Does space-time torsion determine the minimum mass of gravitating particles?

TL;DR

This paper investigates how space-time torsion in Einstein-Cartan theory influences the mass-radius limits of spin-fluid spheres, deriving bounds and potential observational tests, and linking torsion to particle mass constraints.

Contribution

It derives generalized mass-radius bounds for spin-fluid spheres in Einstein-Cartan theory, including implications for particle physics and astrophysical observations.

Findings

Derived upper and lower mass-radius limits for spin-fluid spheres.

Established gravitational redshift bounds for compact objects.

Linked torsion-induced minimum mass to the electron mass.

Abstract

We derive upper and lower limits for the mass-radius ratio of spin-fluid spheres in Einstein-Cartan theory, with matter satisfying a linear barotropic equation of state, and in the presence of a cosmological constant. Adopting a spherically symmetric interior geometry, we obtain the generalized continuity and Tolman-Oppenheimer-Volkoff equations for a Weyssenhoff spin-fluid in hydrostatic equilibrium, expressed in terms of the effective mass, density and pressure, all of which contain additional contributions from the spin. The generalized Buchdahl inequality, which remains valid at any point in the interior, is obtained, and general theoretical limits for the maximum and minimum mass-radius ratios are derived. As an application of our results we obtain gravitational red shift bounds for compact spin-fluid objects, which may (in principle) be used for observational tests of Einstein-Cartan theory in an astrophysical context. We also briefly consider applications of the torsion-induced minimum mass to the spin-generalized strong gravity model for baryons/mesons, and show that the existence of quantum spin imposes a lower bound for spinning particles, which almost exactly reproduces the electron mass.