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Remnant mass and entropy of black holes and modified uncertainty principle

In this paper, we study the thermodynamics of black holes using a generalized uncertainty principle (GUP) with a correction term linear order in the momentum uncertainty. The mass-temperature relation and heat capacity are calculated from which critical and remnant masses are obtained. The results are exact and are found to be identical. The entropy expression gives the famous area theorem upto leading order corrections from GUP. In particular, the linear order term in GUP leads to a $\sqrt{A}$ correction to the area theorem. Finally, the area theorem can be expressed in terms of a new variable termed as reduced horizon area only when the calculation is done to the next higher order correction from GUP.