A new study explores the existence of neutron stars with an exotic feature called "primary scalar hair" within a subfamily of Degenerate-Higher-Order-Scalar-Tensor (DHOST) theories of gravity. These theories, which modify Einstein's General Relativity, predict that neutron stars could possess a fundamental scalar field extending beyond their surface, significantly altering their gravitational and structural properties. The research focuses on static and spherically symmetric solutions for these stellar configurations.

The researchers solved modified Tolman-Oppenheimer-Volkoff (TOV) equations to construct equilibrium configurations, using both polytropic and realistic equations of state. This approach allowed them to analyze the impact of scalar hair on the internal structure of the stars. The resulting scalar field and spacetime metric profiles, as well as the mass-radius relation of these exotic stars, were examined. The results show notable deviations from the predictions of standard General Relativity.

Specifically, the presence of positive scalar charges leads to more compact stars than would be expected under General Relativity. Furthermore, it was found that above a critical threshold of these scalar charges, the solutions lead to singularities. These theoretical predictions open a crucial avenue for observational physics, as future observations of neutron stars, such as precise measurements of their masses and radii, could place stringent constraints on the parameters characterizing beyond-General Relativity effects in these theories and the potential existence of their scalar hair.