High-derivatives and massive electromagnetic models in the Lemaître–Tolman–Bondi spacetime

The Maxwell electromagnetic theory embedded in an inhomogeneous Lemaître–Tolman–Bondi (LTB) spacetime background was described a few years back in the literature. However, terms concerning the mass or high-derivatives were not explored. In this work we studied the inhomogeneous spacetime effects on high-derivatives and massive electromagnetic models. We used the LTB metric and calculated the physical quantities of interest, namely the scale factor, density of the eletromagnetic field and Hubble constant, for the Proca and higher-derivative Podolsky models. We found a new singularity in both models, and that the magnetic field must be zero in the Proca model.