Finite entropy of Schwarzschild anti-de sitter black hole in different coordinates

This paper studies the finite statistical-mechanical entropy of theSchwarzschild anti-de Sitter (AdS) spacetime arising from quantummassless scalar field by using the `brick wall' approach in thePainlev'e and Lemaitre coordinates. At first glance, it seems thatthe results would be different from that in the Schwarzschild-likecoordinate since both the Painlev'e and the Lemaitre spacetimes donot possess the event horizon obviously. However, this paper provesthat the entropies in these coordinates are exactly equivalent tothat in the Schwarzschild-like coordinate.