Spherically symmetric electrovac spacetimes in conformal Killing gravity

Abstract

Recently Harada proposed a third-order gravitational theory for the derivatives of the metric. Mantica and Molinari showed that Harada’s theory may be recast into the form of Einstein’s field equations (EFEs) with an additional source term which is a second-order conformal Killing tensor. Accordingly they named the theory conformal Killing gravity. However, they overlooked the fact that all solutions of the new theory (except those satisfying EFEs) admit a non-trivial second-order Killing tensor. Harada derived an analog of the Schwarzschild solution. Recently Tarciso et al obtained a generalization of Harada’s vacuum solution analogous to the Reissner–Nordström solution. However, like Harada they assumed a restricted form for a static spherically symmetric metric. In this study the most general spherically symmetric static vacuum solution of Harada’s theory and its generalization with a Maxwell electromagnetic field as source were obtained. The validity of Birkhoff’s theorem for static spherically symmetric electrovac fields in conformal Killing gravity is investigated.