Neutrino trapping in extremely compact Tolman VII spacetimes

TL;DR

This paper investigates neutrino trapping in extremely compact Tolman VII spacetimes, extending previous models to more realistic energy density distributions and demonstrating stronger trapping effects that could influence neutron star cooling.

Contribution

It extends neutrino trapping studies from uniform density models to Tolman VII spacetimes, showing enhanced trapping efficiency and potential impact on neutron star cooling.

Findings

Neutrino trapping is significantly stronger in Tolman VII spacetimes.

The trapping efficiency depends on specific parameters of the spacetime.

Results suggest neutrino trapping could affect neutron star cooling processes.

Abstract

Extremely compact objects trap gravitational waves or neutrinos, assumed to move along null geodesics in the trapping regions. The trapping of neutrinos was extensively studied for spherically symmetric extremely compact objects constructed under the simplest approximation of the uniform energy density distribution, with radius located under the photosphere of the external spacetime; in addition, uniform emissivity distribution of neutrinos was assumed in these studies. Here we extend the studies of the neutrino trapping for the case of the extremely compact Tolman VII objects representing the simplest generalization of the internal Schwarzschild solution with uniform distribution of the energy density, and the correspondingly related distribution of the neutrino emissivity that is thus again proportional to the energy density; radius of such extremely compact objects can overcome the photosphere of the external Schwarzschild spacetime. In dependence on the parameters of the Tolman VII spacetimes, we determine the "local" and "global" coefficients of efficiency of the trapping and demonstrate that the role of the trapping is significantly stronger than in the internal Schwarzschild spacetimes. Our results indicate possible influence of the neutrino trapping in cooling of neutron stars.