Spontaneous Lorentz violation requires determining the vacuum from the Hamiltonian density rather than the Lagrangian potential minimum, ruling out quadratic potentials and allowing only stable timelike or lightlike VEVs for smooth potentials.
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Bumblebee gravity is self-consistent in PPN up to 1.5PN order only for λ = −ξ/2, producing non-zero α1, α2, a logarithmic U_B potential, and a pulsar-timing bound |ℓ| ≲ 1.6×10^{-9}.
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Hamiltonian Constraints on Spontaneous Lorentz Symmetry Breaking in the Bumblebee Model
Spontaneous Lorentz violation requires determining the vacuum from the Hamiltonian density rather than the Lagrangian potential minimum, ruling out quadratic potentials and allowing only stable timelike or lightlike VEVs for smooth potentials.
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Dynamic Aspects of Bumblebee Gravity: Post-Newtonian Approach
Bumblebee gravity is self-consistent in PPN up to 1.5PN order only for λ = −ξ/2, producing non-zero α1, α2, a logarithmic U_B potential, and a pulsar-timing bound |ℓ| ≲ 1.6×10^{-9}.