Area spectrum and black hole thermodynamics

Abstract: The role of horizon area quantization on black hole thermodynamics is investigated in this article. The coefficient appearing in the quantization of area is fixed by an appeal to the saturated form of the Landauer's principle. Then by considering transition between discrete states of the event horizon area which in turn is equivalent to transitions between discrete mass states of the black hole, the change in the mass can be obtained. The change in mass is then equated to the product of the Hawking temperature and change in entropy of the black hole between two consecutive discrete states applying the first law of black hole thermodynamics. This gives the corrected Hawking temperature. In particular, we apply this technique to the Schwarzschild black hole, the quantum corrected Schwarzschild black hole, the Reissner-Nordstr\"{o}m black hole which is a charged black hole, and the rotating Kerr black hole geometry, and obtain the corrected Hawking temperature in each of these cases. We then take a step forward by inserting this corrected Hawking temperature in the first law of black hole thermodynamics once again to calculate the entropy of the black hole in terms of the horizon area of the black hole. This leads to logarithmic and inverse corrections to the entropy of the black hole.