Wormholes in Einstein-Born-Infeld theory

Spherically symmetric thin-shell wormholes are studied within the framework of Einstein-Born-Infeld theory. We analyze the exotic matter content, and find that for certain values of the Born-Infeld parameter the amount of exotic matter on the shell can be reduced in relation to the Maxwell case. We also examine the mechanical stability of the wormhole configurations under radial perturbations preserving the spherical symmetry. In addition, in the Appendix the repulsive or attractive character of the wormhole geometries is briefly discussed.

Figure 1

We show the position of the horizons for $m=1$ and $q=1$. The RN geometry (dot-dashed line) corresponds to the extremal case, with only one event horizon, while the other lines show how the position of the horizons changes with the parameter $b\in [1,10]$.

Figure 2

We show the wormhole geometry obtained after performing the cut and paste procedure. The shell on $\Sigma$ is located at the throat radius $r=a$.

Figure 3

We show the energy densities corresponding to wormholes associated to the RN geometry (solid line) and the BI spacetime (dashed line) in terms of the wormhole radius $r_{\mathrm{wh}}$. Here we take $r_{\mathrm{wh}}>r_{\mathrm{hor}}^{+}$ with $r_{\mathrm{hor}}^{+}$ indicating the largest event horizon of both the RN and the BI cases.

Figure 4

We show the stability regions in four different cases: extremal RN with $m=1$, $q=1$ (upper left panel), EBI with $m=1$, $q=1$, $b=1$ (upper right panel), EBI with $m=1$, $q=1$, $b=1.32$ (lower left panel), and EBI with $m=1$, $q=1$, $b=2$ (lower right panel).

Figure 5

We show the stability regions in two extreme cases, corresponding to small charge $q=0.01$ (left panel) and large charge $q=2$ (right panel). In both cases we take $m=b=1$.

Figure 6

We show the regions where the wormholes are attractive or repulsive for $q=m=1$. The dashed zone corresponds to attractive wormholes while the undashed regions are associated to repulsive ones.

Figure 7

We show the regions where the wormholes are attractive or repulsive for $q=m=1$. The dashed zone corresponds to attractive wormholes while the undashed regions are associated to repulsive ones.