Schwarzschild-like Wormholes in Asymptotically Safe Gravity

TL;DR

This paper investigates Schwarzschild-like wormholes within Asymptotically Safe Gravity, revealing that quantum corrections influence energy conditions and matter types, often necessitating exotic or phantom matter, especially in non-asymptotically flat cases.

Contribution

It introduces a framework for analyzing wormholes in ASG, incorporating renormalization group corrections and examining energy conditions and matter types at the throat.

Findings

Radial energy conditions are satisfied only for asymptotically flat wormholes.

Quantum corrections imply the presence of phantom-like matter in wormholes.

Certain conditions allow non-exotic matter in wormholes with excess solid angle.

Abstract

In this paper, we analyze the Schwarzschild-like wormhole in the Asymptotically Safe Gravity(ASG) scenario. The ASG corrections are implemented via renormalization group methods, which, as consequence, provides a new tensor $X_{\mu\nu}$ as a source to improved field equations, and promotes the Newton's constant into a running coupling constant. In particular, we check whether the radial energy conditions are satisfied and compare with the results obtained from the usual theory. We show that only in the particular case of the wormhole being asymptotically flat(Schwarzschild Wormholes) that the radial energy conditions are satisfied at the throat, depending on the chosen values for its radius $r_0$. In contrast, in the general Schwarzschild-like case, there is no possibility of the energy conditions being satisfied nearby the throat, as in the usual case. After that, we calculate the radial state parameter, $\omega(r)$, in $r_0$, in order to verify what type of cosmologic matter is allowed at the wormhole throat, and we show that in both cases there is the possibility of the presence of exotic matter, phantom or quintessence-like matter. Finally, we give the $\omega(r)$ solutions for all regions of space. Interestingly, we find that Schwarzschild-like Wormholes with excess of solid angle of the sphere in the asymptotic limit have the possibility of having non-exotic matter as source for certain values of the radial coordinate $r$. Furthermore, it was observed that quantum gravity corrections due the ASG necessarily imply regions with phantom-like matter, both for Schwarzschild and for Schwarzschild-like wormholes. This reinforces the supposition that a phantom fluid is always present for wormholes in this context.