On symmetry inheritance of nonminimally coupled scalar fields

Abstract

We present the first symmetry inheritance analysis of fields nonminimally coupled to gravity. In this work we are focused on the real scalar field $\varphi$ with nonminimal coupling of the form $\xi {\varphi }^{2}R$. Possible cases of the symmetry noninheriting fields are constrained by the properties of the Ricci tensor and the scalar potential. Examples of such spacetimes can be found among those which are "dressed" with the stealth scalar field, a nontrivial scalar field configuration with the vanishing energy-momentum tensor. We classify the scalar field potentials which allow the symmetry noninheriting stealth field configurations on top of the exact solutions of the Einstein's gravitational field equation with the cosmological constant.

16 pages; slightly revised, published version (expanded discussion, several references added)

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Cited by in corpus (6)

• Kerr black holes with synchronised scalar hair and higher azimuthal harmonic index
• Spacetimes dressed with stealth electromagnetic fields
• Thermal stability of stealth and de Sitter spacetimes in scalar-tensor gravity
• Breaking of scaling symmetry by massless scalar on de Sitter
• Generalizations and challenges for the spacetime block-diagonalization
• Stationary spacetimes with time-dependent real scalar fields