# Constraining a possible time-variation of the gravitational constant through "gravitochemical heating" of neutron stars

## TL;DR

This paper uses neutron star temperature observations and theoretical models of their thermal evolution to set upper limits on the possible rate of change of the gravitational constant over time.

## Contribution

It introduces a novel method to constrain the variation of G by analyzing the thermal state of neutron stars affected by gravitochemical heating.

## Key findings

- Upper limit of |Ġ/G| < 2×10⁻¹⁰ yr⁻¹ with direct Urca reactions
- Stricter upper limit of |Ġ/G| < 4×10⁻¹² yr⁻¹ considering only modified Urca reactions
- Among the most restrictive limits from astrophysical observations

## Abstract

A hypothetical time-variation of the gravitational constant $G$ would make neutron stars expand or contract, so the matter in their interiors would depart from beta equilibrium. This induces non-equilibrium weak reactions, which release energy that is invested partly in neutrino emission and partly in internal heating. Eventually, the star arrives at a stationary state in which the temperature remains nearly constant, as the forcing through the change of $G$ is balanced by the ongoing reactions. Using the surface temperature of the nearest millisecond pulsar (PSR J0437$-$4715) inferred from ultraviolet observations and results from theoretical modelling of the thermal evolution, we estimate two upper limits for this variation: (1) $|\dot G/G| < 2 \times 10^{-10}\mathrm{yr}^{-1},$ if the fast, "direct Urca" reactions are allowed, and (2) $|\dot G/G|<4\times 10^{-12}\mathrm{yr}^{-1},$ considering only the slower, "modified Urca" reactions. The latter is among the most restrictive upper limits obtained by other methods.