Gravitational bending angle with finite distances by Casimir wormholes

Abstract

In this paper, we investigate the gravitational bending angle due to the Casimir wormholes, which consider the Casimir energy as the source. Furthermore, some of these Casimir wormholes regard Generalized Uncertainty Principle (GUP) corrections of Casimir energy. We use the Ishihara method for the Jacobi metric, which allows us to study the bending angle of light and massive test particles for finite distances. Beyond the uncorrected Casimir source, we consider many GUP corrections, namely: the Kempf, Mangano and Mann (KMM) model, the Detournay, Gabriel and Spindel (DGS) model, and the so-called type II model for the GUP principle. We also find the deflection angle of light and massive particles when the receiver and the source are far away from the lens. Contents 1 Introduction 1 2 Casimir wormholes with and without GUP corrections -Review 2 3 Gravitational bending angle of massive particles in a static and spherically symmetric background -Review 4 4 Gravitational bending angle of massive particles with correction of finite distances 6 4.

On the traversability of wormhole solutions in asymptotically safe gravity

“…for the initial condition b(0) (1) = 1. The term of the first order is obtained substituting the b(0) on the right side of (9) together with the replacement ω (0) (u) → ω t + κ(u − 1). The anti-screening function using the Ricci Scalar in this case is…”

“…However, wormholes traversability was only studied more than fifty years later by Morris and Thorne [2]. An important feature of wormholes in Einstein's theory of gravity is that it's traversability requires exotic matter [2], being possible to have wormholes with phantom as energy source [3,4] or even Casimir energy [5][6][7][8][9]. Therefore the search for traversable wormholes in modified theories of gravity [10][11][12][13][14][15][16] without the requirement of exotic matter became an intense topic of research in the literature.…”

Generalized Ellis-Bronnikov wormholes in asymptotically safe gravity

“…Morris and Thorne showed that for the existence of a traversable wormhole necessarily needs the presence of a matter such that at the throat of the wormhole the tension must exceed the total energy density and this leads a violation of all the energy conditions of the general relativity, and they call this type of matter as "exotic" [3]. The presence of exotic matter has been seen in a wide variety of wormholes [4][5][6][7][8][9][10] and what we can do to try to eliminate this problem is appeal to modified theories in a tentative to construct wormholes without the exigence of exotic matter [11][12][13][14][15][16][17] We can expect that quantum effects in the gravitational field provides the existence of wormholes with non-exotic matter satisfying the energy conditions. The problem then would be how do we describe quantum corrections for gravitational systems.…”

Traversable Casimir Wormholes in D Dimensions

“…The author found an appropriate redshift function and proved that in four-dimensional spacetime, the Casimir energy, solely, can be a source of traversable wormholes. After this seminal work, many consequences has been studied [2,[29][30][31][32][33]. In this direction Alencar et al have shown that, differently of the case with D = 4, in D = 3 Casimir energy, solely, can not be a source of wormholes and additional sources must be added [2].…”