  The Gerlach and Sengupta (GS) formalism of coordinate-invariant, first-order,
spherical and nonspherical perturbations around an arbitrary spherical
spacetime is generalized to higher orders, focusing on second-order
perturbation theory. The GS harmonics are generalized to an arbitrary number of
indices on the unit sphere and a formula is given for their products. The
formalism is optimized for its implementation in a computer algebra system,
something that becomes essential in practice given the size and complexity of
the equations. All evolution equations for the second-order perturbations, as
well as the conservation equations for the energy-momentum tensor at this
perturbation order, are given in covariant form, in Regge-Wheeler gauge.
