Kumar, N. Recovering semiclassical Einstein’s equation using generalized entropy. Gen Relativ Gravit 55, 127 (2023). https://doi.org/10.1007/s10714-023-03172-x
Kumar, N. Recovering semiclassical Einstein’s equation using generalized entropy. Gen Relativ Gravit 55, 127 (2023). https://doi.org/10.1007/s10714-023-03172-x
Kumar, N. Recovering semiclassical Einstein’s equation using generalized entropy. Gen Relativ Gravit 55, 127 (2023). https://doi.org/10.1007/s10714-023-03172-x
Kumar, N. Recovering semiclassical Einstein’s equation using generalized entropy. Gen Relativ Gravit 55, 127 (2023). https://doi.org/10.1007/s10714-023-03172-x
Abstract
The classical Einstein’s Field Equation has been derived previously by demanding that the Clausius relation dS = δQ/T holds. In this letter, we show that the semiclassical Einstein’s Field Equation can be recovered using the generalized entropy Sgen by using the non-equilibrium thermodynamics where the Clausius relation is replaced by the entropy balance relation dS = δQ/T +diS, where diS is some internal entropy. Moreover, since the quantum fields violate the classical focusing, we, therefore, have to use quantum focusing in this case. Using then Jacobson’s idea of thermodynamics of spacetime we recover the semiclassical equation of motion. We, therefore, in a sense also show the validity of the semiclassical approximation, a crucial approach for establishing a number of important ideas such as the Hawking effect.
Keywords
Semiclassical Gravity; Generalized Entropy; Quantum Expansion; Thermody-namics of Causal Horizon; Non-equilibrium Thermodynamics of Spacetime
Subject
Physical Sciences, Theoretical Physics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
