Spontaneous Lorentz violation and asymptotic flatness

The Standard Model Extension (SME) is a generic parametrization for Lorentz violation and the phenomenological consequences of minimal gravity sector SME are usually studied using post-Newtonian expansion that requires spacetime to be asymptotically flat. However, there term in this which these approximations unable make predictions; known as $t$ puzzle. present paper studies model spontaneous static spherically symmetric situation, when no additional matter fields present. It shown that, under above mentioned assumptions, only flat solutions exist. This stems from fact fixes asymptotic behavior all pieces curvature tensor.