No-hair theorem for the Galileon

Area of Science:

• Theoretical physics
• General relativity
• Cosmology

Background:

• The no-hair theorems are fundamental in black hole physics, stating black holes are characterized only by mass, charge, and angular momentum.
• Galileon fields, with their unique derivative interactions, challenge the applicability of standard no-hair theorems.
• Understanding black hole solutions with exotic fields is crucial for testing theories beyond the Standard Model and General Relativity.

Purpose of the Study:

• To investigate whether static, spherically symmetric black holes can sustain nontrivial Galileon field configurations.
• To determine the validity of no-hair theorems in the presence of Galileon fields coupled to gravity.
• To explore the influence of different boundary conditions and nonminimal couplings on Galileon black hole solutions.

Main Methods:

• We analyzed the field equations for a Galileon field minimally or nonminimally coupled to gravity.
• We focused on static, spherically symmetric black hole solutions.
• The analysis considered both trivial and cosmological boundary conditions for the Galileon field.

Main Results:

• We proved that static, spherically symmetric black holes cannot support nontrivial Galileon profiles.
• The theorem holds irrespective of the Galileon field's boundary conditions (trivial or cosmological).
• Nonminimal couplings of the covariant Galileon type between the Galileon and gravity do not alter this result.

Conclusions:

• Static black holes are 'hairless' concerning Galileon fields, similar to standard scalar fields.
• The peculiar derivative interactions of Galileon fields do not enable them to form nontrivial black hole solutions.
• This result has implications for modified gravity theories and the search for exotic compact objects.