  We study the stability of static black holes in the third order Lovelock
theory. We derive a master equation for tensor perturbations. Using the master
equation, we analyze the stability of Lovelock black holes mainly in seven and
eight dimensions. We find there are cases where the linear analysis breaks
down. If we restrict ourselves to the regime where the linear analysis is
legitimate, black holes are always stable in seven dimensions. However, in
eight dimensions, there exists a critical mass below which black holes are
unstable. Combining our result in the third order Lovelock theory with the
previous one in Einstein-Gauss-Bonnet theory, we conjecture that small black
holes are unstable in any dimensions. The instability found in this paper will
be important for the analysis of black holes at the LHC.
