From Quantum Relative Entropy to the Semiclassical Einstein Equations
- View PDF HTML (experimental) Abstract:We provide arguments indicating that the semiclassical Einstein equations follow from quantum relative entropy and its proportionality to an area variation.
- Using modular theory, we establish that the relative entropy between the vacuum state and coherent excitations of a scalar quantum field on a bifurcate Killing horizon is given by the energy flux across the horizon.
- Under the assumption of the Bekenstein-Hawking entropy-area formula, this energy flux is proportional to a variation in the surface area of the horizon cross section.
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- View PDF HTML (experimental) Abstract:We provide arguments indicating that the semiclassical Einstein equations follow from quantum relative entropy and its proportionality to an area variation.
- Using modular theory, we establish that the relative entropy between the vacuum state and coherent excitations of a scalar quantum field on a bifurcate Killing horizon is given by the energy flux across the horizon.
- Under the assumption of the Bekenstein-Hawking entropy-area formula, this energy flux is proportional to a variation in the surface area of the horizon cross section.
Sources: Arxiv