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We argue that ``effective'' superluminal travel, potentially caused by the tipping over of light cones in Einstein gravity, is always associated with violations of the null energy condition (NEC). This is most easily seen by working…

General Relativity and Quantum Cosmology · Physics 2009-10-31 Matt Visser , Bruce Bassett , Stefano Liberati

A null line is a complete achronal null geodesic. It is proven that for any quantum fields minimally coupled to semiclassical Einstein gravity, the averaged null energy condition (ANEC) on null lines is a consequence of the generalized…

General Relativity and Quantum Cosmology · Physics 2010-04-06 Aron C. Wall

We prove the Quantum Null Energy Condition (QNEC), a lower bound on the stress tensor in terms of the second variation in a null direction of the entropy of a region. The QNEC arose previously as a consequence of the Quantum Focussing…

High Energy Physics - Theory · Physics 2016-01-20 Raphael Bousso , Zachary Fisher , Jason Koeller , Stefan Leichenauer , Aron C. Wall

The Averaged Null Energy Condition (ANEC) states that the integral along a complete null geodesic of the projection of the stress-energy tensor onto the tangent vector to the geodesic cannot be negative. ANEC can be used to rule out…

General Relativity and Quantum Cosmology · Physics 2015-07-23 Eleni-Alexandra Kontou

We investigate whether the null energy, averaged over some region of spacetime, is bounded below in QFT. First, we use light-sheet quantization to prove a version of the "Smeared Null Energy Condition" (SNEC) proposed in [1], applicable for…

High Energy Physics - Theory · Physics 2021-08-16 Jackson R. Fliss , Ben Freivogel

Energy conditions are attempts to summarise the properties of realistic descriptions of matter via constraints on the energy-momentum tensor. This is, for example, useful when one wants to understand the types of spacetime geometry that can…

High Energy Physics - Theory · Physics 2024-11-19 Hidde Stoffels

We recently showed how it is possible to use a cubic Galileon action to construct classical cosmological solutions that enter a contracting null energy condition (NEC) violating phase, bounce at finite values of the scale factor and exit…

General Relativity and Quantum Cosmology · Physics 2020-11-19 Anna Ijjas , Paul J. Steinhardt

We study the Null Energy Condition (NEC) arising from the Virasoro constraint on the string worldsheet. We then analyze how the NEC in the external spacetime directions emerges under general time-dependent string compactifications. Finally,…

High Energy Physics - Theory · Physics 2026-03-13 Mir Mehedi Faruk

The Improved Quantum Null Energy Condition (INEC) was recently derived from the (restricted) quantum focusing conjecture (QFC), and is a statement about the energy-momentum tensor (EMT) of field theories in Minkowski space-time. It is a…

High Energy Physics - Theory · Physics 2026-01-28 Ido Ben-Dayan , Ayushi Srivastava

Null Energy Condition (NEC) requires the equation of state (EoS) of the universe $w_u$ satisfy $w_u\geq-1$, which implies, for instance in a universe with matter and dark energy dominating…

General Relativity and Quantum Cosmology · Physics 2008-10-28 Taotao Qiu , Yi-Fu Cai , Xin-Min Zhang

The averaged null energy condition (ANEC) requires that the integral over a complete null geodesic of the stress-energy tensor projected onto the geodesic tangent vector is never negative. This condition is sufficient to prove many…

General Relativity and Quantum Cosmology · Physics 2008-11-26 Noah Graham , Ken D. Olum

In discussions of Bousso's Covariant Entropy Bound, the Null Energy Condition is always assumed, as a sufficient {\em but not necessary} condition which helps to ensure that the entropy on any lightsheet shall necessarily be finite. The…

High Energy Physics - Theory · Physics 2010-12-23 Brett McInnes

The Quantum Null Energy Condition (QNEC) is a new local energy condition that a general Quantum Field Theory (QFT) is believed to satisfy, relating the classical null energy condition (NEC) to the second functional derivative of the…

High Energy Physics - Theory · Physics 2018-07-04 Christian Ecker , Daniel Grumiller , Wilke van der Schee , Philipp Stanzer

The quantum null energy condition (QNEC) is a lower bound on the expectation value of the null-null component of the energy-momentum tensor in terms of null variations of the entanglement entropy. A stronger version of the QNEC (the primary…

High Energy Physics - Theory · Physics 2025-06-17 Tanay Kibe , Pratik Roy

The null energy condition (NEC) is a cornerstone of general relativity, and its violation could leave observable imprints in the cosmic gravitational wave spectrum. Theoretical models suggest that NEC violations during inflation can amplify…

General Relativity and Quantum Cosmology · Physics 2025-03-28 Zu-Cheng Chen , Lang Liu

Inflation and dark energy (DE), both featuring accelerated expansion, are crucial components of modern cosmology. As indicated by singularity theorems, null energy condition (NEC) violation is essential for resolving the initial singularity…

General Relativity and Quantum Cosmology · Physics 2025-12-08 Gen Ye , Yong Cai

The Averaged Null Energy Condition (ANEC) requires that the average along a complete null geodesic of the projection of the stress-energy tensor onto the geodesic tangent vector can never be negative. It is sufficient to rule out many…

General Relativity and Quantum Cosmology · Physics 2008-11-26 Christopher J. Fewster , Ken D. Olum , Michael J. Pfenning

The violation of the null energy condition (NEC) may play a crucial role in enabling a scalar field to climb over high potential barriers, potentially significant in the very early universe. We propose a single-field model where the…

Cosmology and Nongalactic Astrophysics · Physics 2024-10-01 Shi Pan , Yong Cai , Yun-Song Piao

Energy conditions, especially the null energy condition (NEC), are generically imposed on solutions to retain a physically sensible classical field theory and they also play an important role in the AdS/CFT duality. Using this duality, we…

High Energy Physics - Theory · Physics 2021-11-03 Carlos Hoyos , Niko Jokela , Jose Manuel Penín , Alfonso V. Ramallo , Javier Tarrío

We analyze four-dimensional Friedmann-Lemaitre-Robertson-Walker cosmologies in type IIB, arising from a M-theory dual, and find that the null energy condition (NEC) has to be obeyed by them (except for the negatively curved case) in order…

High Energy Physics - Theory · Physics 2021-11-02 Heliudson Bernardo , Suddhasattwa Brahma , Keshav Dasgupta , Mir Mehedi Faruk , Radu Tatar