Black hole hair in generalized scalar-tensor gravity

Area of Science:

• Theoretical physics
• General relativity
• Scalar-tensor theories

Background:

• Horndeski's theory is the most general scalar-tensor theory with second-order field equations.
• Black hole solutions in modified gravity are crucial for testing theories beyond Einstein's general relativity.
• The presence of 'hair' on black holes would violate the standard no-hair theorems.

Purpose of the Study:

• To investigate the existence of black hole hair in shift-symmetric Horndeski theories.
• To identify conditions under which black holes in these theories must possess scalar field configurations.
• To re-examine recent no-hair theorems in light of these findings.

Main Methods:

• Analysis of the field equations derived from the action of shift-symmetric Horndeski theory.
• Investigation of scalar field configurations in black hole spacetimes.
• Comparison with existing no-hair theorems.

Main Results:

• Scalar fields in shift-symmetric Horndeski theories generically acquire nontrivial configurations around black holes.
• This nontrivial configuration is linked to a linear coupling with the Gauss-Bonnet invariant.
• Black holes in these theories possess 'hair' unless this coupling is precisely tuned to zero.

Conclusions:

• The presence of black hole hair is a generic feature of shift-symmetric Horndeski theories.
• A recent no-hair theorem may be incomplete due to overlooking the Gauss-Bonnet coupling.
• These findings have implications for the uniqueness of black hole solutions in modified gravity.