Hairy black-holes in shift-symmetric theories
Abstract Scalar hair of black holes in theories with a shift symmetry are constrained by the no-hair theorem of Hui and Nicolis, assuming spherical symmetry, time-independence of the scalar field and asymptotic flatness. The most studied counterexample is a linear coupling of the scalar with the Gau...
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doaj-524b225362f5407088fe1851f53276d72020-11-25T02:50:28ZengSpringerOpenJournal of High Energy Physics1029-84792020-08-012020812410.1007/JHEP08(2020)045Hairy black-holes in shift-symmetric theoriesPaolo Creminelli0Nicolás Loayza1Francesco Serra2Enrico Trincherini3Leonardo G. Trombetta4ICTP, International Centre for Theoretical PhysicsIFIC, Universitat de Valencia — CSICScuola Normale SuperioreScuola Normale SuperioreScuola Normale SuperioreAbstract Scalar hair of black holes in theories with a shift symmetry are constrained by the no-hair theorem of Hui and Nicolis, assuming spherical symmetry, time-independence of the scalar field and asymptotic flatness. The most studied counterexample is a linear coupling of the scalar with the Gauss-Bonnet invariant. However, in this case the norm of the shift-symmetry current J 2 diverges at the horizon casting doubts on whether the solution is physically sound. We show that this is not an issue since J 2 is not a scalar quantity, since J μ is not a diffinvariant current in the presence of Gauss-Bonnet. The same theory can be written in Horndeski form with a non-analytic function G 5 ∼ log X . In this case the shift-symmetry current is diff-invariant, but contains powers of X in the denominator, so that its divergence at the horizon is again immaterial. We confirm that other hairy solutions in the presence of non-analytic Horndeski functions are pathological, featuring divergences of physical quantities as soon as one departs from time-independence and spherical symmetry. We generalise the no-hair theorem to Beyond Horndeski and DHOST theories, showing that the coupling with Gauss-Bonnet is necessary to have hair.http://link.springer.com/article/10.1007/JHEP08(2020)045Black HolesClassical Theories of Gravity |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Paolo Creminelli Nicolás Loayza Francesco Serra Enrico Trincherini Leonardo G. Trombetta |
spellingShingle |
Paolo Creminelli Nicolás Loayza Francesco Serra Enrico Trincherini Leonardo G. Trombetta Hairy black-holes in shift-symmetric theories Journal of High Energy Physics Black Holes Classical Theories of Gravity |
author_facet |
Paolo Creminelli Nicolás Loayza Francesco Serra Enrico Trincherini Leonardo G. Trombetta |
author_sort |
Paolo Creminelli |
title |
Hairy black-holes in shift-symmetric theories |
title_short |
Hairy black-holes in shift-symmetric theories |
title_full |
Hairy black-holes in shift-symmetric theories |
title_fullStr |
Hairy black-holes in shift-symmetric theories |
title_full_unstemmed |
Hairy black-holes in shift-symmetric theories |
title_sort |
hairy black-holes in shift-symmetric theories |
publisher |
SpringerOpen |
series |
Journal of High Energy Physics |
issn |
1029-8479 |
publishDate |
2020-08-01 |
description |
Abstract Scalar hair of black holes in theories with a shift symmetry are constrained by the no-hair theorem of Hui and Nicolis, assuming spherical symmetry, time-independence of the scalar field and asymptotic flatness. The most studied counterexample is a linear coupling of the scalar with the Gauss-Bonnet invariant. However, in this case the norm of the shift-symmetry current J 2 diverges at the horizon casting doubts on whether the solution is physically sound. We show that this is not an issue since J 2 is not a scalar quantity, since J μ is not a diffinvariant current in the presence of Gauss-Bonnet. The same theory can be written in Horndeski form with a non-analytic function G 5 ∼ log X . In this case the shift-symmetry current is diff-invariant, but contains powers of X in the denominator, so that its divergence at the horizon is again immaterial. We confirm that other hairy solutions in the presence of non-analytic Horndeski functions are pathological, featuring divergences of physical quantities as soon as one departs from time-independence and spherical symmetry. We generalise the no-hair theorem to Beyond Horndeski and DHOST theories, showing that the coupling with Gauss-Bonnet is necessary to have hair. |
topic |
Black Holes Classical Theories of Gravity |
url |
http://link.springer.com/article/10.1007/JHEP08(2020)045 |
work_keys_str_mv |
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