José Natário

Position

Professor Auxiliar

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

An elementary derivation of the Montgomery phase formula for the Euler top (2009).

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), to appear in Adv. Theor. Math. Phys. 13 (2009).

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.

Some Local Activities

A Geometria da Relatividade (July 2010)

Mathematical Relativity in Lisbon (June 2009)

A Geometria da Relatividade (July 2005)

Seminário de Física Matemática

Lecture Notes

An Introduction to Riemannian Geometry, with Leonor Godinho (Last update: September 2009)

A Geometria da Relatividade (Last update: January 2008)

Teaching (in portuguese)

Academic Year 2009/2010

1º Semester — Calculus II

Academic Year 2008/2009

1º Semester — Lie Groups and Lie Algebras

2º Semester — Calculus II

Academic Year 2007/2008

2º Semester — Calculus II

Academic Year 2006/2007

1º Semester — Riemannian Geometry

Academic Year 2005/2006

2º Semester — Mathematical Analysis III

1º Semester — Differential Geometry

Academic Year 2004/2005

1º Semester — Differential Geometry

Academic Year 2003/2004

2º Semester — Riemannian Geometry

1º Semester — Mathematical Analysis III

Academic Year 2002/2003

2º Semester — Geometric Mechanics

1º Semester — Mathematical Analysis III

Academic Year 2001/2002

2º Semester — Geometric Mechanics

1º Semester — Mathematical Analysis III

Academic Year 2000/2001

2º Semester — Geometric Mechanics

2º Semester — Mathematical Analysis IV

1º Semester — Mathematical Analysis III

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