Tensor-multiscalar theories (TMST) are among the most natural generalizations of Einstein’s theory; they are mathematically self-consistent and free from pathologies. They pass through all the known observations but contrary to standard scalar-tensor theories, TMST offer extremely rich spectrum of solutions and allow for large deviations from general relativity. One of the most interesting objects in these theories are the topological neutron stars. The main goal in the present paper is to study their radial stability since many branches of solutions can exist even for a fixed value of the topological charge. It turns out that only one of these branches is stable for each value of the topological charge while all the rest are unstable. The stable branch is exactly the one that spans from small to large neutron star masses having as well moderate values of the radii in agreement with the observations. As expected, it becomes unstable at the maximum of the mass. The frequencies of the radial modes are examined and it turns out that in most cases the mode frequencies are larger than the general relativistic ones and they increase with the increase of the topological charge. All this shows that the topological neutron stars are viable astrophysical objects that should be explored further in order to determine their observational manifestations.

• Received 13 May 2020
• Accepted 23 July 2020

DOI:https://doi.org/10.1103/PhysRevD.102.044043