Generating 4-dimensional Wormholes with Yang-Mills Casimir Sources
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913482760257536 |
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| author | Santos, A. C. L. Maluf, R. V. Muniz, C. R. |
| author_facet | Santos, A. C. L. Maluf, R. V. Muniz, C. R. |
| contents | This work presents a new wormhole solution in General Relativity supported by the quantum vacuum fluctuations of the Casimir effect between perfect chromometallic mirrors in $(3+1)$ dimensions, which was recently fitted using first-principle numerical simulations. Initially, we employ a perturbative approach for $x = m r \ll 1$, where $m$ represents the Casimir mass. This approach has proven to be a reasonable approximation when compared with the exact case in this regime. To find well-behaved redshift functions, we impose constraints on the free parameters. As expected, this solution recovers the electromagnetic-like Casimir solution for $m = 0$. Analyzing the traversability conditions, we graphically find that all will be satisfied for $ 0 \leq m \leq 0.20$. On the other hand, all the energy conditions are violated, as usual in this context. Stability from Tolman-Oppenheimer-Volkov (TOV) equation is guaranteed for all $r$ and from the speed of sound for $0.16 \le m \le 0.18$. Therefore, for $0.16 \leq m \leq 0.18$, we will have a stable solution that satisfies all traversability conditions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_08774 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generating 4-dimensional Wormholes with Yang-Mills Casimir Sources Santos, A. C. L. Maluf, R. V. Muniz, C. R. General Relativity and Quantum Cosmology This work presents a new wormhole solution in General Relativity supported by the quantum vacuum fluctuations of the Casimir effect between perfect chromometallic mirrors in $(3+1)$ dimensions, which was recently fitted using first-principle numerical simulations. Initially, we employ a perturbative approach for $x = m r \ll 1$, where $m$ represents the Casimir mass. This approach has proven to be a reasonable approximation when compared with the exact case in this regime. To find well-behaved redshift functions, we impose constraints on the free parameters. As expected, this solution recovers the electromagnetic-like Casimir solution for $m = 0$. Analyzing the traversability conditions, we graphically find that all will be satisfied for $ 0 \leq m \leq 0.20$. On the other hand, all the energy conditions are violated, as usual in this context. Stability from Tolman-Oppenheimer-Volkov (TOV) equation is guaranteed for all $r$ and from the speed of sound for $0.16 \le m \le 0.18$. Therefore, for $0.16 \leq m \leq 0.18$, we will have a stable solution that satisfies all traversability conditions. |
| title | Generating 4-dimensional Wormholes with Yang-Mills Casimir Sources |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2405.08774 |