Invariant Solutions of the Wave Equation on Static Spherically Symmetric Spacetimes Admitting G7 Isometry Algebra

Abstract

Algorithms to construct the optimal systems of dimension of at most three of Lie algebras are given. These algorithms are applied to determine the Lie algebra structure and optimal systems of the symmetries of the wave equation on static spherically symmetric spacetimes admitting G7 as an isometry algebra. Joint invariants and invariant solutions corresponding to three-dimensional optimal systems are also determined.