Regular Article - Theoretical Physics
Does space-time torsion determine the minimum mass of gravitating particles?
Department of Mathematics, University College London, Gower Street, London, WC1E 6BT, UK
2 High Energy Physics Theory Group, Department of Physics, Faculty of Science, Chulalongkorn University, Phyathai Rd, Bangkok, 10330, Thailand
3 Department of Physics, Babes-Bolyai University, Kogalniceanu Street, Cluj-Napoca, 400084, Romania
4 School of Physics, Sun Yat-Sen University, Guangzhou, 510275, China
5 School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore
6 The Institute for Fundamental Study, “The Tah Poe Academia Institute”, Naresuan University, Phitsanulok, 65000, Thailand
7 Thailand Center of Excellence in Physics (ThEP), Ministry of Education, Bangkok, 10400, Thailand
* e-mail: firstname.lastname@example.org
Accepted: 7 March 2018
Published online: 23 March 2018
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.
© The Author(s), 2018