Invariant Transformations and Newman‐Penrose Constants

The relationship between constants of the motion and invariant transformations is discussed. Particular emphasis is placed on strong conservation laws which are of the form ${\mathcal{U}}_{\mathrm{\wedge \; ,\mu \nu }}^{\mathrm{\mu \nu }}\text{≡0}$ . The existence of such a law leads to constants of the motion which are surface integrals and therefore generally do not generate an invariant transformation. However, when there is an associated weak conservation law, such that t^μ,_μ ≡ −$\mathrm{\delta ̄}$ y_AL^A (L^A = 0 are the field equations and$\mathrm{\delta ̄}$ y_A the invariant change in field variables), a nontrivial invariant transformation exists. These results are applied to the discussion of the Newman‐Penrose constants for the electromagnetic field. The conclusion arrived at is$\mathrm{\delta ̄}$ y_A = 0, which suggests that the invariant transformation generated by the Newman‐Penrose constants is trivial.