A note on proper conformal vector fields in Bianchi type I space-times.
A principle involving the variation of the metric tensor in a stationary space-time of general relativity
Algebro-geometric approach to the Ernst equation I. Mathematical Preliminaries
1. Introduction. It is well known that methods of algebraic geometry and, in particular, Riemann surface techniques are well suited for the solution of nonlinear integrable equations. For instance, for nonlinear evolution equations, so called 'finite gap' solutions have been found by the help of these methods. In 1989 Korotkin [9] succeeded in applying these techniques to the Ernst equation, which is equivalent to Einstein's vacuum equation for axisymmetric stationary fields. But, the Ernst equation...
An explicit determination of the Petrov type D spacetimes on which Weyl's neutrino equation and Maxwell's equations satisfy Huygens' principle
By Magri's theorem, self-dual gravity is completely integrable.
Classification of cylindrically symmetric static space-times according to their proper homothetic vector fields.
Complete solution of Hadamard's problem for the scalar wave equation on Petrov type III space-times
Critical phenomena in gravitational collapse
A mini-introduction to critical phenomena in gravitational collapse is combined with a more detailed discussion of how gravity regularizes the 'critical spacetimes' that dominate these phenomena.
Decay estimates for spherically symmetric Yang-Mills fields in Minkowski space-time
Gravity, strings, modular and quasimodular forms
Modular and quasimodular forms have played an important role in gravity and string theory. Eisenstein series have appeared systematically in the determination of spectrums and partition functions, in the description of non-perturbative effects, in higher-order corrections of scalar-field spaces, ...The latter often appear as gravitational instantons i.e. as special solutions of Einstein’s equations. In the present lecture notes we present a class of such solutions in four dimensions, obtained by...
Huygens' principle for the non-self-adjoint scalar wave equation on Petrov type III space-times
Jacobi fields and its application of normal contact Lorentzian manifolds.
Mirror symmetry and conformal flatness in general relativity.
New results on de Sitter quantum field theory
Nonexistence of Petrov type III space-times on which Weyl's neutrino equation or Maxwell's equations satisfy Huygens' principle
On some Ricci-flat metrics of cohomogeneity two on complex line bundles.
On the existence of geodesics in static Lorentz manifolds with singular boundary
Proper homothetic vector fields in Bianchi type-I space-time.
Spherically symmetric generalized Lagrange metrics.
The structure of the space of solutions of Einstein's equations. I. One Killing field