Zicao Fu

We construct traverseable wormholes by starting with simple four-dimensional classical solutions respecting the null energy condition and containing a pair of oppositely charged black holes connected by a non-traverseable wormhole. We then consider the perturbative back-reaction of bulk quantum fields in Hartle–Hawking states. Our geometries have zero cosmological constant and are asymptotically flat except for a cosmic string stretching to infinity that is used to hold the black holes apart. Another cosmic string wraps the non-contractible cycle through the wormhole, and its quantum fluctuations provide the negative energy needed for traversability. Our setting is closely related to the non-perturbative construction of Maldacena, Milekhin, and Popov (MMP), but the analysis is complementary. In particular, we consider cases where back-reaction slows, but fails to halt, the collapse of the wormhole interior, so that the wormhole is traverseable only at sufficiently early times. For non-extremal backgrounds, we find the integrated null energy along the horizon of the classical background to be exponentially small, and thus traversability to be exponentially fragile. Nevertheless, if there are no larger perturbations, and for appropriately timed signals, a wormhole with mouths separated by a distance d becomes traverseable with a minimum transit time . Thus is smaller than for the eternally traverseable MMP wormholes by more than a factor of 2, and approaches the value that, at least in higher dimensions, would be the theoretical minimum. For contrast we also briefly consider a ‘cosmological wormhole’ solution where the back-reaction has the opposite sign, so that negative energy from quantum fields makes the wormhole harder to traverse.

We use Euclidean path integrals to explore the set of bulk asymptotically AdS spacetimes with good CFT duals. We consider simple bottom-up models of bulk physics defined by Einstein-Hilbert gravity coupled to thin domain walls and restrict to solutions with spherical symmetry. The cosmological constant is allowed to change across the domain wall, modeling more complicated Einstein-scalar systems where the scalar potential has multiple minima. In particular, the cosmological constant can become positive in the interior. However, in the above context, we show that inflating bubbles are never produced by smooth Euclidean saddles to asymptotically AdS path integrals. The obstacle is a direct parallel to the well-known obstruction to creating inflating universes by tunneling from flat space. In contrast, we do find good saddles that create so-called "bag-of-gold" geometries which, in addition to their single asymptotic region, also have an additional large semi-classical region located behind both past and future event horizons. Furthermore, without fine-tuning model parameters, using multiple domain walls we find Euclidean geometries that create arbitrarily large bags-of-gold inside a black hole of fixed horizon size, and thus at fixed Bekenstein-Hawking entropy. Indeed, with our symmetries and in our class of models, such solutions provide the unique semi-classical saddle for appropriately designed (microcanonical) path integrals. This strengthens a classic tension between such spacetimes and the CFT density of states, similar to that in the black hole information problem.

We use Euclidean path integrals to explore the set of bulk asymptotically AdS spacetimes with good CFT duals. We consider simple bottom-up models of bulk physics defined by Einstein-Hilbert gravity coupled to thin domain walls and restrict to solutions with spherical symmetry. The cosmological constant is allowed to change across the domain wall, modeling more complicated Einstein-scalar systems where the scalar potential has multiple minima. In particular, the cosmological constant can become positive in the interior. However, in the above context, we show that inflating bubbles are never produced by smooth Euclidean saddles to asymptotically AdS path integrals. The obstacle is a direct parallel to the well-known obstruction to creating inflating universes by tunneling from flat space. In contrast, we do find good saddles that create so-called “bag-of-gold” geometries which, in addition to their single asymptotic region, also have an additional large semi-classical region located behind both past and future event horizons. Furthermore, without fine-tuning model parameters, using multiple domain walls we find Euclidean geometries that create arbitrarily large bags-of-gold inside a black hole of fixed horizon size, and thus at fixed Bekenstein-Hawking entropy. Indeed, with our symmetries and in our class of models, such solutions provide the unique semi-classical saddle for appropriately designed (microcanonical) path integrals. This strengthens a classic tension between such spacetimes and the CFT density of states, similar to that in the black hole information problem.

We describe a class of wormholes that generically become traversable after incorporating gravitational back-reaction from linear quantum fields satisfying appropriate (periodic or anti-periodic) boundary conditions around a non-contractible cycle, but with natural boundary conditions at infinity (i.e., without additional boundary interactions). The class includes both asymptotically flat and asymptotically AdS examples. Simple asymptotically AdS$_3$ or asymptotically AdS$_3 \times S^1$ examples with a single periodic scalar field are then studied in detail. When the examples admit a smooth extremal limit, our perturbative analysis indicates the back-reacted wormhole remains traversable at later and later times as this limit is approached. This suggests that a fully non-perturbative treatment would find a self-supporting eternal traversable wormhole. While the general case remains to be analyzed in detail, the likely relation of the above effect to other known instabilities of extreme black holes may make the construction of eternal traversable wormholes more straightforward than previously expected.

We describe a class of wormholes that generically become traversable after incorporating gravitational back-reaction from linear quantum fields satisfying appropriate (periodic or anti-periodic) boundary conditions around a non-contractible cycle, but with natural boundary conditions at infinity (i.e. without additional boundary interactions). The class includes both asymptotically flat and asymptotically AdS examples. Related constructions can also be performed in asymptotically de Sitter space or in other closed cosmologies. Simple asymptotically AdS ₃ or asymptotically AdS examples with a single periodic scalar field are then studied in detail. When the examples admit a smooth extremal limit, our perturbative analysis indicates the back-reacted wormhole remains traversable at later and later times as this limit is approached. This suggests that a fully non-perturbative treatment would find a self-supporting eternal traversable wormhole. While the general case remains to be analyzed in detail, the likely relation of the above effect to other known instabilities of extreme black holes may make the construction of eternal traversable wormholes more straightforward than previously expected.

The Hubeny-Rangamani causal holographic information (CHI) defined by a region R of a holographic quantum field theory (QFT) is a modern version of the idea that the area of event horizons might be related to an entropy. Here the event horizon lives in a dual gravitational bulk theory with Newton’s constant G _bulk, and the relation involves a factor of 4G _bulk. The fact that CHI is bounded below by the von Neumann entropy S suggests that CHI is coarse-grained. Its properties could thus differ markedly from those of S. In particular, recent results imply that when d ≤ 4 holographic QFTs are perturbatively coupled to d-dimensional gravity, the combined system satisfies the so-called quantum focusing condition (QFC) at leading order in the new gravitational coupling G _d when the QFT entropy is taken to be that of von Neumann. However, by studying states dual to spherical bulk (anti-de Sitter) Schwarschild black holes in the conformal frame for which the boundary is a (2 + 1)-dimensional de Sitter space, we find the QFC defined by CHI is violated even when perturbing about a Killing horizon and using a single null congruence. Since it is known that a generalized second law (GSL) holds in this context, our work demonstrates that the QFC is not required in order for an entropy, or an entropy-like quantity, to satisfy such a GSL.

The quantum null energy condition (QNEC) is a conjectured relation between a null version of quantum field theory energy and derivatives of quantum field theory von Neumann entropy. In some cases, divergences cancel between these two terms and the QNEC is intrinsically finite. We study the more general case here where they do not and argue that a QNEC can still hold for bare (unrenormalized) quantities. While the original QNEC applied only to locally stationary null congruences in backgrounds that solve semiclassical theories of quantum gravity, at least in the formal perturbation theory at a small Planck length, the quantum focusing conjecture can be viewed as the special case of our bare QNEC for which the metric is on shell.