Following the previous investigations, the next step should be to compare the surface gravity (5)with the definition of surface gravity in the unified first law (4)to derive f. But, unfortunately we do not have a proper definition of surface gravity in modified gravity as an extension of (4). Here, a theory permitting any devi-ation from Einstein theory (no cosmological constant) is treated as modified gravity, since the original Misner–Sharp mass used in the unified first law does not permit a cosmological constant [12,13]. In this sense, a gravity with a cosmological constant is regarded as a “modified gravity”. So we have to switch to the first perspective,