Abstract
In full Horndeski theories, we show that the static and spherically symmetric black hole (BH) solutions with a static scalar field whose kinetic term is nonvanishing on the BH horizon are generically prone to ghost/Laplacian instabilities. We then search for asymptotically Minkowski hairy BH solutions with a vanishing on the horizon free from ghost/Laplacian instabilities. We show that models with regular coupling functions of and result in no-hair Schwarzschild BHs in general. On the other hand, the presence of a coupling between the scalar field and the Gauss-Bonnet (GB) term , even with the coexistence of other regular coupling functions, leads to the realization of asymptotically Minkowski hairy BH solutions without ghost/Laplacian instabilities. Finally, we find that hairy BH solutions in power-law gravity are plagued by ghost instabilities. These results imply that the GB coupling of the form plays a prominent role for the existence of asymptotically Minkowski hairy BH solutions free from ghost/Laplacian instabilities.
- Received 5 May 2022
- Accepted 19 July 2022
DOI:https://doi.org/10.1103/PhysRevD.106.044003
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