José Natário

Position

Professor Associado

Member of the Center for Mathematical Analysis, Geometry and Dynamical Systems

Education

D.Phil. (Mathematical Sciences), 2000, University of Oxford

Mestre em Matemática Aplicada, 1996, Instituto Superior Técnico

Licenciado em Matemática Aplicada e Computação, 1994, Instituto Superior Técnico

Research Interests

General Relativity, Mathematical Physics, Geometry

Research Papers

Mathisson's helical motions for a spinning particle - are they unphysical? (joint with Filipe Costa, Carlos Herdeiro and Miguel Zilhão), Phys. Rev. D 85 (2012) 024001 (11 pages).

Spherical linear waves in de Sitter spacetime (joint with João L. Costa e Artur Alho) (2011).

Optimal time travel in the Gödel universe (2011).

The rocket problem in general relativity (joint with Pedro G. Henriques) (2011).

An elementary derivation of the Montgomery phase formula for the Euler top, J. Geom. Mech. 2 (2010) 113-118.

Formation of Higher-dimensional Topological Black Holes (joint with Filipe Mena and Paul Tod), Ann. Henri Poincaré 10 (2010) 1359-1376.

Painlevé-Gullstrand Coordinates for the Kerr Solution, Gen. Rel. Grav. 41 (2009) 2579-2586.

Matching stationary spacetimes (joint with Filipe Mena), J. Geom. Phys. 59 (2009) 448-458.

Avoiding closed timelike curves with a collapsing rotating null dust shell (joint with Filipe Mena and Paul Tod), Class. Quantum Grav. 25 (2008) 045016 (6 pages).

Greybody Factors for d-Dimensional Black Holes (joint with Troels Harmark and Ricardo Schiappa), Adv. Theor. Math. Phys. 14 (2010) 727-794.

Gravitational Collapse to Toroidal and Higher Genus asymptotically AdS Black Holes (joint with Filipe Mena and Paul Tod), Adv. Theor. Math. Phys. 12 (2008) 1163-1181.

Tangent Euler top in General Relativity, Comm. Math. Phys. 281 (2008) 387-400.

Quasi-Maxwell interpretation of the spin-curvature coupling, Gen. Rel. Grav. 39 (2007) 1477-1487.

Relativity and singularities - a short introduction for mathematicians, Resenhas IME-USP 6 (2005) 309-335.

Newtonian limits of warp drive spacetimes, Gen. Rel. Grav. 38 (2006) 475-484.

Homogeneous cosmologies from the quasi-Maxwell formalism (joint with João Costa), J. Math. Phys. 46 (2005) 082501 (17 pages).

On the classification of asymptotic quasinormal frequencies for d-dimensional black holes and quantum gravity (joint with Ricardo Schiappa), Adv. Theor. Math. Phys. 8 (2004) 1001-1131.

Asymptotic quasinormal frequencies for black holes in non--asymptotically flat spacetimes (joint with Vitor Cardoso and Ricardo Schiappa), J. Math. Phys. 45 (2004) 4698-4713.

Linking, legendrian linking and causality (joint with Paul Tod), Proc. London Math. Soc. (3) 88 (2004) 251-272.

Linking and causality in (2+1)-dimensional static spacetimes, Class. Quantum Grav. 19 (2002) 3115-3126.

Warp drive with zero expansion, Class. Quantum Grav. 19 (2002) 1157-1165.

Local Activities

A Geometria da Relatividade (July 2010)

Mathematical Relativity in Lisbon (June 2009)

A Geometria da Relatividade (July 2005)

Seminário de Física Matemática

Talks

Cosmic censorship in spherical symmetry (November 2011)

Formation of Higher-dimensional Topological Black Holes (April 2010)

Asymptotic Quasi-normal Frequencies for d-Dimensional Black Holes (February 2009)

Greybody Factors for d-Dimensional Black Holes (December 2008)

Avoiding closed timelike curves with a collapsing rotating null dust shell (September 2008)

An Overview of Mathematical General Relativity (March 2005)

Warp Drive (April 2003)

Public Lectures

The Hidden Geometry (March 2010)

A Relatividade do Tempo (March 2010)

A Geometria Escondida (February 2011)

Bilhares Matemáticos (March 2009)

Book

General Relativity Without Calculus

Lecture Notes

An Introduction to Riemannian Geometry, with Leonor Godinho (Last update: July 2011)

Como Rodam as Coisas (Last update: February 2011)

Teaching (mostly in Portuguese)

Academic Year 2011/2012

Semester 1 — Riemannian Geometry

Academic Year 2010/2011

Semester 1 — Calculus II

Semester 1 — Geometric Mechanics

Academic Year 2009/2010

Semester 1 — Calculus II

Semester 2 — Mathematical Relativity

Academic Year 2008/2009

Semester 1 — Lie Groups and Lie Algebras

Semester 2 — Calculus II

Academic Year 2007/2008

Semester 2 — Calculus II

Academic Year 2006/2007

Semester 1 — Riemannian Geometry

Academic Year 2005/2006

Semester 1 — Differential Geometry

Semester 2 — Mathematical Analysis III

Academic Year 2004/2005

Semester 1 — Differential Geometry

Academic Year 2003/2004

Semester 1 — Mathematical Analysis III

Semester 2 — Riemannian Geometry

Academic Year 2002/2003

Semester 1 — Mathematical Analysis III

Semester 2 — Geometric Mechanics

Academic Year 2001/2002

Semester 1 — Mathematical Analysis III

Semester 2 — Geometric Mechanics

Academic Year 2000/2001

Semester 1 — Mathematical Analysis III

Semester 2 — Mathematical Analysis IV

Semester 2 — Geometric Mechanics

Students (in Portuguese)

MSc

Sílvia Guerra (2006/2007), Integrabilidade do Fluxo Geodésico num Elipsóide

João Costa (2002/2003), Cosmologias em Espaçotempos Estacionários

Undergraduate Thesis

Patrícia Engrácia (2002/2003), Universo de Gödel

Course Project

Rui Pinto (2008/2009), A Conjectura de Censura Cósmica de A a B

Diagonal Seminar

Ana Rita Nunes (2006/2007), A Forma do Universo

Ana Knopfly (2002/2003), Problema Restrito dos 3 Corpos

Ida Griffith (2001/2002), Transformações de Lorentz e de Möbius