Wormhole geometries in Einstein-aether theory

TL;DR

This work demonstrates that traversable wormholes in Einstein–aether theory can be supported by ordinary matter under specific combinations of the aether coupling constants. By analyzing static, spherically symmetric wormhole geometries with three distinct coupling-constant classes and three shape functions (power-law, logarithmic, hyperbolic), the authors show that the null and weak energy conditions can be satisfied at the throat and, in one class, throughout the entire spacetime. The results yield explicit constraints on the couplings (e.g., c2>0 in Class I, c3−c4>1/2 in Class II, and −1<c2<0 in Class III) and reveal that energy-condition requirements can be more restrictive than existing bounds. Together, these findings suggest Einstein–aether theory can alleviate the exotic-matter requirement for wormholes and provide testable predictions for Lorentz-violating gravity scenarios.

Abstract

We present the first analysis of traversable wormhole solutions within the framework of Einstein-aether theory. We show that the corresponding field equations admit three distinct wormhole geometries, obtained by adopting three different classes of combinations for the aether coupling constants. We examine the null and weak energy conditions for three types of wormhole shape functions. Our findings reveal that, in contrast to Einstein gravity, by choosing appropriate parameter values, wormhole geometries can satisfy the energy conditions at the wormhole throat. We also nd that in one class, wormholes can satisfy the energy conditions not only at the wormhole throat but also throughout the entire spacetime. Furthermore, the requirement of energy condition satisfaction, imposes some constraints on the values of aether coupling constants. By comparing these constraints with those previously obtained from theoretical and observational analyses, we nd that the satisfaction of energy conditions put more stringent limits on the allowed values of the aether couplings.

Figures (12)

• Figure 1: The blue regions in these figures indicate where ${\rm EC1}>0$, ${\rm EC2}>0$, and ${\rm EC3}>0$ are satisfied simultaneously, meaning that the weak and null energy conditions are respected for the wormhole solutions in the EA theory. In these figures, we set $r_0=1$ and $d=5$. Fig. (a) shows that, by varying the coupling $c_2$, the WEC is satisfied near the wormhole throat if $c_2>0$ with $n=1$. In Fig. (b) the variation of the exponent $n$ versus $c_2$ is depicted for the radial distance $r=1.5$, and it is evident that the WEC is also satisfied for $c_2>0$.
• Figure 2: Satisfaction of the NEC and WEC for arbitrary values of the radial coordinate $r$ in the wormhole solutions of the EA theory is illustrated in these figures, plotted for $c_2=\frac{1}{2}, d=5$, and $r_0=1$. In (a), the blue regions indicate where ${\rm EC2}>0$ and ${\rm EC3}>0$, showing that the NEC is satisfied for appropriate values of $n$ over nearly all radial distances outside the wormhole throat. A small gap appears around $r=2.5$ where the NEC is violated; however, within this gap, the NEC is satisfied for negative values of $c_2$ in the range $-\frac{2}{3}<c_2<0$. A similar analysis is presented in (b) for the WEC, which is satisfied over a more limited region compared to the NEC.
• Figure 3: Satisfaction of the energy conditions for arbitrary values of the radial coordinate $r$ in the case of wormhole solutions with a logarithmic shape function in the EA theory. The blue regions in (a) indicate where ${\rm EC2}>0$ and ${\rm EC3}>0$ simultaneously, implying that the NEC is satisfied. In (b), the blue regions correspond to the domain where all EC1, EC2, EC3 are positive, meaning that the WEC is respected. Our analysis shows that, for appropriate positive values of $c_2>0$, both the NEC and WEC are satisfied for nearly all radial distances outside the wormhole throat. These figures are plotted for $r_0=2$; however, we have verified that varying $r_0$ (within the bound $r_0>1$) does not significantly affect this overall behavior.
• Figure 4: The wormhole solutions with the hyperbolic shape function satisfy the NEC (panel a) and WEC (panel b) in the blue regions. By choosing a suitable value of the coupling constant of the EA theory such that $c_2>0$, the NEC is satisfied both at the wormhole throat and at large radial distances. The WEC is also respected around the wormhole throat for appropriate values within the bound $c_2>0$. In these figures we set $r_0=2$; however varying $r_0$ within the bound $r_0>0$ does not alter this overall behavior.
• Figure 5: The inequalities ${\rm EC1}>0$, ${\rm EC2}>0$, and ${\rm EC3}>0$ are satisfied simultaneously in the blue regions, indicating that both the WEC and NEC are respected for the wormhole solutions with the power-law shape function in the EA theory. Here, we set $r_0=1$, $n=1$, and $e=3$. It is evident that, except for a narrow interval around $r=2$ (twice the throat radius), the WEC and NEC are satisfied throughout the spacetime for the wormhole solutions of the EA theory, provided that the combination $c_3-c_4>0$ .