# Cosmological perturbations of an $S$-matrix field

Comments: 12 pages, 4 figures

We consider the cosmological perturbations of an $S$-matrix field in an $R^4$-space-time. In particular, we consider the perturbations in the vicinity of a black hole. We study the perturbations of the scalar and electromagnetic fields in the vicinity of the black hole and show that the two fields obey the small-scale Lorenz laws. Furthermore, we show that the perturbations of the scalar fields in the vicinity of the black hole are completely determined by the dynamics of the black hole, while the electromagnetic field perturbations are entirely determined by the dynamics of the black hole.