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.
Highlights
In a series of papers published around one hundred years ago, Cartan proposed an extension of Einstein’s theory of general relativity in which the spin properties of matter act as an additional source for the gravitational field, influencing the geometry of space-time [1,2,3,4]
It is interesting to note that the concept of spin was introduced into theories of gravity, even before it was introduced into quantum mechanics, by Uhlenbeck and Goudsmit in 1925 [9]
Perfect fluids with spin were first studied by Weyssenhoff and Raabe [10] and are commonly referred to as Weyssenhoff fluids. (See [11] for a detailed discussion of their physical geometric properties.) Later, an important development in the application of Einstein–Cartan gravity was the proposal by Kopczynski [12] and Trautman [13] that the spin contributions of a Weyssenhoff fluid may avert the initial singularity at the Big Bang, by stopping the collapse in closed cosmological models at a minimum radius Rmin 1 cm
Summary
In a series of papers published around one hundred years ago, Cartan proposed an extension of Einstein’s theory of general relativity in which the spin properties of matter act as an additional source for the gravitational field, influencing the geometry of space-time [1,2,3,4]. Since a small but positive cosmological constant is still required in Einstein–Cartan theory, in order to explain latetime accelerated expansion [33], these results must be generalized to include the effects of spin (in the matter fluid) and torsion (in the space-time) in order to obtain realistic mass limits, either for fundamental particles or compact astrophysical objects. We obtain a spin-dependent generalization of the Buchdahl limit for the maximum mass–radius ratio of stable compact objects, which incorporates the effects of both torsion and dark energy, and we rigorously prove that a lower bound exists for spin-fluid objects, even in the absence of a cosmological constant.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
