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.
Stationary Einstein-vector-Gauss-Bonnet black holes
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abstract
We study spontaneously vectorized black holes in Einstein-vector-Gauss-Bonnet theory with a quadratic coupling function. Besides the static, spherically symmetric black holes carrying an electric charge, there are uncharged static, axially symmetric black holes that possess a magnetic dipole moment. Both types possess radial excitations. The magnetic black holes are prolate. They are hotter than the Schwarzschild black holes and possess lower free energy. The domain of existence of the rotating vectorized black holes is bounded by the Kerr black holes, the spherically and axially symmetric static black holes, and the critical solutions.
fields
gr-qc 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
New class of exact rotating black holes with primary hair in 5D generalized Proca theory, generalizing Myers-Perry via Kerr-Schild form with light-like Proca field.
citing papers explorer
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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.
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Rotating black holes with primary hair in five-dimensional generalized Proca theory
New class of exact rotating black holes with primary hair in 5D generalized Proca theory, generalizing Myers-Perry via Kerr-Schild form with light-like Proca field.