Fermion-antifermion pairs in magnetized spacetime generated by a point source

TL;DR

This paper analyzes fermion-antifermion pairs in a magnetized, conical spacetime background, deriving analytical solutions for their spectra and exploring implications for condensed matter systems and black hole physics.

Contribution

It introduces exact solutions for fermion-antifermion pairs in a magnetized conical spacetime and connects these findings to black hole metrics and potential condensed matter applications.

Findings

Spectra of pairs are influenced by spacetime background.

Analytical solutions for the Dirac equation with position-dependent mass.

Connection between spinning point source metric and BTZ black hole near-horizon geometry.

Abstract

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, \(\alpha\). 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 \(\mathcal{S}(r) = -\alpha_c/r\), 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 \(\alpha = 1\) 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 (\(\propto \alpha_c^2\)) reflects the influence of the parameter \(\alpha\) 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