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Thirty years of studies of integrable reductions of Einstein's field equations
Einstein equations string gravity supergravity integrability
2010/12/20
More than thirty years passed since the first discoveries of various aspects of integrability
of the symmetry reduced vacuum Einstein equations and electrovacuum Einstein- Maxwell equations were made...
Null Asymptotics of Solutions of the Einstein-Maxwell Equations in General Relativity and Gravitational Radiation
Null Asymptotics of Solutions Einstein-Maxwell Equations General Relativity Gravitational Radiation
2010/12/21
We prove that for spacetimes solving the Einstein-Maxwell (EM) equations,the electromagnetic eld contributes at highest order to the nonlinear memory e ect of gravitational waves.
On the hyperbolicity of Maxwell's equations with a local constitutive law
hyperbolicity of Maxwell's equations local constitutive law
2010/12/20
Maxwell’s equations are considered in metric-free form, with a local but otherwise arbitrary constitutive law. After splitting Maxwell’s equations into evolution equations and constraints, we derive t...
A Physical Space Approach to Bilinear Wave Equations Estimates
Bilinear Wave Equations Estimates Space
2014/4/3
A paper written in collaboration with I. Rodnianski and T. Tao in which we expereiment with new proofs of bilinear estimates which have the potential to generalize to quasilinear equations.