Effects of a linear central potential induced by the Lorentz symmetry violation on the Klein-Gordon oscillator

Inspired by the Standard Model Extension, we have investigated a possible scenario arising from the Lorentz symmetry violation governed by a background tensor field on a scalar field subject to the Klein-Gordon oscillator, where this possible scenario gives rise to a linear central potential. We analyse the behaviour of the relativistic quantum oscillator under the influence of a Coulomb-type scalar potential in this background. Then, we solve the Klein-Gordon equation analytically and discuss the influence of the background which violates the Lorentz symmetry in the relativistic energy levels.