Global structure of the Zipoy–Voorhees–Weyl spacetime and the (delta)= 2 Tomimatsu–Sato spacetime

Starting from the SO(2, 2n) Chern–Simons form in (2n + 1) dimensions, we calculate the variation of conserved quantities in Lovelock gravity and Lovelock–Maxwell gravity through the covariant formalism developed in [23]. Despite the technical complexity of the Lovelock Lagrangian, we obtain a remarkably simple expression for the variation of the charges ensuing from the diffeomorphism covariance of the theory. The viability of the result is tested in specific applications and the formal expression for the entropy of Lovelock black holes is recovered.