Built on

R. Penrose, “Gravitational Collapse and Space-Time Singularities,” Phys. Rev. Lett
1965
Earlier work this paper cites.
H. Epstein, V. Glaser, and A. Jaffe, “Nonpositivity of Energy Density in Quantized Field Theories,” Nuovo Cim
1965
Earlier work this paper cites.
S. W. Hawking, “Gravitational Radiation from Colliding Black Holes,” Phys. Rev. Lett
1971
Earlier work this paper cites.
Cambridge University Press, 1973
S. W. Hawking and G. F. R. Ellis, The Large Scale Structure of Space-Time · 1973
Earlier work this paper cites.
J. D. Bekenstein, “Black Holes and Entropy,” Phys. Rev
1973
Earlier work this paper cites.
R. M. Wald and U. Yurtsever, “General proof of the averaged null energy condition for a massless scalar field in two-dimensional curved space-time,” Phys. Rev
1991
Earlier work this paper cites.
S. W. Hawking, “The Chronology Protection Conjecture,” Phys. Rev
1992
Earlier work this paper cites.
P. Martín-Moruno and M. Visser, “Classical and quantum flux energy conditions for quantum vacuum states,” Phys. Rev
Original
1993
Earlier work this paper cites.
D. Wands, “Extended gravity theories and the Einstein-Hilbert action,” Class. Quant. Grav
1994
Earlier work this paper cites.
J. L. Friedman, K. Schleich, and D. M. Witt, “Topological censorship,” Phys. Rev. Lett
1995
Earlier work this paper cites.
L. H. Ford and T. A. Roman, “Averaged Energy Conditions and Quantum Inequalities,” Phys. Rev
1995
Earlier work this paper cites.
L. H. Ford and T. A. Roman, “The Quantum Interest Conjecture,” Phys. Rev
1999
Earlier work this paper cites.
R. Bousso, “A Covariant entropy conjecture,” JHEP
1999
Earlier work this paper cites.
E. E. Flanagan, D. Marolf, and R. M. Wald, “Proof of classical versions of the Bousso entropy bound and of the generalized second law,” Phys. Rev
2000
Earlier work this paper cites.
S. de Haro, S. N. Solodukhin, and K. Skenderis, “Holographic reconstruction of space-time and renormalization in the AdS / CFT correspondence,” Commun. Math. Phys
2001
Earlier work this paper cites.
A. Ashtekar, C. Beetle, and J. Lewandowski, “Geometry of generic isolated horizons,” Class. Quant. Grav
2002
Earlier work this paper cites.
N. Graham and K. D. Olum, “Achronal averaged null energy condition,” Phys. Rev
Original
2007
Earlier work this paper cites.
V. E. Hubeny, M. Rangamani, and T. Takayanagi, “A Covariant holographic entanglement entropy proposal,” JHEP
Original
2007
Earlier work this paper cites.

Similar

A. Schwimmer and S. Theisen, “Entanglement Entropy, Trace Anomalies and Holography,” Nucl. Phys
Original
2008
Cited alongside, same era.
J. Oliva and S. Ray, “Classification of Six Derivative Lagrangians of Gravity and Static Spherically Symmetric Solutions,” Phys. Rev
Original
2010
Cited alongside, same era.
L.-Y. Hung, R. C. Myers, and M. Smolkin, “Some Calculable Contributions to Holographic Entanglement Entropy,” JHEP
Original
2011
Cited alongside, same era.
V. E. Hubeny and M. Rangamani, “Causal Holographic Information,” JHEP
Original
2012
Cited alongside, same era.
B. Czech, J. L. Karczmarek, F. Nogueira, and M. Van Raamsdonk, “The Gravity Dual of a Density Matrix,” Class. Quant. Grav

Then

W. R. Kelly and A. C. Wall, “Holographic proof of the averaged null energy condition,” Phys. Rev
Original
2015
Later among the works it cites.
N. Engelhardt and A. C. Wall, “Quantum Extremal Surfaces: Holographic Entanglement Entropy Beyond the Classical Regime,” JHEP
Original
2015
Later among the works it cites.
A. C. Wall, “A Second Law for Higher Curvature Gravity,” Int. J. Mod. Phys
Original
2015
Later among the works it cites.
R.-X. Miao and W.-z. Guo, “Holographic Entanglement Entropy for the Most General Higher Derivative Gravity,” JHEP
Original
2015
Later among the works it cites.
R. Bousso, Z. Fisher, S. Leichenauer, and A. C. Wall, “Quantum focusing conjecture,” Phys. Rev

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Reading the bibliography…

2017

The Quantum Null Energy Condition in Curved Space

Fu, Zicao, Koeller, Jason, Marolf, Donald

Understand

The quantum null energy condition (QNEC) is a conjectured bound on components $(T_{kk} = T_{ab} k^a k^b$) of the stress tensor along a null vector $k^a$ at a point $p$ in terms of a second $k$-derivative of the von Neumann entropy $S$ on one side of a null congruence $N$ through $p$ generated by $k^a$.

The conjecture has been established for super-renormalizeable field theories at points $p$ that lie on a bifurcate Killing horizon with null tangent $k^a$ and for large-N holographic theories on flat space.
While the Koeller-Leichenauer holographic argument clearly yields an inequality for general $(p,k^a)$, more conditions are generally required for this inequality to be a useful QNEC.
For $d\le 3$, for arbitrary backgroud metric satisfying the null convergence condition $R_{ab} k^a k^b \ge 0$, we show that the QNEC is naturally finite and independent of renormalization scheme when the expansion $\theta$ and shear $\sigma_{ab}$ of $N$ at point $p$ satisfy $\theta |_p= \dot{\theta}|_p =0$, $\sigma_{ab}|_p=0$.