By dimensional reduction, Einstein-Hermitian equations of n + 1 dimensional closed Kähler manifolds lead to vortex equations of n dimensional closed Kähler manifolds. A Yang-Mills-Higgs functional to unitary bundles over closed Kähler manifolds has topological invariance by adding the additional terms which have ghost fields. Henceforth we achieve the matter (Higgs field) coupled topological fi...

The pathways along which A. Einstein and D. Hilbert independently came to the gravitational field equations are traced. Some of the papers that assert a point of view on the history of the derivation of the gravitational field equations “that radically differs from the standard point of view” are critically analyzed. It is shown that the conclusions drawn in these papers are completely groundless.

We prove the stability of de Sitter space-time as a solution to Einstein-Vlasov system with massless particles. The semi-global Minkowski is also addressed. proof relies on conformal techniques, namely Friedrich's Einstein field equations. exploit invariance Vlasov equation cotangent bundle and adapt Kato's local existence theorem for symmetric hyperbolic systems long enough time solutions evol...