Traversable Asymptotically Flat Wormholes with Short Transit Times (1908.03273v2)

Abstract: We construct traversable 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-traversable 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 traversable 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 traversable with a minimum transit time $t_{\text{min transit}} = d + \text{logs}$. Thus $\frac{t_{\text{min transit}}}{d}$ is smaller than for the eternally traversable 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.

• The paper demonstrates that negative integrated null energy from quantum back-reaction enables transient traversability in asymptotically flat wormholes.
• The paper uses a perturbative approach with cosmic strings to stabilize oppositely charged black holes while inducing essential quantum fluctuations for short transit times.
• The paper finds that transit times can approach theoretical minima, highlighting potential quantum gravity applications alongside exponential fragility challenges.

Overview of "Traversable Asymptotically Flat Wormholes with Short Transit Times"

The paper, authored by Zicao Fu, Brianna Grado-White, and Donald Marolf, explores the intricate domain of traversable wormholes within asymptotically flat spacetimes. Building upon the classical framework of general relativity, this paper primarily investigates the influence of quantum field perturbations on wormhole geometries initially comprised of oppositely charged black holes connected by non-traversable wormholes under the constraint of the null energy condition (NEC).

Methodology

The authors employ a perturbative approach to explore how the back-reaction from quantum fields, specifically described in Hartle-Hawking states, modifies these classical wormholes. Unlike constructions within anti-de Sitter (AdS) space that utilize explicit non-local couplings between boundary conditions, this work focuses on asymptotically flat spacetimes. Asymmetry is introduced via cosmic strings, which not only hold the black hole pairs at a fixed distance but also induce quantum fluctuations necessary to achieve traversability. Notably, the paper draws parallels with the Maldacena, Milekhin, and Popov (MMP) model but extends the analysis to different geometric backgrounds and transient states where the wormhole becomes traversable only for a finite duration.

Results

The central finding is that the integrated null energy along the black hole horizon remains exceptionally small but negative, facilitating a traversable structure. Specifically, the ratio of minimum transit time $t_{\text{min transit}}$ to the separation distance $d$ for signals through the wormhole is reduced to nearly half compared to the eternally traversable MMP wormholes. At large separations, the transit time approaches the theoretical minimum expected for higher-dimensional analogues, namely $t_{\text{min transit}} \approx d$.

The practical implication is the formation of wormholes that allow for relatively rapid transit across their mouths, though this is at the cost of "exponential fragility". Indeed, maintaining salient traversability demands careful management of perturbations, as even minuscule additional energy perturbations may disrupt the process.

Implications and Future Directions

The paper presents a critical step in understanding the dynamics of traversable wormholes outside the AdS context, laying groundwork for potential applications in quantum gravity, particularly in the context of holography and information paradox discussions. The manifested exponentially fragile nature of these constructs opens up intriguing questions regarding the underlying balance of energies and the structural stability of wormholes once perturbed beyond minute levels. Further exploration of stable configurations, potentially those anchored by additional cosmic constructs, could be invaluable for addressing these stability concerns.

Additionally, the divergent nature of results in the extremal limit prompts the need for a non-perturbative examination, which could reveal additional insights into the capacity of such structures to remain traversable indefinitely. Moreover, expanding the investigation to encompass varying spacetime dimensions or incorporating additional quantum field contributions could further refine theoretical predictions about possible exotic spacetime topologies.

In essence, while the traversable wormholes described require complex configurations and are sensitive to perturbations, they embody an important theoretical concept closer to enabling transient bridges across spacetime that adhere to the constraints imposed by general relativity and quantum theory. The paper propels forward our conceptual grasp of such entities and sets the stage for deeper inquiries into their viability and implications within broader physical theories.