Quantum Fluctuations from Thermal Fluctuations in Jacobson Formalism
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 holes will 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.
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