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 J2 diverges at the horizon casting doubts on whether the solution is physically sound. We show that this is not an issue since J2 is not a scalar quantity, since Jμ 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 G5∼ 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.

Hairy black-holes in shift-symmetric theories

Serra F.;Trincherini E.;
2020

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 J2 diverges at the horizon casting doubts on whether the solution is physically sound. We show that this is not an issue since J2 is not a scalar quantity, since Jμ 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 G5∼ 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.
2020
Settore FIS/02 - Fisica Teorica, Modelli e Metodi Matematici
Black Holes; Classical Theories of Gravity; High Energy Physics - Theory; High Energy Physics - Theory; astro-ph.CO; General Relativity and Quantum Cosmology
File in questo prodotto:
File Dimensione Formato  
2004.02893.pdf

accesso aperto

Tipologia: Submitted version (pre-print)
Licenza: Solo Lettura
Dimensione 449.08 kB
Formato Adobe PDF
449.08 kB Adobe PDF
Creminelli2020_Article_HairyBlack-holesInShift-symmet (1).pdf

accesso aperto

Tipologia: Published version
Licenza: Creative Commons
Dimensione 374.14 kB
Formato Adobe PDF
374.14 kB Adobe PDF

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/89264
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 16
  • ???jsp.display-item.citation.isi??? 11
social impact