Dr. Leon Escobar

Forschungsinteressen / Research interests

  • Mathematical general relativity
  • Numerical relativity
  • Cosmological models
  • Spectral methods

Kurze Beschreibung / Short description

One of  main research interests is about analytic and numerical studies of inhomogeneous cosmological models. In particular, I am interested in to study the behavior of inhomogeneous perturbations of well known cosmological space-times with the purpose of investigate many interesting open questions like the BKL and the cosmic no-hair conjectures. Additionally, by using spectral methods I am interested in the numerical computation of the total mass for compact manifolds, which was recently introduced by Szabados. Unlike the standard formulas of the ADM or the Komar mass, this new mathematical tool allows to define the notion of the total mass in cosmological scenarios.

On the other hand, regarding to asymptotically flat space-times, I am interested in to investigate alternative methods for the numerical construction of initial data. In particular, in contrast to traditional methods which reduce the problem to the solution of an  elliptic system of equations, I explore a new method that allows to find initial data by  solving a hyperbolic system, which is more convenient for numerical implementation.

Finally, but not the least, by means of analytical and numerical methods I am interested in to study  the Bartnik quasi-local mass and static metric extension conjectures.

 

Open source codes

As part of my PhD project, I have written some Python modules for the implementation of the so-called spin-weighted spherical harmonics. These functions are a generalization of the well known spherical harmonics and form a smooth base to describe functions on the two-sphere. Here, there are two modules written by myself which provide a Python environment to deal with those functions numerically. The first of them is for general spin-weighted spherical harmonics functions whereas the second one deals with axial symmetric functions. These modules can be freely downloaded under the GNU General Public License (GPL). If you find any mistake in the code or problem regarding to its implementation, do not hesitate to let me know.

Download codes

PhD Thesis

Studies of spacetimes with spatial topologies S3 and S1 X S2, Doctoral dissertation, University of Otago. (2016)

Preprints

  1. Beyer, F., Escobar, L., & Frauendiener, J. (2017). Asymptotics of solutions of a hyperbolic formulation of the constraint equations. arXiv preprint arXiv:1706.06700.

Publications

  1. Beyer, F., Escobar, L., & Frauendiener, J. (2017). Criticality of inhomogeneous Nariai-like cosmological models. Physical Review D, 95(8), 084030.
  2. Beyer, F., Escobar, L., & Frauendiener, J. (2016). Numerical solutions of Einstein’s equations for cosmological spacetimes with spatial topology S 3 and symmetry group U (1). Physical Review D, 93(4), 043009.
  3. Beyer, F., & Escobar, L. (2013). Graceful exit from inflation for minimally coupled Bianchi A scalar field models. Classical and Quantum Gravity, 30(19), 195020.
  4. Arango, J., Escobar, L., & Reyes, C. (2012). Figuras de Chladni en tambores. Lecturas matemáticas, 33(1), 5-18.

Kontakt / Contact information

Fachbereich Mathematik
Universität Tübingen
Auf der Morgenstelle 10
72076 Tübingen

Deutschland / Germany

Tel: +49-(0)7071/29-72419
E-Mail senden
Raum: C 6 P 22

Email: escobar@math.uni-tuebingen.de