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Black hole hair in generalized scalar-tensor gravity (1312.3622v2)

Published 12 Dec 2013 in gr-qc and hep-th

Abstract: The most general action for a scalar field coupled to gravity that leads to second order field equations for both the metric and the scalar --- Horndeski's theory --- is considered, with the extra assumption that the scalar satisfies shift symmetry. We show that in such theories the scalar field is forced to have a nontrivial configuration in black hole spacetimes, unless one carefully tunes away a linear coupling with the Gauss--Bonnet invariant. Hence, black holes for generic theories in this class will have hair. This contradicts a recent no-hair theorem, which seems to have overlooked the presence of this coupling.

Citations (322)

Summary

  • The paper demonstrates that black holes in shift-symmetric Horndeski theories inevitably develop nontrivial scalar hair, challenging traditional no-hair theorems.
  • The authors use perturbative solutions to reveal that the scalar hair emerges without an independent conserved charge, classifying it as hair of the second kind.
  • The study’s implications point toward future observational tests via gravitational wave signatures and modified astrophysical phenomena.

Overview of "Black hole hair in generalized scalar-tensor gravity"

The paper "Black hole hair in generalized scalar-tensor gravity" by Thomas P. Sotiriou and Shuang-Yong Zhou investigates the intriguing question of whether black holes can possess "hair" — that is, additional information beyond mass, charge, and angular momentum — in the context of generalized scalar-tensor theories of gravity. The authors focus specifically on a class of theories within Horndeski's formulation that respects shift symmetry, which implies that the scalar field remains invariant under constant shifts.

Key Assertions and Numerical Results

The paper challenges the conventional no-hair theorem, which posits that black holes cannot have scalar hair if the scalar field minimally couples to gravity. Specifically, the authors demonstrate that in shift-symmetric Horndeski theories, a nontrivial scalar configuration is inevitable near black hole spacetimes unless a linear coupling with the Gauss-Bonnet invariant is finely tuned away. This finding contradicts prior assertions from recent no-hair theorem studies, which overlooked the critical role of this coupling.

The paper presents specific numerical results associated with the scalar field configuration around black holes. Through perturbative solutions, the authors identify that the scalar field configuration does not lead to an independent conserved charge, classifying the resulting hair as "hair of the second kind." Such a configuration stems from ensuring regularity at the black hole horizon and other boundary conditions imposed during their derivations.

Theoretical Implications

This paper enriches the theoretical landscape of black hole physics by suggesting potential deviations from the predictions of General Relativity. The possibility of detecting black hole hair in these gravity models suggests new avenues for indirect observations of scalar fields through astrophysical phenomena and gravitational waves. Furthermore, understanding black hole solutions in these extended theories could provide insight into quantum gravity effects or modifications to gravity on cosmological scales.

Practical Implications and Future Directions

In practical terms, using black holes as a probe for scalar fields could reshape our understanding of the universe's fundamental forces. While the paper provides a solid theoretical framework, direct observational evidence remains challenging. Future research should focus on deriving observable predictions, such as distinct gravitational wave signatures or electromagnetic emissions influenced by scalar configurations around black holes. Such efforts would be pivotal in testing these theories against empirical data from telescopes and gravitational observatories like LIGO and Virgo.

Additionally, the extension of this work to scenarios involving matter and cosmological backgrounds could further elaborate on the nature and detection of scalar hair, potentially adding to the growing body of literature that seeks to unify these theories with the standard cosmological model.

Conclusion

The paper by Sotiriou and Zhou represents a significant advancement in the paper of scalar-tensor gravity theories, providing compelling arguments against long-standing assumptions about black hole characteristics in this context. As research continues to investigate the vast implications of these findings, it opens up potential pathways for new theoretical developments and innovative empirical tests, bridging the gap between gravity's theoretical underpinnings and observable universe phenomena.