The Quantum Focusing Conjecture and the Improved Energy Condition

Abstract

By rearranging its terms, the Quantum Focusing Conjecture (QFC) can be viewed as a quantum energy condition, and we can consider various limits. A recent restricted version is a limiting form where the quantum focusing vanishes $\Theta \to 0$, and has been proven for Braneworld scenario. As a result, we derive an improved quantum null energy condition (INEC) $T_{kk}\ge \frac{\hslash }{2\pi \mathcal{A}}\left(S_{out}^{\prime \prime }-\frac{1}{2}\theta S_{out}^{\prime }\right)$, that can be proven with field theory techniques. We sketch the beginning of a proof, and briefly discuss possible interpretations in the absence of one.

5 pages, 2 figures