Quantum fluctuations from thermal fluctuations in Jacobson formalism

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.