Buracos de minhoca do tipo Schwarzschild na teoria assintoticamente segura da gravidade

Abstract

In this work we analyze the traversability conditions of wormholes using a fluid with a position dependent state parameter as a source in the context of Asymptotically Safe Quantum Gravity (ASG), as well as using it to study the distribution of matter over space-time of two classes of specific solutions: Schwarzschild-like and the generalized Ellis-Bronnikov ones. Corrections due to ASG theory are implemented using the renormalization group methods, which, as a consequence, provides a new tensor Xµν as a source for the modified field equations and promotes the Newton’s constant G0 into a function of the curvature invariant. In the study of wormhole traversability conditions, we considered the cases of spherical or pseudospherical wormholes, where we restricted ourselves only to regions close to the wormhole throat. We use the specific case of the Ricci scalar as an invariant of curvature to use as a function cutoff f = ξ R and we use a fluid with an equation of state of the form pr = ω(r)ρ as source, that is, with the position-dependent state parameter. We show that, contrary to what was thought, in both cases we will have the possibility of crossing with non-exotic matter. In particular, we studied in the context of ASG the specific types of wormholes: Schwarzschildlike and generalized Ellis-Bronnikov wormholes. In this case, we check whether the radial energy conditions are satisfied and compare the results with those obtained from the usual theory. For the Schwarzschild-like class we show that only in the particular case of the Schwarzschild Wormhole that the radial energy conditions are satisfied in its throat, depending on the value chosen for its radius rt. In contrast, in the more general Schwarzschild-like case, there is no possibility for the radial energy conditions to be satisfied at the throat, as in the usual case. Finally, we study the class of generalized Ellis-Bronnikov solutions in the context of ASG using the Ricci scalar, the squared Ricci tensor and the Kretschmann scalar to define the function cutoff. We show that ASG solves the problem of exotic matter in the throat only when we use the Ricci scalar and that only for a particular generalized solution. Furthermore, we found a region near the throat where the radial energy conditions can be satisfied, contrary to what is predicted in the usual theory.