New method to generate exact scalar-tensor solutions

Bertrand Chauvineau (1)

1 LAGRANGE - Joseph Louis LAGRANGE

A new method is proposed, that establishes a one to one correspondance between the whole set of static axially symmetric vacuum general relativity solutions and a specific class of stationary axially symmetric scalar-Einstein (Rab=∂aφ∂bφ) solutions for any mass and angular momentum. The method explicitly takes advantage of the Kerr metric Ricci flatness. This also results in a class of stationary axially symmetric vacuum, ie Kerrlike, Brans-Dicke solutions. A particular solution, that is asymptotically flat, is more closely considered. It converges to Kerr for a vanishing scalar charge, but fails to converge to the Fisher-Janis-Newman-Winicour solution for a vanishing “rotation parameter.” This solution exhibits a set of singular points, with a naked subset having a ringlike structure.

Mots clés: field theory: scalar; General relativity; Ricci; rotation; family; structure; singularity; angular momentum; Brans-Dicke model; symmetry: axial; space-time: vacuum state; metric: Kerr; charge: scalar; alternative theories of gravity

Domaines: Relativité Générale et Cosmologie Quantique [gr-qc]

Bertrand Chauvineau. New method to generate exact scalar-tensor solutions. Physical Review D, 2019, 100 (2), pp.024051. ⟨10.1103/PhysRevD.100.024051⟩. ⟨hal-01974756⟩