José Natário

José Natário


Phone (351) 218 417 114
Email jnatar@math.ist.utl.pt
Office Mathematics Building, 4th floor, room 4.29
Postal Address   Departamento de Matemática
Instituto Superior Técnico
Av. Rovisco Pais
1049-001 Lisboa, Portugal



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

On the global uniqueness for the Einstein-Maxwell-scalar field system with a cosmological constant. Part 1: Well posedness and breakdown criterion (joint with João L. Costa, Pedro M. Girão and Jorge Drumond Silva), to appear in Class. Quantum Grav. (2014).

On the global uniqueness for the Einstein-Maxwell-scalar field system with a cosmological constant. Part 2: Structure of the solutions and stability of the Cauchy horizon (joint with João L. Costa, Pedro M. Girão and Jorge Drumond Silva), 2014.

On the global uniqueness for the Einstein-Maxwell-scalar field system with a cosmological constant. Part 3: Mass inflation and extendibility of the solutions (joint with João L. Costa, Pedro M. Girão and Jorge Drumond Silva), 2014.

Relativistic elasticity of rigid rods and strings, to appear in Gen. Rel. Grav. (2014).

A Minkowski-type inequality for convex surfaces in the hyperbolic 3-space, 2013.

Optimal escape from circular orbits around black holes, Gen. Rel. Grav. 45 (2013) 811-818.

Spacetime dynamics of spinning particles - exact gravito-electromagnetic analogies (joint with Filipe Costa and Miguel Zilhão), 2012.

Gravito-electromagnetic analogies (joint with Filipe Costa), Gen. Rel. Grav. 46 (2014) 1792.

The problem of a self-gravitating scalar field with positive cosmological constant (joint with João L. Costa e Artur Alho), Ann. Henri Poincaré 14 (2013) 1077-1107.

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), J. Math. Phys. 53 (2012) 052501 (9 pages).

Optimal time travel in the Gödel universe, Gen. Rel. Grav. 44 (2012) 855-874.

The rocket problem in general relativity (joint with Pedro G. Henriques), J. Optim. Theory Appl. 154 (2012) 500-524.

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 L. 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.




Books

An Introduction to Riemannian Geometry, with Leonor Godinho

General Relativity Without Calculus, with a small errata




Talks

Relativistic elasticity of rigid rods and strings (July 2014)

Gravito-electromagnetic analogies (April 2014)

Strong cosmic censorship with a cosmological constant (December 2013)

Bernoulli's elastic curves, rockets, and time travel (July 2013)

Optimal time travel in the Gödel universe (January 2013)

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)




Local Activities

Mira Fernandes Lectures on Mathematical Relativity (June 2013)

A Geometria da Relatividade (July 2010)

Mathematical Relativity in Lisbon (June 2009)

A Geometria da Relatividade (July 2005)

Mathematical Physics Seminar




Public Lectures (mostly in Portuguese)

O GPS e a Teoria da Relatividade (March 2014)

A Linguagem Secreta do Universo (October 2012)

The Hidden Geometry (March 2010)

A Relatividade do Tempo (February 2014)

A Geometria Escondida (December 2013)

Bilhares Matemáticos (March 2009)




Semi-popular articles (in Portuguese)

O GPS e a Teoria da Relatividade (May 2013)

O Teorema de Gauss-Bonnet (March 2012)

Como Rodam as Coisas (February 2011)

Espaço-tempo de Minkowski: a Física como Geometria (June 2010)

O que é a curvatura de uma superfície? (January 2010)




Teaching (mostly in Portuguese)


Calculus II

Semester 2 — 2012/2013

Semester 1 — 2010/2011

Semester 1 — 2009/2010

Semester 2 — 2008/2009

Semester 2 — 2007/2008


Differential Geometry

Semester 1 — 2013/2014

Semester 1 — 2005/2006

Semester 1 — 2004/2005


Geometric Mechanics

Semester 1 — 2012/2013

Semester 1 — 2010/2011

Semester 2 — 2002/2003

Semester 2 — 2001/2002

Semester 2 — 2000/2001


Lie Groups and Lie Algebras

Semester 1 — 2012/2013

Semester 1 — 2008/2009


Mathematical Relativity

Semester 2 — 2011/2012

Semester 2 — 2009/2010


Mathematical Analysis III

Semester 2 — 2005/2006

Semester 1 — 2003/2004

Semester 1 — 2002/2003

Semester 1 — 2001/2002

Semester 1 — 2000/2001


Mathematical Analysis IV

Semester 2 — 2000/2001


Riemannian Geometry

Semester 1 — 2011/2012

Semester 1 — 2006/2007

Semester 2 — 2003/2004




Students (mostly in Portuguese)


MSc

Pedro Oliveira (2012/2013), Min-Oo's Conjecture: Positive Mass Theorem in the de Sitter Universe

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

Pedro Peres (2012/2013), Viagens no tempo no Universo de Gödel

Pedro Filipe (2012/2013), Determinação da parametrização e curvatura de uma superfície em R3 com a métrica medida por observadores estacionários no espaço-tempo de Schwarzschild

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


Gulbenkian program "Novos Talentos em Matemática"

Francisco Lopes (2011/2012), Geodésicas Nulas em Relatividade Geral

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


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