Abstract: We find exact solutions to Maxwell equations written in terms of fourvector potentials in non-rotating, as well as in Gdel and Kerr spacetimes. We show that Maxwell equations can be reduced to two uncoupled secondorder differential equations for combinations of the components of the four-vector potential. Exact electromagnetic waves solutions are written on given gravitational field backgrounds where they evolve. We find that in non-rotating spherical symmetric spacetimes, electromagnetic waves travel along null geodesics. However, electromagnetic waves on Gdel and Kerr spacetimes do not exhibit that behavior.

Abstract: High performance Fe3O4 modified graphene assembled porous carbon (mGAPC) based epoxy paint coated on Polyethylene (PE) foam is realized by spray technique to fabricate light weight electromagnetic absorbers. The mGAPC as a pigment in a standard composition of commercial paint was optimized and the influence of solvent and additives are studied to achieve X-band (8.2-12.4 GHz) electromagnetic wave absorption (EA) in the hybrid foam (HF). From the comparative studies, the hybrid foams obtained from epoxy paint with toluene as solvent (without Mn-octate as additive) showed a Reflection Loss (RL) -19 dB (in the range of 8.3-8.7 GHz), which was further increased with the coating cycles up to -43 dB (in 10.2-11.2 GHz).The observed rise is attributed to increase in localized interfacial polarization that arises at the combined interfaces of mGAPC. The result showed 99% loss, which projects a promising EA paint for practical applications. Further thickness dependent studies of EA in Paint Coat HF1, reveals that with increasing thickness from 0.3 to 2 mm, the RL also increases from -19 to -43 dB with changing absorption band. The superior EA properties are correlated to the percolation threshold, pigment dispersibility and further correlated to the strong absorption, destructive interference, multiple internal reflections and interfacial polarization of the radiation in the hybrid foam. Moreover, considering the paint lowest thickness similar to 0.3 mm with -19 dB of RL, the hybrid foam promises a cost-effective, fine, light-weight EA/ RL material for secure electronic devices and packaging in civil and defence applications.