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arXiv · 2506.10409

Analytical solutions of CPT-odd Maxwell equations in Schwarzschild spacetime

Hao Wang·Zhi Xiao·Bing Sun
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Abstract

In this work, we present the CPT-violating (CPTV) Maxwell equations in curved spacetime using the Newman-Penrose (NP) formalism. We obtain a semi-analytical solution to the Maxwell equations in Schwarzschild spacetime under the assumption that the CPT-odd $\left(k_{AF}\right)^\mu$ term exhibits spherical symmetry in the Schwarzschild background. Retaining only terms up to linear order in the $\left(k_{AF}\right)^\mu$ coefficient, we obtain perturbative solutions by treating the solutions of the Lorentz-invariant Maxwell equations as the zeroth-order approximation and incorporating the $\left(k_{AF}\right)^\mu$ terms as an additional source term alongside the external charge current. Each resulting NP scalar field can be factorized into two components: the radial component is expressed in terms of hypergeometric functions, while the angular component is described by spin-weighted spherical harmonics.

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Hao Wang, Zhi Xiao, Bing Sun. 2025-06-12. Analytical solutions of CPT-odd Maxwell equations in Schwarzschild spacetime. https://arxiv.org/abs/2506.10409

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