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.
Static and rotating solutions for Vector-Galileon theories
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abstract
We consider a particular truncation of the generalized Proca field theory in four dimensions for which we construct a static and axisymmetric rotating black hole "stealth solutions", namely solutions with (Anti) de Sitter or Kerr metric but non-trivial vector field. The static configuration is promoted to a backreacting black hole with asymptotic (Anti) de Sitter behavior by turning on a nonlinear electrodynamic source given as a fixed power of the Maxwell invariant. Finally we extend our solutions to arbitrary dimensions.
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Spacetime symmetries generate stealth Proca vector fields on arbitrary backgrounds, enabling exact Proca-haired rotating black holes in all dimensions.
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.
A review thesis covering Mukhanov parametrization, general scalar-tensor theories, and new slow-roll techniques for canonical and noncanonical inflation observables.
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Proca-type Hair of Rotating Black Holes in Higher Dimensions
Spacetime symmetries generate stealth Proca vector fields on arbitrary backgrounds, enabling exact Proca-haired rotating black holes in all dimensions.