Lorentzian wormholes in Lovelock gravity

In this paper, we introduce the $n$-dimensional Lorentzian wormhole solutions of third order Lovelock gravity. In contrast to Einstein gravity and as in the case of Gauss-Bonnet gravity, we find that the wormhole throat radius $r_0$ has a lower limit that depends on the Lovelock coefficients, the dimensionality of the spacetime, and the shape function. We study the conditions of having normal matter near the throat, and find that the matter near the throat can be normal for the region $r_0\le r\le r_{\max }$, where $r_{\max }$ depends on the Lovelock coefficients and the shape function. We also find that the third order Lovelock term with negative coupling constant enlarges the radius of the region of normal matter, and conclude that the higher order Lovelock terms with negative coupling constants enlarge the region of normal matter near the throat.

Figure 1

$\rho -\tau$ (solid line), $\rho +p$ (bold line) and $\rho$ (dotted line) vs $r$ for power law shape function with $n=8$, $m=2$, $r_0=.1$, ${\alpha }_2=-.5$, and ${\alpha }_3=-.5$.

Figure 2

$\rho -\tau$ (solid line), $\rho +p$ (bold line) and $\rho$ (dotted line) vs $r$ for power law shape function with $n=8$, $m=2$, $r_0=r_c=.88$, ${\alpha }_2=-1$, and ${\alpha }_3=.2$.

Figure 3

$\rho -\tau$ (solid line), $\rho +p$ (bold line) and $\rho$ (dotted line) vs $r$ for logarithmic shape function with $n=8$, $r_0=1.1$, ${\alpha }_2=-.5$, and ${\alpha }_3=-.5$.

Figure 4

$\rho -\tau$ (solid line), $\rho +p$ (bold line) and $\rho$ (dotted line) and vs $r$ for hyperbolic shape function with $n=8$, $r_0=r_c=.785$, ${\alpha }_2=-.5$, and ${\alpha }_3=-.5$.

Figure 5

$\rho -\tau$ vs $r$ for hyperbolic shape function with $n=8$, $r_0=.1$, ${\alpha }_2=-.5$, ${\alpha }_3=0$ (solid line) and ${\alpha }_3=-1$ (dotted line).