Black hole solution in third order Lovelock gravity has no Gauss-Bonnet limit
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 eld equations in the third order Lovelock gravity. These two complex solutions could not be accepted as the solutions of the Einstein’s eld equations which are supposed to be real values function on entire real r axis. A new solution which is only valid if the third order Lovelock parameter is small is introduced which can be considered as the natural extension of the general relativity (GR) to the third order Lovelock modied theory of gravity. We also generalize the discussion to the higher dimensional third order Lovelock gravity coupled to the matter sources with cosmological constant.