Vainshtein screening for slowly rotating stars

Timothy Anson (1) , Eugeny Babichev (1, 2)

1 IJCLab - Laboratoire de Physique des 2 Infinis Irène Joliot-Curie
2 IAP - Institut d'Astrophysique de Paris

We study the Vainshtein mechanism in the context of slowly rotating stars in scalar-tensor theories. While the Vainshtein screening is well established for spherically symmetric spacetimes, we examine its validity in the axisymmetric case for slowly rotating sources. We show that the deviations from the general relativity solution are small in the weak-field approximation outside the star: the solution for the frame-dragging function is the same as in general relativity at leading order. Moreover, in most cases the corrections are suppressed by powers of the Vainshtein radius provided that the screening operates in spherical symmetry. Outside the Vainshtein radius, the frame dragging function receives corrections that are not suppressed by the Vainshtein radius, but which are still subleading. This suggests that the Vainshtein mechanism in general can be extended to slowly rotating stars and that it works analogously to the static case inside the Vainshtein radius. We also study relativistic stars and show that for some theories the frame-dragging function in vacuum does not receive corrections at all, meaning that the screening is perfect outside the star.

Mots clés: General relativity; alternative theories of gravity; star: rotation; screening: Vainshtein; symmetry: rotation; star: relativistic; general relativity: solution; approximation: weak field; symmetry: axial; higher-order: 0; suppression; gravitation: scalar tensor; space-time; field equations: solution; vacuum state; Lagrangian formalism; field theory: scalar; matter: coupling; Minkowski

Domaines: Relativité Générale et Cosmologie Quantique [gr-qc]; Physique des Hautes Energies - Théorie [hep-th]

Timothy Anson, Eugeny Babichev. Vainshtein screening for slowly rotating stars. Physical Review D, 2020, 102 (4), pp.044046. ⟨10.1103/PhysRevD.102.044046⟩. ⟨hal-02628167⟩