Static compact objects in Einstein-Cartan theory

Abstract

We generalize the Tolman-Oppenheimer-Volkoff equations for space-times endowed with a Weyssenhoff like torsion field in the Einstein-Cartan theory. The new set of structure equations clearly show how the presence of torsion affects the geometry of the space-time. We obtain new exact solutions for compact objects with non-null intrinsic spin surrounded by vacuum, explore their properties and discuss how these solutions should be smoothly matched to an exterior space-time.We study how the intrinsic spin of matter changes the Buchdahl limit for the maximum compactness of stars. Moreover, under rather generic conditions, we prove that in the context of a Weyssenhoff like torsion, no static, spherically symmetric compact objects supported only by the intrinsic spin can exist. We also provide some algorithms to generate new solutions. * paulo.luz@ist.utl.pt † sante.carloni@gmail.com 1 We should remark that here, and in the following, the word "spin" will be used exclusively to represent the quantum spin of the particles that source the gravitational field equations. In no case the word spin will be associated to any form of rotation of the compact objects we will analyze.

Consistent solution of Einstein-Cartan equations with torsion outside matter

“…With Eq. 159 in [43], a solution was presented for inner stars with junction to the outside leading to B(r) = (a + br 2 ) 2 which would mean with our solution…”

“…Further treatments can be performed numerically dependent on the given momentum and density profile via the equation of state. Exact solutions for the inner region of compact objects are discussed in [41,43,67], for rotating stars in [42] and possible upper limits of masses of stars in [44].…”

“…In the exterior of stars we can set p = 0 and n = 0 and should obtain the external Schwarzschild solution. The effective mass (43) and the Oppenheimer-Volkov equation (46) read then…”

“…Asymptotic flat solutions have been considered with respect to gravitational lensing in [41] and rotating and expanding solutions are presented in [42]. The inner star objects with spin and torsion are considered in [43] and mass bounds in [44].…”

Two-fluid stellar objects in General Relativity: the covariant formulation

“…In addition, in [7,8] it was shown that the generating theorems proposed by Boonserm et al in [20,21] can be easily formulated and extended to more complex cases. The 1+1+2 TOV equations have also been used to uncover new features of relativistic stellar objects in Einstein-Cartan gravity in [22].…”