  In this paper, we study the physical properties of black holes in the
framework of the recently proposed Einstien-Bel-Robinson gravity. We show that
interestingly the theory propagates a transverse and massive graviton on a
maximally symmetric background with positive energy. There is also a single
ghost-free branch that returns to the Einstein case when \beta\to 0. We find
new black hole solutions to the equations, both approximate and exact, the
latter being a constant curvature black hole solution, and discuss
inconsistencies with metrics that were previously claimed to be approximate
solutions to the equations. We obtain the conserved charges of the theory and
briefly study the thermodynamics of the black hole solutions.
