Black holes in quartic-order beyond-generalized Proca theories

Ryotaro Kase*, Masato Minamitsuji, Shinji Tsujikawa

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

19 Citations (Scopus)


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 ct on the Friedmann–Lemaître–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.

Original languageEnglish
Pages (from-to)541-550
Number of pages10
JournalPhysics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
Publication statusPublished - 2018 Jul 10
Externally publishedYes

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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