# Traversable wormhole Wormholes are **traversable** if one can go in from one side and come out from the other (or *another*, in the case of more than two boundaries). Black holes with multiple entrances are non-traversable wormholes: people can enter from different exterior regions and meet inside, but nobody can come out. Traversable wormholes are hence more interesting than non-traversable ones from a sci-fi perspective: they can be used for space travel. Whether they are efficient or not is another question. Unfortunately, in order to not violate [[0091 Boundary causality|causality]], the wormholes need to be necessarily long so that it takes at least the same amount of time to go through one than to go around. That makes them inefficient transportation portals. Nevertheless, they still have scientific value just like hidden passages do even though it takes longer to follow such paths. It is important to distinguish two slightly different notions of traversable wormholes. We will call them intra-universe and inter-universe ones. An intra-universe traversable wormhole resides in one single universe in the sense that the spacetime only has one asymptotic boundary. An inter-universe traversable wormhole would be a spacetime with more than one asymptotic boundary where signals can travel from one boundary to another. ## Energy conditions ### Classical - all sensible classical matter satisfies [[0480 Null energy condition|NEC]] - topological censorship: [[0480 Null energy condition|NEC]] -> no traversable wormhole ### Quantum - ANEC can be violated - maybe true in general curved spacetime: SCAANEC ### AANEC - [[2007#Graham, Olum]] ### SCAANEC (self-consistent AANEC) - integrating Raychaudhuri -> $\Delta \theta\le-\int\langle T_{++}\rangle d\lambda$ - SCAANEC => $\Delta \theta\le0$ along achronal null geodesics - so, if traversable (which requires $\Delta \theta >0$ because ingoing light rays are converging while outgoing ones are diverging), must be chronal (i.e. have a faster path from outside) ### Casimir - Stability of traversable wormholes depends on Casimir energy. - In practice one has to calculate the contribution of the transverse-traceless component of the metric perturbation on a curved spacetime background. - This implies the study of an eigenvalue equation involving a modified form of the Lichnerowicz operator. - For arbitrary background spacetimes, however, such an operator does not display transverse-traceless properties, a fact that impedes the determination of the eigenvalues. - To circumvent this problem, see [[GarattiniNicolini2021]][](https://arxiv.org/abs/2105.05105) ## Refs - topological censorship - [[1993#Friedman, Schleich, Witt]] - AdS - [[2016#Gao, Jafferis, Wall]] - [[MaldacenaStanfordYang2017]] - [[2018#Maldacena, Qi]] - [[BintanjaEspindolaFreivogelNikolakopoulou2021]][](https://arxiv.org/abs/2102.06628) - eternal from CFT couplings - [[DeBoerJahnkeKimPedraza2022]][](https://arxiv.org/abs/2211.13262) - worldsheet - [[2023#Harvey, Jensen]] - 3d eternal - [[2025#Kawamoto, Maeda, Nakamura, Takayanagi]] - via non-local trace and Janus deformation - flat space - [[MaldacenaMilekhinPopov2018]] - [[FuGrado-WhiteMarolf2019]] - [[2023#Bilotta]]: double-trace deformation to near-horizon, near extremal region of Kerr - creation - [[2019#Horowitz, Marolf, Santos, Wang]] - explicit many-body quantum protocols - [[GaoJafferis2019]]: teleportation in SYK model - [[BrownGharibyanLeichenauerLinNezamiSaltonSusskindSwingleWalter2019]][](https://arxiv.org/abs/1911.06314) - reviews - Master thesis by Miritescu [](https://www.imperial.ac.uk/media/imperial-college/research-centres-and-groups/theoretical-physics/msc/dissertations/2020/Catalina-Miritescu-Dissertation.pdf) - [[Kundu202110]][](https://arxiv.org/pdf/2110.14958.pdf) - variants - multi-boundary - [[AlBalushiWangMarolf2020]] - [[2020#Emparan, Grado-White, Marolf, Tomasevic]] - experimental - [[NezamiLinBrownGharibyanLeichenauerSaltonSusskindSwingleWalter2021]][](https://arxiv.org/pdf/2102.01064.pdf) - [[SchusterKobrinGaoCongKhabiboullineLinkeLukinMonroeYoshidaYao2021]][](https://arxiv.org/pdf/2102.00010.pdf) - [[BintanjaEspindolaFreivogelNikolakopoulou2021]] - the CFT states are simple so maybe realised in labs - entropy - [[ChakrabortyGuhaGoswami2021]][](https://arxiv.org/pdf/2106.16114.pdf): tests a few proposals - other related work - tunnelling through eternal traversable wormhole [[ZhouZhang2020]]@[pdf](https://arxiv.org/pdf/2009.02641.pdf) - higher dim [](https://arxiv.org/abs/2011.13807) - smeared NEC [[FreivogelKontouKrommydas2020]] - relations to bra-ket wormholes, 2 traversable wormholes = 4 [[0201 Sachdev-Ye-Kitaev model|SYK]] [](https://arxiv.org/pdf/2011.12962.pdf) - [[Maeda2021]][](https://arxiv.org/pdf/2107.07052.pdf): violates [[0480 Null energy condition|NEC]] only at Planck scale ![[A0005 Spaceship entering snowy wormhole.png]]\[*A spaceship entering a (hopefully traversable) wormhole that looks manmade.*\]