Neutron stars in massive scalar-Gauss-Bonnet gravity: Spherical structure and time-independent perturbations

Abstract

The class of scalar-tensor theories with the scalar field coupling to the Gauss-Bonnet invariant has drawn great interest since solutions of spontaneous scalarization were found for black holes in these theories. We contribute to the existing literature a detailed study of the spontaneously scalarized neutron stars (NSs) in a typical theory where the coupling function of the scalar field takes the quadratic form and the scalar field is massive. The investigation here includes the spherical solutions of the NSs as well as their perturbative properties, namely the tidal deformability and the moment of inertia, treated in a unified and extendable way under the framework of spherical decomposition. We find that while the mass, the radius, and the moment of inertia of the spontaneously scalarized NSs show very moderate deviations from those of the NSs in general relativity (GR), the tidal deformability exhibits significant differences between the solutions in GR and the solutions of spontaneous scalarization for certain values of the parameters in the scalar-Gauss-Bonnet theory. With the mass and the tidal deformability of NSs attainable in the gravitational waves from binary NS mergers, the radius measurable using the X-ray satellites, and the moment of inertia accessible via the high-precision pulsar timing techniques, future multi-messenger observations can be contrasted with the theoretical results and provide us necessary information for building up theories beyond GR.

Constraining scalarization in scalar-Gauss-Bonnet gravity through binary pulsars

“…Other couplings have also been used in the literature with the most prominent example being f (ϕ) = ϕ 2 [26] that matches (17) for very small scalar fields. Even though such quadratic coupling is the simplest one admitting scalarization, it leads to unstable scalarized black holes [36] and the behavior of the scalarized neutron star branches look also somewhat peculiar compared to the exponential coupling [29]. This can be cured (at least for black holes) with adding higher order ϕ terms in the coupling function [37,38] or a self-interacting scalar field potential [39].…”

“…Even though scalarization in sGB gravity originally attracted a lot of attention in the context of black holes , it is possible to scalarize also neutron stars [26,28,29]. Thus one can impose constraints on the theory through binary pulsar observations which is the goal of the present paper.…”