black-hole state. These configurations are described by…

We consider the region $\mathscr{T}$ in spacetime containing future-trapped closed surfaces and its boundary $\B$, and derive some of their general properties. We then concentrate on the case of spherical symmetry, but the methods we use…

We consider one- and two-dimensional (1D and 2D) optical or matter-wave media with a maximum of the local self-repulsion strength at the center, and a minimum at periphery. If the central area is broad enough, it supports ground states in…

Static, spherically symmetric configurations of gravity with nonminimally coupled scalar fields are considered in D-dimensional space-times in the framework of generalized scalar-tensor theories. We seek special cases when the system has no…

A new class of black hole solutions of the five dimensional minimal gauged supergravity is presented. They are characterized by the mass, the electric charge, two equal magnitude angular momenta and the magnitude of the magnetic potential…

Solitons are typically stable objects in 1D models, but their straightforward extensions to 2D and 3D settings tend to be unstable. In particular, the ubiquitous nonlinear Schroedinger (NLS) equation with the cubic self-focusing, creates…

We study black holes in a modified gravity scenario involving a scalar field quadratically coupled to the Gauss-Bonnet invariant. The scalar is assumed to be in a spontaneously broken phase at spatial infinity due to a bare Higgs-like…

In this paper, we base our analysis on the assumption that the existence of a photon sphere is an intrinsic feature of any ultra-compact gravitational structure with spherical symmetry. Utilizing the concept of a topological photon sphere,…