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.
Black holes in quartic-order beyond-generalized Proca theories
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abstract
The generalized Proca theories with second-order equations of motion can be healthily extended to a more general framework in which the number of propagating degrees of freedom remains unchanged. In the presence of a quartic-order nonminimal coupling to gravity arising in beyond-generalized Proca theories, the speed of gravitational waves $c_t$ on the Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmological background can be equal to that of light $c$ under a certain condition. By using this condition alone, we show that the speed of gravitational waves in the vicinity of static and spherically symmetric black holes is also equivalent to $c$ for the propagation of odd-parity perturbations along both radial and angular directions. As a by-product, the black holes arising in our beyond-generalized Proca theories are plagued by neither ghost nor Laplacian instabilities against odd-parity perturbations. We show the existence of both exact and numerical black hole solutions endowed with vector hairs induced by the quartic-order coupling.
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gr-qc 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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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.