arXiv subjects
Publications and source records attributed to P. Lankinen.
We prove that a completely symmetric and trace-free rank-4 tensor is, up to sign, a Bel-Robinson type tensor, i.e., the superenergy tensor of a tensor with the same algebraic symmetries as the Weyl tensor, if and only if it satisfies a certain quadratic identity. This may be seen as the first Rainich theory result for rank-4 tensors.
We study Rainich-like conditions for symmetric and trace-free tensors T. For arbitrary even rank we find a necessary and sufficient differential condition for a tensor to satisfy the source free field equation. For rank 4, in a generic case, we combine these conditions with previously obtained algebraic conditions to obtain a complete set of algebraic and differential conditions on T for it to be a superenergy tensor of a Weyl candidate tensor satisfying the Bianchi vacuum equations. By a result of Bell and Szekeres this implies that in vacuum, generically, T must be the Bel-Robinson tensor of the spacetime. For the rank 3 case we derive a complete set of necessary algebraic and differential conditions for T to be the superenergy tensor of a massless spin 3/2 field satisfying the source free field equation.