The Return of the Singularities: Applications of the Smeared Null Energy  Condition

Freivogel, Ben; Kontou, Eleni-Alexandra; Krommydas, Dimitrios

doi:10.21468/scipostphys.13.1.001

Cited by 8 publications

(8 citation statements)

References 59 publications

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“…In Appendix B we explore one "light-ray limit" of the DSNEC in showing how to reproduce the SNEC. The SNEC has been used as an assumption to a semiclassical singularity theorem for null geodesic incompleteness [16]. However in the context of field theory alone, the SNEC bound is not very useful as one must then make sense of the UV cutoff.…”

Section: Discussionmentioning

confidence: 99%

“…The first semiclassical singularity theorem for timelike geodesic incompleteness was recently proven [26] and the required initial contraction estimated for cosmological spacetimes. An analogous theorem for null geodesic incompleteness was proven using SNEC as an assumption [16]. While we do not prove a singularity theorem in this work, the derivation of DSNEC is partly inspired by the need to have a semiclassical replacement of the NEC as an assumption to singularity theorems.…”

Section: Relation To Previous Workmentioning

confidence: 94%

“…• Null QEIs: The first null QEIs bounds were obtained in two spacetime dimensions, starting with Flanagan [14] for free fields in flat and curved spacetimes. Fewster and Hollands [15] proved a null QEI for classes of interacting conformal field theories (CFTs), a result recently generalized to curved spacetimes [16].…”

Section: Relation To Previous Workmentioning

confidence: 99%

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The double smeared null energy condition

2023

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The null energy condition (NEC), an important assumption of the Penrose singularity theorem, is violated by quantum fields. The natural generalization of the NEC in quantum field theory, the renormalized null energy averaged over a finite null segment, is known to be unbounded from below. Here, we propose an alternative, the double smeared null energy condition (DSNEC), stating that the null energy smeared over two null directions has a finite lower bound. We rigorously derive DSNEC from general worldvolume bounds for free quantum fields in Minkowski spacetime. Our method allows for future systematic inclusion of curvature corrections. As a further application of the techniques we develop, we prove additional lower bounds on the expectation values of various operators such as conserved higher spin currents. DSNEC provides a natural starting point for proving singularity theorems in semi-classical gravity.

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Section: Discussionmentioning

confidence: 99%

Section: Relation To Previous Workmentioning

confidence: 94%

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The double smeared null energy condition

2023

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“…Even the weakest classical energy condition, the null energy condition (NEC), is known to be violated once quantum effects are considered. It is possible to prove singularity theorems assuming only the averaged energy conditions [41][42][43][44], integrated over some regions instead of being valid pointwise, which are believed to hold at the semi-classical level. (Even taking into account Hawking evaporation, which of course violates NEC, a singularity theorem can still be proved [45].)…”

Section: The Roles Of Singularities and Why They Might Persist In Qua...mentioning

confidence: 99%

On Black Hole Thermodynamics, Singularity, and Gravitational Entropy

Ong

2022

Preprint

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Black holes were found to possess properties that mirror ordinary thermodynamical systems in the landmark paper by Bardeen, Carter and Hawking almost half a century ago. Since then much progress has been made, but many fundamental issues remain. For example, what are the underlying degrees of freedom of a black hole horizon that give rise to said thermodynamical properties? Furthermore, classical black holes also harbor a spacetime singularity. Although it is often believed that quantum gravity would "cure" the singularity, as emphasized by Penrose, this viewpoint requires a deeper examination. In this review, I will examine the possibility that singularities remain in quantum gravity, the roles they may play, and the possible links between singularity and black hole thermodynamics. I will also discuss how -inspired by Penrose's Weyl curvature hypothesis -gravitational entropy for a black hole can be defined using curvature invariants, and the surprising implication that the entropy of black holes in different theories of gravity are different manifestations of spacetime curvature, i.e., their underlying microstructures could be different. Finally, I review the "Hookean law" recently established for singly rotating Myers-Perry black holes (including 4-dimensional Kerr black holes) that connect black hole fragmentation -a consequence of the second law of black hole thermodynamicswith the maximum "Hookean force", as well as with the thermodynamic geometry of Ruppeiner. This also suggests a new way to study black hole microstructures, and hints at the possibility that some black holes are beyond the Hookean regime (and thus have different microstructures). While examining the remarkable connections between black hole thermodynamics, spacetime singularities and cosmic censorship, as well as gravitational entropy, I shall point out some subtleties, provide some new thoughts, and raise some hard but fundamental questions, including whether black hole thermodynamics is really just "ordinary thermodynamics" or something quite different.

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“…The idea is to first replace the pointwise energy conditions of the classical theorems with a condition of the form of QEIs [13,14]. Then show that there exist quantum fields that obey such a condition [15,16]. We should note that the singularity theorems (as the area theorem) use a geometric condition, the null (or timelike) convergence condition…”

Section: Introductionmentioning

confidence: 99%

A generalization of the Hawking black hole area theorem

Kontou,

Sacchi

2024

Gen Relativ Gravit

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Hawking’s black hole area theorem was proven using the null energy condition (NEC), a pointwise condition violated by quantum fields. The violation of the NEC is usually cited as the reason that black hole evaporation is allowed in the context of semiclassical gravity. Here we provide two generalizations of the classical black hole area theorem: first, a proof of the original theorem with an averaged condition, the weakest possible energy condition to prove the theorem using focusing of null geodesics. Second, a proof of an area-type result that allows for the shrinking of the black hole horizon but provides a bound on it. This bound can be translated to a bound on the black hole evaporation rate using a condition inspired from quantum energy inequalities. Finally, we show how our bound can be applied to two cases that violate classical energy conditions.

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The Return of the Singularities: Applications of the Smeared Null Energy Condition

Cited by 8 publications

References 59 publications

The double smeared null energy condition

The double smeared null energy condition

On Black Hole Thermodynamics, Singularity, and Gravitational Entropy

A generalization of the Hawking black hole area theorem

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