Research interests

My research activity is concerned with various aspects of theoretical gravitation and, more specifically, on what is known as Mathematical Relativity, which attempts to tackle physically relevant problems in Gravitation with a high mathematical content. I have worked on many different problems including spacetime matching theory, self-gravitating objects in equilibrium, black hole uniqueness. local characterization of spacetimes, interplay between global expansion and local physics or averaging in cosmology. One of my main research topics is the study of quasi-local black holes in terms of marginally outer trapped surfaces (MOTS). Another closely related subject is geometric inequalities, specially the Penrose inequality, which conjectures a lower bound for the total mass of a spacetime in terms of the area of its outermost MOTS. Additional broad areas of my research are perturbation theory and hypersurface geometry. More recently I have been involved on the asymptotic properties of spacetimes with positive cosmological constant and in understanding black hole shadows.

In my research I have always tried to consider general problems, rather than studying specific cases. My research achievements have been diverse. To mention just a few prominent ones, we have developed a fully general matching theory across hypersurfaces of arbitrary causal character and a completely general perturbed matching theory up to second order in the non-null case. The latter has had several interesting implications for slowly rotating stars. We introduced the notion of stability of MOTS and studied the formation and evolution of such objects. I have proved several black hole uniqueness theorems, one of which actually establishes the weak cosmic censorship in the stationary vacuum setting. On the local characterization of spacetimes I introduced a tensor (nowadays often called Mars-Simon tensor) whose vanishing characterizes the Kerr metric and which has has many interesting applications. This has also been extended to the Kerr-de Sitter case, i.e. when a cosmological constant is present. I developed a completely new framework to study the abstract geometry of hypersurfaces of any causal character, which has already had interesting applications, e.g. to obtain for the first time the field equations for arbitrary thin shells. I have several results on the Penrose inequality, including a fully general Penrose-like inequality in the null case. In fact, one of my long term goals is concerned with the full resolution of the general Penrose inequality conjecture. Among the more recent achievements, we have introduced the notion of multiple Killing horizon and we have investigated the possibility of extracting all physical parameters from a sufficiently precise measurement of a back hole shadow.

In the last few years I have been involved in understanding the free data at null infinity in the case of positive cosmological constant in arbitrary dimension, in particular in connection with the existence of symmetries in the physical spacetime. This has lead us to characterize and extend the Kerr-de Sitter family of metric in arbitrary dimension in terms of the conformal class of the conformal Killing vector at the (conformally flat) scri that defines the free data of the solution.

In my research I have always tried to consider general problems, rather than studying specific cases. My research achievements have been diverse. To mention just a few prominent ones, we have developed a fully general matching theory across hypersurfaces of arbitrary causal character and a completely general perturbed matching theory up to second order in the non-null case. The latter has had several interesting implications for slowly rotating stars. We introduced the notion of stability of MOTS and studied the formation and evolution of such objects. I have proved several black hole uniqueness theorems, one of which actually establishes the weak cosmic censorship in the stationary vacuum setting. On the local characterization of spacetimes I introduced a tensor (nowadays often called Mars-Simon tensor) whose vanishing characterizes the Kerr metric and which has has many interesting applications. This has also been extended to the Kerr-de Sitter case, i.e. when a cosmological constant is present. I developed a completely new framework to study the abstract geometry of hypersurfaces of any causal character, which has already had interesting applications, e.g. to obtain for the first time the field equations for arbitrary thin shells. I have several results on the Penrose inequality, including a fully general Penrose-like inequality in the null case. In fact, one of my long term goals is concerned with the full resolution of the general Penrose inequality conjecture. Among the more recent achievements, we have introduced the notion of multiple Killing horizon and we have investigated the possibility of extracting all physical parameters from a sufficiently precise measurement of a back hole shadow.

In the last few years I have been involved in understanding the free data at null infinity in the case of positive cosmological constant in arbitrary dimension, in particular in connection with the existence of symmetries in the physical spacetime. This has lead us to characterize and extend the Kerr-de Sitter family of metric in arbitrary dimension in terms of the conformal class of the conformal Killing vector at the (conformally flat) scri that defines the free data of the solution.

Publications list