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Register a new userGravitational bending angle with finite distances by Casimir wormholes
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Added by
Icaro Daniel Dias De Carvalho
Publication date
2021
fields
Physics
and research's language is
English
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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 in the case of the receiver and the source are far away from the lens. In this case, we also compute the optical scalars: convergence and shear for these Casimir wormholes as a gravitational weak lens.
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We discuss a possible extension of calculations of the bending angle of light in a static, spherically symmetric and asymptotically flat spacetime to a non-asymptotically flat case. We examine a relation between the bending angle of light and the Gauss-Bonnet theorem by using the optical metric. A correspondence between the deflection angle of light and the surface integral of the Gaussian curvature may allow us to take account of the finite distance from a lens object to a light source and a receiver. Using this relation, we propose a method for calculating the bending angle of light for such cases. Finally, this method is applied to two examples of the non-asymptotically flat spacetimes to suggest finite-distance corrections: Kottler (Schwarzschild-de Sitter) solution to the Einstein equation and an exact solution in Weyl conformal gravity.
Continuing work initiated in an earlier publication [Ishihara, Suzuki, Ono, Kitamura, Asada, Phys. Rev. D {bf 94}, 084015 (2016) ], we discuss a method of calculating the bending angle of light in a static, spherically symmetric and asymptotically flat spacetime, especially by taking account of the finite distance from a lens object to a light source and a receiver. For this purpose, we use the Gauss-Bonnet theorem to define the bending angle of light, such that the definition can be valid also in the strong deflection limit. Finally, this method is applied to Schwarzschild spacetime in order to discuss also possible observational implications. The proposed corrections for Sgr A$^{ast}$ for instance are able to amount to $sim 10^{-5}$ arcseconds for some parameter range, which may be within the capability of near-future astronomy, while also the correction for the Sun in the weak field limit is $sim 10^{-5}$ arcseconds.
This work investigates the influence of the Lorentz symmetry breaking in the bending angle of massive particles and light for bumblebee black hole solutions. The solutions analyzed break the Lorentz symmetry due to a non-zero vacuum expectation value of the bumblebee field. We use the Ishihara method, which allows us to study the bending angle of light for finite distances, and it is applicable to non-asymptotically flat spacetimes when considering the receiver viewpoint. In order to analyze the deflection of massive particles, we systematize the Ishihara method for its application in the Jacobi metric. This systematization allows the study of the deflection angle of massive particles using the Gauss-Bonnet theorem. We consider two backgrounds: the first was found by Bertolami et al. and is asymptotically flat. The second was found recently by Maluf et al. and is not asymptotically flat due to an effective cosmological constant.
By using the Gauss-Bonnet theorem, the bending angle of light in a static, spherically symmetric and asymptotically flat spacetime has been recently discussed, especially by taking account of the finite distance from a lens object to a light source and a receiver [Ishihara, Suzuki, Ono, Asada, Phys. Rev. D 95, 044017 (2017)]. We discuss a possible extension of the method of calculating the bending angle of light to stationary, axisymmetric and asymptotically flat spacetimes. For this purpose, we consider the light rays on the equatorial plane in the axisymmetric spacetime. We introduce a spatial metric to define the bending angle of light in the finite-distance situation. We show that the proposed bending angle of light is coordinate-invariant by using the Gauss-Bonnet theorem. The non-vanishing geodesic curvature of the photon orbit with the spatial metric is caused in gravitomagnetism, even though the light ray in the four-dimensional spacetime follows the null geodesic. Finally, we consider Kerr spacetime as an example in order to examine how the bending angle of light is computed by the present method. The finite-distance correction to the gravitomagnetic deflection angle due to the Suns spin is around a pico-arcsecond level. The finite-distance corrections for Sgr A$^{ast}$ also are estimated to be very small. Therefore, the gravitomagnetic finite-distance corrections for these objects are unlikely to be observed with present technology.
In this paper we show that wormholes in (2+1) dimensions (3-D) cannot be sourced solely by both Casimir energy and tension, differently from what happens in a 4-D scenario, in which case it has been shown recently, by the direct computation of the exact shape and redshift functions of a wormhole solution, that this is possible. We show that in a 3-D spacetime the same is not true since the arising of at least an event horizon is inevitable. We do the analysis for massive and massless fermions, as well as for scalar fields, considering quasi-periodic boundary conditions and find that a possibility to circumvent such a restriction is to introduce, besides the 3-D Casimir energy density and tension, a cosmological constant, embedding the surface in a 4-D manifold and applying a perpendicular weak magnetic field. This causes an additional tension on it, which contributes to the formation of the wormhole. Finally, we discuss the possibility of producing the condensed matter analogous of this wormhole in a graphene sheet and analyze the electronic transport through it.
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