Traversable wormholes satisfying the weak energy condition in third-order Lovelock gravity

TL;DR

This paper constructs traversable wormhole solutions in third-order Lovelock gravity that satisfy the weak energy condition, revealing conditions under which normal matter can support such wormholes in higher-dimensional spacetime models.

Contribution

It provides explicit wormhole solutions in third-order Lovelock gravity with matter satisfying energy conditions, linking wormhole existence to a negative effective cosmological constant.

Findings

Wormhole solutions satisfy energy conditions for specific parameters.

Existence of traversable wormholes implies a negative effective cosmological constant.

Solutions include asymptotically flat and non-flat wormholes supported by normal matter.

Abstract

In this paper, we consider third order Lovelock gravity with a cosmological constant term in an n-dimensional spacetime $\mathcal{M}^{4}\times \mathcal{K}^{n-4}$, where $\mathcal{K}^{n-4} $ is a constant curvature space. We decompose the equations of motion to four and higher dimensional ones and find wormhole solutions by considering a vacuum $\mathcal{K}^{n-4} $ space. Applying the latter constraint, we determine the second and third order Lovelock coefficients and the cosmological constant in terms of specific parameters of the model, such as the size of the extra dimensions. Using the obtained Lovelock coefficients and $\Lambda$, we obtain the 4-dimensional matter distribution threading the wormhole. Furthermore, by considering the zero tidal force case and a specific equation of state, given by $\rho =(\gamma p-\tau )/[\omega (1+\gamma )]$, we find the exact solution for the shape function which represents both asymptotically flat and non-flat wormhole solutions. We show explicitly that these wormhole solutions in addition to traversibility satisfy the energy conditions for suitable choices of parameters and that the existence of a limited spherically symmetric traversable wormhole with normal matter in a 4-dimensional spacetime, implies a negative effective cosmological constant.