A no-go theorem shows that negative effective mass squared for the vector field in vector-tensor gravity always accompanies ghost or gradient instabilities, blocking spontaneous vectorization in stationary axisymmetric black holes.
Hod, Marginally stable Schwarzschild-black-hole- non-minimally-coupled-Proca-field bound-state con- figurations, Phys
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No-go theorem for spontaneous vectorization
A no-go theorem shows that negative effective mass squared for the vector field in vector-tensor gravity always accompanies ghost or gradient instabilities, blocking spontaneous vectorization in stationary axisymmetric black holes.