Quasi-normal modes of rotating black holes and neutron stars: gravitational waves and AdS/CFT correspondence

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The topic of this research proposal is the investigation of black holes and neutron stars in the context of General Relativity and in generalized theories of gravity. We propose to study the properties of such compact objects in the presence of additional fields, like scalars and gauge fields, or extra dimensions, as motivated by string theory and other candidate theories of quantum gravity. The research we propose has two main objectives. -The first direction will focus on the gravitational wave emission of different astrophysically relevant objects, like black holes and neutron stars. Gravitational waves have been detected recently by the LIGO collaboration. The analysis indicates that the sources of these detections are coalescing astrophysical black holes. The continuous enhancement of sensitivity will allow to detect gravitational waves from other sources as well, like neutron stars mergers, white dwarf collisions, and possibly other unknown phenomena. The objective is to study gravitational wave emission in generalized theories of gravity. We shall study the presence of phenomenological signatures of a given theory in several observable properties of the physical objects, such as the relation between the ringdown frequencies of gravitational waves with some global parameters, rotational properties, and possible breaking of universal relations (Eikonal limit, I-love-Q). By comparing the detected gravitational waves with the predictions of each theory we can constrain the parameters and field content of the theory. -The second direction will focus on the study of higher dimensional black holes. These objects are interesting in the context of string theory, which predicts the existence of extra dimensions, and the AdS/CFT correspondence. The correspondence conjectures that fields propagating in a D-dimensional gravitational theory are dual to quantum fields propagating on its (D-1)-dimensional boundary. In particular black holes in 5 dimensions can be used to describe thermal states in a 4 dimensional conformal field theory. This correspondence allows to use geometrical objects like black holes to explore the properties of strongly interacting quantum systems. The purpose is to study the properties of new black holes and possible generalizations of known solutions in the context of supergravity, especially asymptotically AdS solutions and supersymmetry. We will study the thermodynamic properties of these black holes, the domain of existence and stability of the different families of solutions, and possible connections of these solutions with particle theory and condensed matter models.