New strategies for black hole physics

Resum

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.