In this thesis we apply new approaches and develop new techniques to address various issues related to fundamental aspects of modern gravitational theory and black holes. We study the behavior of black branes in the large D approximation, that is, we consider a space with a very large number of dimensions. This approach allows us to obtain a set of very simple equations that capture many of the physical phenomena of gravity. This technique uses the fact that the gravitational field around a massive object decays faster the higher the dimension, so when you take the very large D limit it becomes concentrated in a very thin region of size 1/D around the horizon of the black hole. In this way, the horizon can be viewed as a membrane suspended in an essentially flat background geometry. The region where the black hole lives is, in some sense, excluded from the background space. We use the large D effective equations to investigate the phases and stability of black strings at different values of the dimension D and the compactification length L. In some cases, the Gregory-Laflamme instability of the uniform black strings can lead to stable non-uniform black strings. The transition type changes at a certain critical value of D ~ 13.5. We use 1/D corrections to estimate the value of the critical dimension, which turns out to be very accurate. Possible violations of Weak Cosmic Censorship in black hole collisions at D > 4 are also explored. The large D technique, through the effective equations, provides a powerful tool for analyzing such scenarios that would otherwise be very difficult to tackle using numerical simulations at finite D. It has recently been shown that rotating black holes can be described as Gaussian lumps on a black brane. The Strong Cosmic Censorship conjecture for highly charged Reissner-Nordström black holes has recently been called into question in asymptotically de Sitter spacetimes. To go beyond previous studies, this thesis includes the results of nearly extremal Reissner-Nordström nonlinear simulations. In order to perform the nonlinear (spherically symmetric) integrations, a new spectral code has been developed in double-null coordinates. Any continuous system that can be described as a quantum field theory will react to a change in the geometry where it is located. It will do so by changing its distribution of energy density, pressure and stresses. That is, the system is polarized, and its stress-energy tensor acquires a non-trivial quantum expectation value. In this context, the holographic duality, also known as AdS/CFT correspondence, is extremely useful for extracting valuable qualitative information from the system. Perturbations of the geometry of the AdS boundary will produce tidal deformations in the geometry of the bulk. To calculate this deformations, we solve the equations for a linearized perturbation of the geometry that satisfies suitable boundary conditions. Finally, we study a subset of Horndeski's theories whose equations of motion are locally well posed. However, it is necessary to determine whether global solutions exist and whether they are sufficiently well behaved. A worrisome possibility (which has been confirmed by numerical simulations) is a change in the character of the equation of motion, from hyperbolic to parabolic and finally to elliptical. This causes a change in the causal structure of the geometry.

En aquesta tesi aplicarem nous enfocaments i desenvoluparem noves tècniques per tractar diversos temes relacionats amb aspectes fonamentals de la teoria gravitacional moderna i els forats negres. Estudiem el comportament de les branes negres en l’aproximació large D, és a dir, considerem un espaitemps amb un nombre molt gran de dimensions. Aquest enfocament ens permet obtenir un conjunt d’equacions molt simples que recullen molts dels fenòmens físics de la gravetat. En alguns casos, la inestabilitat de Gregory-Laflamme de les cordes negres uniformes pot conduir a cordes negres no uniformes estables. S’exploren també possibles esdeveniments de violació de la Censura Còsmica Feble en col·lisions de forats negres a D > 4. La tècnica de large D, mitjançant les equacions efectives, proporciona una eina potent per analitzar aquest tipus d’escenaris que d’altra manera serien molt complicats d’abordar mitjançant simulacions numèriques a D finita. Recentment s’ha posat en dubte la conjectura de Censura Còsmica Forta per a forats negres de Reissner-Nordström altament carregats en espaitemps asimptòticament de Sitter. Per anar més enllà dels estudis anteriors, en aquesta tesi s’inclouen els resultats de simulacions completament no lineals de Reissner-Nordström altament carregats. Qualsevol sistema continu que es pugui descriure com una teoria quàntica de camps reaccionarà davant un canvi en la geometria on està situat. En aquest context, la correspondència AdS/CFT és extremadament útil per extreure informació qualitativa i valuosa del sistema. Les pertorbacions en la geometria de la frontera d’AdS produiran deformacions de marea en la geometria de l’interior. Per calcular aquesta deformació, resolem les equacions per a una pertorbació linealitzada de la geometria que satisfà una condició de contorn adequada a l’infinit. Finalment, s’estudia un subconjunt de les teories de Horndeski les equacions del moviment de les quals són localment ben plantejades. Tot i això, cal determinar si existeixen solucions globals i si aquestes solucions són prou ben comportades. Una possibilitat preocupant (que s’ha confirmat amb simulacions numèriques), és un canvi del caràcter de l’equació de moviment, d’hiperbòlica a parabòlica i finalment a el·líptica.

Programa de Doctorat en Física