Schwarzschild (Anti-) de Sitter Black Hole Thermodynamics And The Extended Uncertainty Principle (EUP)

Using Heisenberg’s uncertainty principle, the temperature of a black hole can be obtained. Using temperature, entropy and heat capacity of the black hole can also be calculated. The uncertainty principle for the de Sitter space has been corrected. Here we first briefly introduce the Extended Uncertainty Principle EUP, which is a correction version of the Heisenberg Uncertainty Principle, then use it to obtain the corrected temperature, entropy and heat capacity, and compare each with the standard version of the Uncertainty Principle. Although the corrected temperature and heat capacity have been discussed in various ways in other works, here we obtain a new entropy for the Schwarzschild black hole in (anti-)de Sitter space, which firstly has a logarithmic form and is secondly related to the cosmological constant, Λ. In addition, the results show that, in general, there is no major difference between the corrected temperature and the standard temperature, but the heat capacity for standard, Schwarzschild-de Sitter (dS) and Schwarzschild anti-de Sitter (AdS) black holes is different.