Alfonso Garcí­a-Parrado




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:

Departamento de Matemáticas, Edificio Albert Einstein 2ª planta,
Campus de Rabanales, Universidad de Córdoba.
Universidad de Córdoba
ESPAÑA

My full CV can be downloaded here.



Research interests

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.

Global lorentzian 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 gravity

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".

Higher dimensional gravity

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.

Computer algebra.

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.

Publications

My full publication list can be reached in the following links:

Teaching

Information about my teaching at "Escuela Politécnica Superior" of Córdoba university can be found here.

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:

  • Introduction to probability. Sample space and definition of a probability space.
  • Conditional probability. Bayes theorem.
  • Random variable and probability distributions. Continuous and discrete probability distributions.
  • The binomial distribution.
  • The Poisson distribution.
  • The hypergeometric distribution.
  • The normal distribution
  • The central limit theorem.
  • Notion of sample statistic.
  • Estimators.
  • Confidence intervals.

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:

  • Package xTensor: coordinate-free tensor analysis.
  • Package xCoba: tensor analysis in coordinates.
  • Package xTerior: exterior calculus and its applications.
  • Package Spinors: Penrose's spinor analysis in General Relativity.