Corrections to the Cardy-Verlinde formula at the Planck scale

Abstract

The possible corrections to the thermodynamic quantities of higher dimensional Schwa-rzschild black hole have been investigated by considering the generalized uncertainty principle (GUP) and the modified dispersion relation (MDR) separately. The quantum gravitational corrections to the Hawking temperature, energy and entropy of the black hole have been calculated based on both the GUP and the MDR analysis. The explicit form of the corrections are worked out up to the sixth power of the Planck length. The impacts of GUP and MDR have been used separately to obtain the quantum gravitational corrections to the Cardy-Verlinde (C-V) formula. It has been shown that the usual C-V entropy formula receives some new corrections. Also the renormalized form of the C-V formula has been introduced by redefining Virasoro operator and central charge within both the GUP and the MDR. Through comparison of the corrections obtained from GUP and MDR approaches it has been found that the results of these two alternative approaches should be identical if one uses the suitable expansion coefficients.