Energy and first law of thermodynamics for Born–Infeld–anti-de-Sitter black hole

We calculate the local energy and the energy density of the Reisner–Norström–anti-de-Sitter black hole, study the first law of thermodynamics and show the Smarr formula for the Born–Infeld–anti-de-Sitter black hole. Applying the first law of thermodynamics to the black hole region, we analyse the three energy exchange processes between the black hole region and the outer and the inner regions.