Ellis–Bronnikov Wormholes in Asymptotically Safe Gravity

Abstract

In this paper, we investigate the simplest wormhole solution—the Ellis–Bronnikov one—in the context of the asymptotically safe gravity (ASG) at the Planck scale. We work with three models, which employ the Ricci scalar, Kretschmann scalar, and squared Ricci tensor to improve the field equations by turning the Newton constant into a running coupling constant. For all the cases, we check the radial energy conditions of the wormhole solution and compare them with those that are valid in general relativity (GR). We verified that asymptotic safety guarantees that the Ellis–Bronnikov wormhole can satisfy the radial energy conditions at the throat radius, r0, within an interval of values of the latter, which is quite different from the result found in GR. Following this, we evaluate the effective radial state parameter, ω(r), at r0, showing that the quantum gravitational effects modify Einstein’s field equations in such a way that it is necessary to have a very exotic source of matter to generate the wormhole spacetime–phantom or quintessence-like matter. This occurs within some ranges of the throat radii, even though the energy conditions are or are not violated there. Finally, we find that, although at r0 we have a quintessence-like matter, upon growing r, we inevitably came across phantom-like regions. We speculate whether such a phantom fluid must always be present in wormholes in the ASG context or even in more general quantum gravity scenarios.

Schwarzschild-like Wormholes in Asymptotically Safe Gravity

“…These features have been shown in Figure 1 for the squared Ricci tensor model, and in Figure 2 for the Kretschmann model, where we basically have the same behavior. These results are analogous to those found for other asymptotically flat wormholes, such as Ellis-Bronnikov one, studied in [71], where the authors showed that is the possible that the radial energy conditions are satisfied nearby the throat, but the presence of exotic matter, such as phantom or quintessence, is always necessary.…”

“…As we can see, the quantum improvement leads to the inevitable presence of phantomlike matter regions as source to generate the wormhole spacetime. These results are very similar with the Ellis-Bronnikov wormhole [72][73][74] case, which was studied by Alencar et al [71]. They found that for the ASG context the radial energy conditions are satisfied in the throat for a range of values of r 0 , and for this is necessary a exotic matter, like quintessencial fluid threading the wormhole throat.…”

“…In order to test this, the authors of Ref. [71] studied the quantum improvement of the Ellis-Bronnikov wormhole due to ASQG. They found that, despite of the fact that nonexotic matter is possible at the wormhole throat, in other regions of spacetime a Phantom matter is necessary.…”

On the traversability of wormhole solutions in asymptotically safe gravity

“…In [49], the authors have shown that improved pseudospherical wormholes could be traversible with nonexotic matter, while spherical ones could not. In [50], the authors investigated the Ellis-Bronnikov wormhole solution in the ASG context and it was showed that, for a perfect fluid, it is not possible to get a traversible Ellis-Bronnikov wormhole without exotic matter, and in order to be traversible the wormhole requires very exotic phantom-like matter in some regions of the modified spacetime and even at the throat. And more recently, it was showed in [51] that Schwarzschild-like wormholes exhibit the possibility of having nonexotic matter as source for certain values of the radial coordinate.…”

Exact solution for a traversable wormhole in a curvature-coupled antisymmetric background field

“…Classical and quantum-modified theories of gravity, applied in the study of wormholes, were quite discussed in the literature [27][28][29][30][31]. Still concerning such objects, a class of modified theories as those embodying background fields coupled to the gravity, with spontaneously Lorentz symmetry breaking, were analyzed in Refs.…”