My research is in general relativity and I am interested in questions about spacetime singularities and cosmic censorship. The cosmic censorship conjecture was proposed by Roger Penrose in the sixties and the hypothesis is that spacetime singularities are always hidden within black holes and cannot be seen (i.e. there are no "naked singularities"). In my research I primarily work on global existence for solutions to Einstein's equations and in particular to the Einstein-Vlasov system where the matter is modelled by kinetic theory. A global existence theorem is the first step towards an understanding of cosmic censorship. I am also interested in kinetic equations in general (on a flat background spacetime) such as the Maxwell-Vlasov system, the Vlasov-Poisson system and the relativistic Boltzmann equation. 

List of publications

	Bounds on M/R for charged objects with positive cosmological constant. arXiv:1201.5725. Joint with C. Böhmer and A. Mussa.
	Black hole formation from a complete regular past for collisionless matter. arXiv:1201.3510.
	The Einstein-Vlasov system/Kinetic theory. Living Rev. Relativity 14 (2011) 4.
	Existence of axially symmetric static solutions of the Einstein-Vlasov system. Commun. Math. Phys. 308, 23-47 (2011). Joint with M. Kunze and G. Rein.
	Regularity results for the spherically symmteric Einstein-Vlasov system. Ann. H. Poincaré 11, 781-803 (2010).
	Formation of trapped surfaces for the spherically symmetric Einstein-Vlasov system. J. Hyperbolic Diff. Eqs. 7, 707-731 (2010). Joint with G. Rein.
	Bounds on M/R for static objects with a positive cosmological constant. Class. Quantum Grav. 26, 195007 (2009). Joint with C. Böhmer.
	A numerical investigation of the steady states of the spherically symmetric Einstein-Vlasov-Maxwell system. Class. Quantum Grav. 26, 145003 (2009). Joint with M. Eklund and G. Rein.
	The asymptotic behaviour in Schwarzschild time of Vlasov matter in spherically symmetric gravitational collapse. Math. Proc. Camb. Phil. Soc. 149, 173-188 (2010). Joint with G. Rein.
	Gravitational collapse and the formation of black holes for the spherically symmetric Einstein-Vlasov system. Quarterly of Appl. Math. 68, 17-42 (2010). Joint with M. Kunze and G. Rein.
	Sharp bounds on the critical stability radius for relativistic charged spheres. Commun. Math. Phys. 288, 715-730 (2009).
	The formation of black holes in spherically symmetric gravitational collapse. Mathematische Annalen 350, 683-705 (2011). Joint with M. Kunze and G. Rein.
	Sharp bounds on 2m/r of general spherically symmetric static objects. J. Diff. Equations 245, 2243-2266 (2008).
	Global existence for the spherically symmetric Einstein-Vlasov system with outgoing matter. Commun. Partial Diff. Eqs. 33, 656-668 (2008). Joint with M. Kunze and G. Rein.
	An investigation of the Buchdahl inequality for spherically symmetric static shells. Journal of physics: Conference series 66, 012008 (2007), XXIXth Spanish relativity meeting (ERE 2006): Einstein's legacy: from theoretical paradise to astrophysical observations.
	On the steady states of the spherically symmetric Einstein-Vlasov system. Class. Quantum Grav. 24, 1809-1832 (2007). Joint with G. Rein.
	On static shells and the Buchdahl inequality for the spherically symmetric Einstein-Vlasov system. Commun. Math. Phys. 274, 409-425 (2007).
	On the Buchdahl inequality for spherically symmetric static shells. Commun. Math. Phys. 274, 399-408 (2007).
	A numerical investigation of the stability of steady states and critical phenomena for the spherically symmetric Einstein-Vlasov system. Class. Quantum Grav. 23 3659-3677 (2006). Joint with G. Rein.
	On global existence for the spherically symmetric Einstein-Vlasov system in Schwarzschild coordinates. Indiana Univ. Math. Journal. 56, 523-552 (2007).
	The Einstein-Vlasov system/Kinetic theory. Liv. Rev. Relativity 8 (2005).
	Global classical solutions to the spherically symmetric Nordstr\"{o}m-Vlasov system. Math. Proc. Camb. Phil. Soc., 138 (2005), 533-539. Joint with S. Calogero and G. Rein.
	Analytical and numerical results on the Einstein-Vlasov collapsing system. In the Proceedings of the Dynamics and Thermodynamics of Black Holes and Naked Singularities (2005). http//:www.mate.polimi.it/bh
	On blowup for the gain-term-only classical and relativistic Boltzmann equation. Math. Methods Appl. Sci. 27 (2004), 2231-2240. Joint with S. Calogero and R. Illner.
	Existence of CMC and constant areal time foliations in T^2 symmetric spacetimes with Vlasov matter. Comm. Partial Differential Equations 29 (2004), 237-262. Joint with A.D. Rendall and M. Weaver.
	The Einstein-Vlasov system/Kinetic theory. Liv. Rev. Relativity 5 (2002).
	On the Einstein-Vlasov system with hyperbolic symmetry. Math. Proc. Camb. Phil. Soc., 134 (2003), 529-549. Joint with G. Rein and A. Rendall.
	Global foliations of matter spacetimes with Gowdy symmetry. Commun. Math. Phys. 206 (1999), 337-366.
	Controlling the propagation of the support for the relativistic Vlasov equation with a selfconsistent Lorentz invariant field. Indiana Univ. Math. Journal, 45 (1996), 617-642.
	Global existence of smooth solutions in three dimensions for the semiconductor Vlasov-Poisson-Boltzmann equation. Nonlinear Anal. : Th. Meth. Appl., 28 (1997), 1193-1211.
	Regularity of the gain term and strong L^1 convergence to equilibrium for the relativistic Boltzmann equation, SIAM J. Math. Anal., 27 (1996), 1386-1405.
	Discontinuous formation and desorption of clusters during particles adsorption at surfaces, Biophysical Chemistry 54 (1995), 211-218.

Relativity on the web

	Albert-Einstein-Institut
	Living reviews
	Los Alamos e-Print archive