Abstract
We calculate the normalized vacuum energy density for a massless scalar field confined in a region limited by two parallel plates, placed in the background spacetime generated by a black hole in third order Lovelock gravity, in four dimensions, in the weak field approximation. The obtained result is compared with the similar one in the framework of general relativity. We also calculate the thermal corrections to the Casimir energy for both contexts, namely, general relativity and third order Lovelock gravity. Thus, we analyze and compare the regimes of low and high temperatures for both cases.
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