Research Interest
- Newtonian Limit of General Relativity. We are interested in
finding rigourous results on the Newtonian Limit of General Relativity,
that is on the existence of slow solutions to the field equations. Results
have been obtained on the Cauchy problem starting with global asymptotically
flat initial slices, more recently we have obtained estimates for asymptotically
null initial surfaces, this allows to control the gravitational radiation
output of an isolated source in the slow motion limit.
- Relativistic Dissipative Fluids. We study several aspects of
these fluid theories, as defined by Liu, Muller and Ruggeri, and Geroch
and Lindbloom. In particular stability of solutions, aproach to equilibrium,
statistical origin, shock waves.
- Symmetric Hyperbolic Systems. We study the symmetric hyperbolicity
of Einstein's equations as a tool for proving several rigouruos results,
but also to improve on numerical techniques for evolving these equations.
In particular we are interested in formulations which allows to prescrive
different types of gauge conditions. Results along these lines are some
one parameter families of variables whose evolution is symmetric hyperbolic.
Resently we are working in extending some of these results to Ashtekar
variables.
- Boundary Conditions for General Relativity. We are interesting
in obtaining rigourous results on the evolution of space time on bounded
domains, as neede to fully trust numerical calculations which use this
schema.