A proof is given that the space L of solutions of the linearized vacuum Einstein equation around a Schwarzschild black hole is parametrized by two scalar fields, which are gauge invariant combinations of perturbed algebraic and differential invariants of the Weyl tensor and encode the information on the odd (-) and even (+) sectors L ±. These fields measure the distortion of the geometry caused...

With the formulation of the gauge group as a Banach-Lie group of suitable Sobolev type, the Cauchy problem for the Yang-Mills equation in physical space-time reduces rigorously to the case of the temporal gauge. In this gauge there exist spatially global strong solutions for given data for field and potential that are L(2) together with one or two derivatives (respectively). Regarding global ex...

In this article we examine some points in the moduli space of M-Theory at which there arise enhanced gauge symmetries. In particular, we examine the “trivial” points of enhanced gauge symmetry in the moduli space of M-Theory on S × S1/Z2 as well as the points of enhanced gauge symmetry in the moduli space of M-Theory on K3 and those in the moduli space of M-Theory on T 5/Z2 × S. Also, we employ...

This paper focuses on the relationships between stratified $L$-conver-gence spaces, stratified strong $L$-convergence spaces and stratifiedlevelwise  $L$-convergence spaces. It has been known that: (1) astratified $L$-convergence space is precisely a left-continuousstratified levelwise $L$-convergence space; and (2) a  stratifiedstrong $L$-convergence space is naturally a stratified $L$-converg...

We develop a method for calculating the Lyapunov characteristic exponents of lattice gauge theories. The complete Lyapunov spectrum of SU(2) gauge theory is obtained and Kolmogorov-Sinai entropy is calculated. Rapid convergence with lattice size is found. In Ref.1, we have studied chaos in lattice gauge systems by obtaining the largest Lyapunov exponents. The method used there, though straightf...