  This study investigates the production of neutral scalar boson pairs in
static electromagnetic fields resulting from Lorentz-symmetry violation (LSV),
with a focus on the parity-even sector of the CPT-even photon sector in the
Standard Model Extension (SME). Utilizing a cross-configuration involving
inhomogeneous static electric fields and homogeneous static magnetic fields,
the analysis of the probability of bosons pair production identifies three
different regimes determined by critical magnetic field. Below the critical
value, creation is exponentially suppressed; at the critical value, the number
density of created bosons remains constant, and above the critical field, there
is exponential amplification. This behavior prompts an additional investigation
using von Neumann entanglement entropy to analyze fluctuations in the bosonic
vacuum.
