PhD subjects

Black holes are very interesting objects, whose physics brings Quantum Mechanics and General Relativity, the two pillars of modern physics, into sharp contrast. If one considers black holes quantum-mechanically one can argue that they behave as thermodynamic objects, whose entropy (also known as the Bekenstein-Hawking entropy) is given by the area of the event horizon in units of the Planck length squared. For astrophysical black holes, like that in the center of the Milky Way, this area is quite large, giving a huge entropy S = 10^90. Hence, we expect this black hole to have e^(10^90) microstates.



On the other hand, in Einstein’s General Relativity, black hole solutions are unique. Hence, General Relativity predicts that the black hole has one microstate, while Quantum Mechanics predicts it has e^(10^90). This is the biggest unexplained discrepancy in Theoretical Physics, and is at the root of Hawking’s Black Hole Information Paradox. Using arguments from Quantum Information Theory, it can be shown that this discrepancy can only be resolved if there exists a structure with rather unusual properties that replaces the black-hole horizon.



This thesis has three directions. The first is to analyze the existing examples of such horizon-replacing structure within the framework of the AdS-CFT correspondence. The second is to construct novel horizon-sized structure for supersymmetric and non-supersymmetric black holes. The third is to ascertain whether the existence of this horizon-sized structure has an imprint on the gravitational waves emitted during black-hole mergers and detectable using ground and space-based gravitational-wave detectors.



Applicants are expected to have a solid background in General Relativity and Quantum Field Theory. Knowledge of basic String Theory notions is a bonus.

N=4 supersymmetric Yang-Mills Theory (N=4 SYM) is a four-dimensional toy model for the Quantum Chromodynamics (QCD), which is believed to describe the strong interactions. In the last two decades, powerful techniques have been developed for the spectrum of excitations. The main tool for solving the spectral problem is the so called Quantum spectral curve (QSC), which represents a system of coupled functional equations.



Integrability can be used also more complicated quantities like the multi-gluon amplitudes or the correlation functions. The so-called hexagon bootstrap method gives a prescription how to decompose the observable into elementary blocks named hexagon form factors. The method is very powerful and in principle gives closed expressions for the correlation functions as series of virtual particle contributions. However the integration measure over the virtual particles is singular and needs to be carefully regularised.



The thesis will be focused on the construction of a consistent renormalisation procedure, which is expected to admit a formulation in terms of the QSC. The project supposes good knowledge of mathematics, in particular complex analysis and representation theory of Lie algebras, as well as reasonable knowledge of quantum mechanics and quantum field theory.

In recent years we have seen the rise of gravitational wave astronomy as a formidable tool for probing the strong field regime of gravity, the physics of massive objects such as black holes and neutron stars, and the dark universe. The next generation of gravitational wave interferometers will improve the current sensitivity, allowing us to enter a new regime of precision physics and increasing the potential for discovery in astro and fundamental physics.



In this thesis, we will develop theoretical predictions in gravitational wave physics, in general relativity and its extensions, possibly in the presence of cosmological media. These predictions will concern the emission of gravitational radiation from the vibrations of single black holes (the so-called quasi-normal modes) or from binaries of compact objects, and the propagation of gravitational waves.



We will use techniques based on quantum field theory and effective field theory, applied to gravitational systems, and perturbation theory techniques such as post-Newtonian and post-Minkowskian expansions. The work will be mainly analytical, possibly using symbolic computational softwares, and may require some numerical calculations to obtain quantitative results.