Since 2020 I am a "Beatriz Galindo" senior research fellow at Córdoba University in Spain. My position has a dual role with teaching and research duties.
Address:
My full CV can be downloaded here.
My research profile corresponds to a theoretical physicist and to an applied mathematician. I have mainly worked in general relativity and its applicatins to differential geometry.
The analysis of space-time global causal structure has been traditionally carried out through the notion of conformal equivalence between Lorentzian manifolds.
A generalization of this is the notion of causal equivalence between Lorentzian manifolds which is based on the concept of causal map:
Initial data characterizations in general relativity
Einstein field equations can be formulated as an initial value problem. If we demand that the Cauchy data development be a known exact solution, we need to append extra
conditions to the initial data, giving rise to an initial data characterization. In my work initial data characterizations for the Schwarzschild, Kerr, type D solutions, vacuum
spacetimes with conformal Killing vectors and vacuum Killing-Yano spacetimes have been obtained.
Finsler geometry is a generalization of the pseudo-Riemannian geometric framework
by introducing a notion of anisotropy. A natural question is how to translate Einstein's geometric gravity theory to this new framework. This is
something that has sparked interest among many researchers during decades. In collaboration with Prof. Ettore Minguzzi from Florence university
(Italy) we have developed a formalism to carry out computations in pseudo-Finsler spaces modelled in pseudo-Minkowski spaces and we have introduced a
new "anisotropic gravitational theory".
Motivated by string theory, research in higher dimensional general relativity has experienced an impressive growth in the last years.
I have interests in the study of exact solutions in higher dimensions representing black holes and the generalization of the Newman-Penrose and
G.H.P. formalisms to dimensions greater than 4.
An IDEAL (Intrinsic, Deductive and Algorithmic) characterization of a spacetime or exact solution of
Einstein field equations is a set of conditions
involving only the metric tensor and its Levi-Civita connection. The simplest IDEAL characterization is
that of flat space which is characterized by the vanishing of the Riemann tensor. Drawing on earlier work
by Ferrando and Sáez I have developed an Ideal characterization of the family of vacuum solutions that
are conformal to the Kerr black hole.
I am involved in the development of software to work with differential geometry and general relativity that is being used
by researchers all around the world.
My full publication list can be reached in the following links:
Information about my teaching at
Online lectures on general relativity and differential geometry
I have a youtube channel where I have posted lectures about general relativity and
differential Geometry. See here for more information.
A brief course on probability & statistics
Brief course taught at the undergraduate level at the University of the Basque country in Spain.
The course material can be downloaded here (in Spanish).
Course contents:
Course about the xAct system for tensor analysis
Graduate course taught at the
Institute of Theoretical Physics of Charles University
in Prague (Czech Republic).
The course slides can be found here.
Course contents:
Publications
Teaching