Eur. Phys. J. C (2017) 77: 608
https://doi.org/10.1140/epjc/s10052-017-5194-x

Regular Article - Theoretical Physics

Quantum fluctuations from thermal fluctuations in Jacobson formalism

¹ Irving K. Barber School of Arts and Sciences, University of British Columbia-Okanagan, Kelowna, BC, V1V 1V7, Canada
² Department of Physics and Astronomy, University of Lethbridge, Lethbridge, AB, T1K 3M4, Canada
³ Mathematics Department, Faculty of Science, Damascus University, Damascus, Syria
⁴ Laboratoire de Physique Corpusculaire de Clermont-Ferrand, Université Clermont Auvergne, 4, Avenue Blaise Pascal, 63178, Aubière Cedex, France
⁵ Department of Physics and Astronomy, King Saud University, Riyadh, 11451, Saudi Arabia

^* e-mail: salwams@ksu.edu.sa

Received: 5 March 2017
Accepted: 4 September 2017
Published online: 14 September 2017

Abstract

In the Jacobson formalism general relativity is obtained from thermodynamics. This is done by using the Bekenstein–Hawking entropy–area relation. However, as a black hole gets smaller, its temperature will increase. This will cause the thermal fluctuations to also increase, and these will in turn correct the Bekenstein–Hawking entropy–area relation. Furthermore, with the reduction in the size of the black hole, quantum effects will also start to dominate. Just as the general relativity can be obtained from thermodynamics in the Jacobson formalism, we propose that the quantum fluctuations to the geometry can be obtained from thermal fluctuations.