Wormholes in Dilatonic Einstein-Gauss-Bonnet Theory

Abstract: We construct traversable wormholes in dilatonic Einstein-Gauss-Bonnet theory in four spacetime dimensions, without needing any form of exotic matter. We determine their domain of existence, and show that these wormholes satisfy a generalised Smarr relation. We demonstrate linear stability with respect to radial perturbations for a subset of these wormholes.

Wormholes in Dilatonic Einstein-Gauss-Bonnet Theory

The paper "Wormholes in Dilatonic Einstein-Gauss-Bonnet Theory" by Panagiota Kanti, Burkhard Kleihaus, and Jutta Kunz explores traversable wormhole solutions within the framework of Dilatonic Einstein-Gauss-Bonnet (DEGB) theory in four-dimensional spacetime. This research contributes significantly to the field of theoretical physics by illustrating the ability to construct stable, traversable wormholes without relying on exotic matter.

Context and Motivation

The study of wormholes in gravity theories stems from early investigations by Einstein and Rosen, and later by Wheeler, spotlighting wormholes' potential to act as bridges between different universes or distant regions within a single universe. Previous models, particularly Schwarzschild wormholes, posed limitations due to dynamic nature and instability under perturbations, leading to proposals involving exotic matter to support traversable configurations. However, this paper circumvents these challenges by invoking the DEGB theory, derived from heterotic string theory, which introduces higher-curvature gravitational terms enhancing potential stability and traversability.

DEGB Theory

DEGB theory expands the conventional Einstein-Hilbert action by including a dilaton field and a Gauss-Bonnet term. The paper employs this modified theory, emphasizing the inherent viability of wormholes supported by these higher-order terms. The effective action considered is:

$$S = \frac{1}{16 \pi}\int d^4x \sqrt{-g} \left[R - \frac{1}{2} \partial_\mu \phi \,\partial^\mu \phi + \alpha e^{-\gamma \phi} R^2_{\rm GB} \right],$$

where $R^2_{\rm GB}$ is the Gauss-Bonnet term involving quadratic curvature contributions, and $\phi$ is the dilaton field that couples exponentially to the Gauss-Bonnet term.

Key Findings

• Existence of Traversable Solutions: The study delivers static, spherically symmetric wormhole solutions within DEGB theory, notably without invoking phantom fields or other exotic matter. The wormhole throat remains open under such configurations, relying purely on the Gauss-Bonnet term.
• Domain of Existence: A detailed numerical analysis reveals the boundary conditions for wormhole solutions, elucidating constraints on the parameters such as $f_0$ (a measure of curvature radius relative to throat radius) and the scaled parameter $\alpha/r_0^2$.
• Stability Analysis: Perturbative stability with respect to radial fluctuations is rigorously examined. It is affirmed that a segment of the parameter space allows for linearly stable wormhole solutions, underscoring practical viability.

Implications and Future Perspectives

The theoretical implications of this study are profound. The existence of traversable wormholes supported by non-exotic, string theory-inspired corrections positions DEGB theory as a promising candidate for revising our understanding of potential methods for connecting distant spacetime regions. While the paper solidly outlines static solutions, the prospects for stationary rotating wormhole solutions suggest intriguing avenues for further exploration.

Furthermore, the astrophysical relevance—looking into the behaviors of such configurations under realistic settings—remains an open yet promising area for future research.

Conclusion

This paper expands the scope of wormhole research within the context of string theory corrections, underscoring the role of DEGB theory in facilitating stable, traversable wormhole structures. The findings challenge traditional perspectives necessitating exotic matter and encourage ongoing investigation into the astrophysical applicability of such solutions.