I-Love-Q, Spontaneously: Slowly Rotating Neutron Stars in Scalar-Tensor Theories

TL;DR

This paper extends the Hartle-Thorne formalism to model slowly rotating neutron stars in scalar-tensor theories, revealing that universal I-Love-Q relations are preserved and indistinguishable from general relativity within current observational constraints.

Contribution

It develops a general framework for modeling rotating neutron stars in scalar-tensor theories, including spontaneous scalarization, and demonstrates the robustness of I-Love-Q relations across theories.

Findings

I-Love-Q relations hold in scalar-tensor theories with minimal deviations from GR.

Current binary-pulsar constraints limit observable differences in neutron star parameters.

The formalism can be applied to f(R) gravity and used as a benchmark for numerical models.

Abstract

We construct models of slowly rotating, perfect-fluid neutron stars by extending the classical Hartle-Thorne formalism to generic scalar-tensor theories of gravity. Working at second order in the dimensionless angular momentum, we compute the mass M, radius R, scalar charge q, moment of inertia I and spin-induced quadrupole moment Q, as well as the tidal and rotational Love numbers. Our formalism applies to generic scalar-tensor theories, but we focus in particular on theories that allow for spontaneous scalarization. It was recently discovered that the moment of inertia, quadrupole moment and Love numbers are connected by approximately universal (i.e., equation-of-state independent) "I-Love-Q" relations. We find that similar relations hold also for spontaneously scalarized stars. More interestingly, the I-Love-Q relations in scalar-tensor theories coincide with the general relativistic ones within less than a few percent, even for spontaneously scalarized stars with the largest couplings allowed by current binary-pulsar constraints. This implies that astrophysical measurements of these parameters cannot be used to discriminate between general relativity and scalar-tensor theories, even if spontaneous scalarization occurs in nature. Because of the well known equivalence between f(R) theories and scalar-tensor theories, the theoretical framework developed in this paper can be used to construct rotating compact stellar models in f(R) gravity. Our slow-rotation expansion can also be used as a benchmark for numerical calculations of rapidly spinning neutron stars in generic scalar-tensor theories.