Fermion-antifermion pairs in magnetized spacetime generated by a point source
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arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866913675574509568 |
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| author | Guvendi, A. Mustafa, O. |
| author_facet | Guvendi, A. Mustafa, O. |
| contents | In this research, we study fermion-antifermion pairs in a magnetized spacetime induced by a point-like source and characterized by an angular deficit parameter, \(α\). In the rest frame, the relative motion (\(\propto r\)) of these pairs is analyzed using exact solutions of a two-body Dirac equation with a position-dependent mass expressed as \(m(r) = m_0 + \mathcal{S}(r)\). We select the Lorentz scalar potential \(\mathcal{S}(r) = -α_c/r\), which modifies the rest mass in a manner analogous to an attractive Coulomb potential, and derive analytical solutions to the resulting radial wave equation. Our findings are applicable to pairs in flat spacetime when \(α= 1\) without loss of generality. We elucidate how the spectra of such pairs are influenced by the spacetime background. Additionally, we observe that even the well-known non-relativistic energy (\(\propto α_c^2\)) reflects the influence of the parameter \(α\) in positronium-like fermion-antifermion systems. We propose that our results can also be extended to study charge carriers in magnetized monolayer materials. Furthermore, we demonstrate that the metric for a 2+1-dimensional spinning point source background can be transformed into the metric describing the near-horizon region of a rotating BTZ black hole, a result not previously reported in the literature. This metric holds potential for providing meaningful insights into topics such as holographic superconductivity and quantum critical phenomena in future research |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_01103 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fermion-antifermion pairs in magnetized spacetime generated by a point source Guvendi, A. Mustafa, O. General Relativity and Quantum Cosmology In this research, we study fermion-antifermion pairs in a magnetized spacetime induced by a point-like source and characterized by an angular deficit parameter, \(α\). In the rest frame, the relative motion (\(\propto r\)) of these pairs is analyzed using exact solutions of a two-body Dirac equation with a position-dependent mass expressed as \(m(r) = m_0 + \mathcal{S}(r)\). We select the Lorentz scalar potential \(\mathcal{S}(r) = -α_c/r\), which modifies the rest mass in a manner analogous to an attractive Coulomb potential, and derive analytical solutions to the resulting radial wave equation. Our findings are applicable to pairs in flat spacetime when \(α= 1\) without loss of generality. We elucidate how the spectra of such pairs are influenced by the spacetime background. Additionally, we observe that even the well-known non-relativistic energy (\(\propto α_c^2\)) reflects the influence of the parameter \(α\) in positronium-like fermion-antifermion systems. We propose that our results can also be extended to study charge carriers in magnetized monolayer materials. Furthermore, we demonstrate that the metric for a 2+1-dimensional spinning point source background can be transformed into the metric describing the near-horizon region of a rotating BTZ black hole, a result not previously reported in the literature. This metric holds potential for providing meaningful insights into topics such as holographic superconductivity and quantum critical phenomena in future research |
| title | Fermion-antifermion pairs in magnetized spacetime generated by a point source |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2502.01103 |