Corrections to the Cardy-Verlinde formula at the Planck scale |
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| Institution: | 1. Key Laboratory of Optical Astronomy, National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012, China;2. School of Physics, University of Chinese Academy of Sciences, Beijing 100049, China;3. School of Computer Science and Technology, Taiyuan University of Science and Technology, Taiyuan 030024, China;1. Yunnan Observatories, Chinese Academy of Sciences (CAS), P.O. Box 110, 650216 Kunming, P.R. China;2. Key Laboratory for the Structure and Evolution of Celestial Objects, Chinese Academy of Sciences, 650216 Kunming, P.R. China;3. University of the Chinese Academy of Sciences, Yuquan Road 19#, Sijingshang Block, 100049 Beijing, P.R. China;1. Universidade Federal de Itajubá, Instituto de Física e Química, Itajubá-MG, Brazil;2. Universidade de São Paulo, Instituto de Astronomia, Geofísica e Ciências Atmosféricas, São Paulo - SP, Brazil;1. Harish-Chandra research Institute, Chhatnag Road, Jhunsi, Allahabad-211019, India;2. Current affiliation: Nicolaus Copernicus Astronomical Centre, Bartycka 18, 00-716, Warsaw, Poland;3. Institute of Theoretical and Computational Physics, Department of Physics, University of Crete, 700 13 Heraklion, Greece;4. Current affiliation : Inter-University Centre for Astronomy and Astrophysics (IUCAA), Pune University Campus, Pune - 411 007, India |
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| 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. |
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