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Register a new userRaychadhuri equations and gravitational collapse in Einstein-Cartan theory
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The Raychaudhuri equations for the expansion, shear and vorticity are generalized in a spacetime with torsion for timelike as well as null congruences. These equations are purely geometrical like the original Raychuadhuri equations and could be reduced to them when there is no torsion. Using the Einstein-Cartan-Sciama-Kibble field equations the effective stress-energy tensor is derived. We also consider an Oppenheimer-Snyder model for the gravitational collapse of dust. It is shown that the null energy condition (NEC) is violated before the density of the collapsing dust reaches the Planck density, hinting that the spacetime singularity may be avoided if there is a non-zero torsion,i.e. if the collapsing dust particles possess intrinsic spin.
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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 spin surrounded by vacuum, explore their properties and discuss how these solutions should be smoothly matched to an exterior space-time. We study how spin 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 spin can exist. We also provide some algorithms to generate new solutions.
In this work a static solution of Einstein-Cartan (EC) equations in 2+1 dimensional space-time is given by considering classical spin-1/2 field as external source for torsion of the space-time. Here, the torsion tensor is obtained from metricity condition for the connection and the static spinor field is determined as the solution of Dirac equation in 2+1 spacetime with non-zero cosmological constant and torsion. The torsion itself is considered as a non-dynamical field.
We present results from a numerical study of spherical gravitational collapse in shift symmetric Einstein dilaton Gauss-Bonnet (EdGB) gravity. This modified gravity theory has a single coupling parameter that when zero reduces to general relativity (GR) minimally coupled to a massless scalar field. We first show results from the weak EdGB coupling limit, where we obtain solutions that smoothly approach those of the Einstein-Klein-Gordon system of GR. Here, in the strong field case, though our code does not utilize horizon penetrating coordinates, we nevertheless find tentative evidence that approaching black hole formation the EdGB modifications cause the growth of scalar field hair, consistent with known static black hole solutions in EdGB gravity. For the strong EdGB coupling regime, in a companion paper we first showed results that even in the weak field (i.e. far from black hole formation), the EdGB equations are of mixed type: evolution of the initially hyperbolic system of partial differential equations lead to formation of a region where their character changes to elliptic. Here, we present more details about this regime. In particular, we show that an effective energy density based on the Misner-Sharp mass is negative near these elliptic regions, and similarly the null convergence condition is violated then.
Gravitational stability of torsion and inflaton field in a four-dimensional spacetime de Sitter solution in scalar-tensor cosmology where Cartan torsion propagates is investigated in detail. Inflaton and torsion evolution equations are derived by making use of a Lagrangean method. Stable and unstable modes for torsion and inflatons are found to be dependent of the background torsion and inflaton fields. Present astrophysical observations favour a stable mode for torsion since this would explain why no relic torsion imprint has been found on the Cosmic Background Radiation in the universe.
The qBounce experiment offers a new way of looking at gravitation based on quantum interference. An ultracold neutron is reflected in well-defined quantum states in the gravity potential of the Earth by a mirror, which allows to apply the concept of gravity resonance spectroscopy (GRS). This experiment with neutrons gives access to all gravity parameters as the dependences on distance, mass, curvature, energy-momentum as well as on torsion. Here, we concentrate on torsion.
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