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This paper proves that if eternal neutral black holes satisfy some generalconditions and matter fields only appear in the outside of the Killing horizon,the strong energy condition is a sufficient condition to insure that the vacuumSchwarzschild black hole has the fastest action growth of the same totalenergy. This result is consistent with the bound of computational complexitygrowth rate and gives a strong evidence for the holographic complexity-actionconjecture.

Strong energy condition and complexity growth bound in holography