Analytical solutions of CPT-odd Maxwell equations in Schwarzschild spacetime

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.