Abstract
In this work, we consider a Yukawa modification of the Casimir wormhole. With the help of an Equation of State, we impose Zero Tidal Forces. We will examine two different approaches: in a first approach, we will fix the form of the shape function of the Casimir wormholes modified by a Yukawa term in three different ways and finally a superposition of different profiles. In the second approach, we will consider the original Casimir source modified by a Yukawa term in three different ways and we will deduce the form of the shape function In both the approaches the reference energy density will be that of the Casimir source. Connection with the Absurdly Benign Traversable Wormhole are also discussed.
Highlights
Yukawa in 1935 [1] proposed to describe nonrelativistic strong interactions between nucleons with the help of a potential whose profile isV (r ) = − α exp (−μr ) . (1) rThis is nothing but the screened version of the Coulomb potential with α describing the strength of the interaction and 1/μ its range
We will consider the original Casimir source modified by a Yukawa term in three different ways and we will deduce the form of the shape function In both the approaches the reference energy density will be that of the Casimir source
The paper is organized as follows: in Sect. 2 we study three different combinations of the Casimir wormhole shape function with a Yukawa term, in Sect. 3 we explore the consequences of a superposition of the profiles considered in Sect. 2, in Sect. 4 we adopt the reverse procedure, namely we fix the form of the energy density and we deduce the form of the shape function, investigating three different profiles
Summary
Yukawa in 1935 [1] proposed to describe nonrelativistic strong interactions between nucleons with the help of a potential whose profile is. [17], we have found that the Casimir wormhole described by φ (r ) = ln 4r 3r + r0 and b(r ) = 2r0 + r02 , (12) 3 3r does not satisfy the ZTF condition. We will consider the Casimir wormhole shape function deformed by a Yukawa profile satisfying the ZTF condition: in this way we have the possibility of building a new family of solutions which have a vanishing redshift function. We assume that the Casimir relationship ω = 3 holds, at least on the throat There exists another reason to consider a Yukawa deformation to the Casimir wormhole. 2 we study three different combinations of the Casimir wormhole shape function with a Yukawa term, in Sect.
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