# Correction of Cardy–Verlinde formula for Fermions and Bosons with modified dispersion relation

## Abstract

Cardy–Verlinde formula links the entropy of conformal symmetry field to the total energy and its Casimir energy in a D-dimensional space. To correct black hole thermodynamics, modified dispersion relation can be used which is proposed as a general feature of quantum gravity approaches. In this paper, the thermodynamics of Schwarzschild four-dimensional black hole is corrected using the modified dispersion relation for Fermions and Bosons. Finally, using modified thermodynamics of Schwarzschild four-dimensional black hole, generalization for Cardy–Verlinde formula is obtained. - Highlights: • The modified Cardy–Verlinde formula obtained using MDR for Fermions and Bosons. • The modified entropy of the black hole used to correct the Cardy–Verlinde formula. • The modified entropy of the CFT has been obtained.

- Authors:

- Publication Date:

- OSTI Identifier:
- 22617501

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Annals of Physics; Journal Volume: 380; Other Information: Copyright (c) 2017 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BLACK HOLES; BOSONS; CONFORMAL INVARIANCE; DISPERSION RELATIONS; ENTROPY; FERMIONS; FOUR-DIMENSIONAL CALCULATIONS; QUANTUM GRAVITY; SYMMETRY BREAKING; THERMODYNAMICS

### Citation Formats

```
Sadatian, S. Davood, E-mail: sd-sadatian@um.ac.ir, and Dareyni, H.
```*Correction of Cardy–Verlinde formula for Fermions and Bosons with modified dispersion relation*. United States: N. p., 2017.
Web. doi:10.1016/J.AOP.2017.03.009.

```
Sadatian, S. Davood, E-mail: sd-sadatian@um.ac.ir, & Dareyni, H.
```*Correction of Cardy–Verlinde formula for Fermions and Bosons with modified dispersion relation*. United States. doi:10.1016/J.AOP.2017.03.009.

```
Sadatian, S. Davood, E-mail: sd-sadatian@um.ac.ir, and Dareyni, H. Mon .
"Correction of Cardy–Verlinde formula for Fermions and Bosons with modified dispersion relation". United States.
doi:10.1016/J.AOP.2017.03.009.
```

```
@article{osti_22617501,
```

title = {Correction of Cardy–Verlinde formula for Fermions and Bosons with modified dispersion relation},

author = {Sadatian, S. Davood, E-mail: sd-sadatian@um.ac.ir and Dareyni, H.},

abstractNote = {Cardy–Verlinde formula links the entropy of conformal symmetry field to the total energy and its Casimir energy in a D-dimensional space. To correct black hole thermodynamics, modified dispersion relation can be used which is proposed as a general feature of quantum gravity approaches. In this paper, the thermodynamics of Schwarzschild four-dimensional black hole is corrected using the modified dispersion relation for Fermions and Bosons. Finally, using modified thermodynamics of Schwarzschild four-dimensional black hole, generalization for Cardy–Verlinde formula is obtained. - Highlights: • The modified Cardy–Verlinde formula obtained using MDR for Fermions and Bosons. • The modified entropy of the black hole used to correct the Cardy–Verlinde formula. • The modified entropy of the CFT has been obtained.},

doi = {10.1016/J.AOP.2017.03.009},

journal = {Annals of Physics},

number = ,

volume = 380,

place = {United States},

year = {Mon May 15 00:00:00 EDT 2017},

month = {Mon May 15 00:00:00 EDT 2017}

}