Black hole solution in third order Lovelock gravity has no Gauss-Bonnet limit

Understand

We revisit the spherically symmetric third order Lovelock black hole solution in 7-dimensions.

• We show that the general solution for the metric function does not admit the Gauss-Bonnet (GB) limit.
• This is not expected due to the linear superposition of the second (GB) and third order Lovelock Lagrangians in the general action.
• It is found that the two branches of the GB solutions are indeed the limit of the other two complex solutions of the field equations in the third order Lovelock gravity.