Effective Dynamics of Black Hole Horizons

Abstract

In this thesis we present a new aspect pertaining to the effective field theory of general relativity in the limit of a large number D of dimensions. We demonstrate that the theory initially developed to capture the physics of asymptotically flat branes also contains a new family of localized solutions that can be identified with higher dimensional black holes such as the Schwarzschild-Thangerlini or the Myers-Perry black holes in the limit of a large number of spacetime dimensions. Using this technique we have explored several new aspects of these black hole solutions.

We show that the effective large D equations for the asymptotically flat brane also contain an analytic solution that is a gaussian blob (with the same topology as the flat membrane). The blob actually corresponds to a magnification of the geometry near the cap (north-pole) of the black hole. We calculate their (slow) quasi-normal spectrum, which captures the stability of Schwarzschild black holes and also the instability of ultraspinning Myers-Perry black holes.

Additionally we find novel class of rotating black bar solutions, that appear as stationary objects in the effective theory since they can not radiate gravitational waves which are decoupled from the effective theory.

We describe a method that allows to construct (Maxwell) charged solutions form every non- charged solution that the large D theory contains. Using this method we construct charged and rotating black holes in the Einstein-Maxwell theory.

Furthermore we explore the solutions that branch of from the (ultra-spinning) Myers-Perry (MP) black hole and the non-linear extensions of the zero-modes of the analytically known black bar.

We study the evolution of higher dimensional black hole collisions by solving numerically the effective equations of motion. We demonstrate that in these collisions it is possible to form black holes with elongated horizons such as black bars and dumbbells. At high enough angular momentum the black bars and dumbbells can be so elongated that they are susceptible to a Greggory-Laflamme type instability, that leads to the a pinch off of the horizon towards a naked singularity. Accordingly this demonstrates a novel example of a violation of weak cosmic censorship in the quintessential process of general relativity: the collision of black holes.

Furthermore we study the evolution and decay of ultraspinning MP black holes, and observe remarkably rich structure in the intermediate states of the decay.

Lastly, we study how entropy production and irreversibility appear in the large D effective theory. With this tool we study how black hole entropy is generated in several highly dynamical processes, such as the fusion of black holes and the fission of unstable solutions into multiple black holes. We find the black hole fusion is highly irreversible, while fission which follows the decay of unstable black strings generates much less entropy. Additionally we describe how in processes that contain fusion and fission the intermediate state is quasi-thermalized.

En esta tesis hemos presentado un nuevo aspecto perteneciente a la teoría efectiva de la relatividad general en el límite de un gran número de dimensiones. Hemos demostrado que la teoría desarrollada inicialmente para capturar la física de las branas asintóticamente planas también contiene una nueva familia de soluciones localizadas que pueden ser identificadas con agujeros negros de dimensiones más altas como los agujeros negros de Schwarzschild- Thangerlini o de Myers-Perry en el límite de gran D. Usando esta técnica hemos explorado varios aspectos nuevos de dichos agujeros negros.

Encontramos una nueva clase de soluciones de barras negras giratorias, que aparecen como objetos estacionarios en la teoría efectiva

Describimos un método que permite construir soluciones cargadas a partir de cada solución no cargada. Usando este método construimos agujeros negros cargados y giratorios en la teoría de Einstein-Maxwell.

Estudiamos la evolución de las colisiones de agujeros negros en dimensiones superiores usando las ecuaciones efectivas. Demostramos que en estas colisiones es posible formar agujeros negros con horizontes alargados como barras negras o con forma de mancuernas. Con un momento angular lo suficientemente alto, las barras negras pueden ser tan alargadas que son susceptibles a una inestabilidad tipo Greggory-Laflamme, que lleva a una rotura del horizonte y a una singularidad desnuda. Por consiguiente, esto demuestra un ejemplo novedoso de una violación de la hipótesis de 'cosmic censorship' (censura cósmica).

Además estudiamos la evolución y el decaimiento de los agujeros negros MP ultraspinning, y observamos una estructura notablemente rica en los estados intermedios del decaimiento.