Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new user2+1 dimensional solution of Einstein Cartan equations
174
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
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.
rate research
Read More
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.
We present a general solution of the coupled Einstein-Maxwell field equations (without the source charges and currents) in three spacetime dimensions. We also admit any value of the cosmological constant. The whole family of such $Lambda$-electrovacuum local solutions splits into two distinct subclasses, namely the non-expanding Kundt class and the expanding Robinson-Trautman class. While the Kundt class only admits electromagnetic fields which are aligned along the geometrically privileged null congruence, the Robinson-Trautman class admits both aligned and also more complex non-aligned Maxwell fields. We derive all the metric and Maxwell field components, together with explicit constraints imposed by the field equations. We also identify the most important special spacetimes of this type, namely the coupled gravitational-electromagnetic waves and charged black holes.
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.
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.
We perform a covariant 1+3 split of the Newton-Cartan equations. The resulting 3-dimensional system of equations, called textit{the 1+3-Newton-Cartan equations}, is structurally equivalent to the 1+3-Einstein equations. In particular it features the momentum constraint, and a choice of adapted coordinates corresponds to a choice of shift vector. We show that these equations reduce to the classical Newton equations without the need for special Galilean coordinates. The solutions to the 1+3-Newton-Cartan equations are equivalent to the solutions of the classical Newton equations if space is assumed to be compact or if fall-off conditions at infinity are assumed. We then show that space expansion arises as a fundamental field in Newton-Cartan theory, and not by construction as in the classical formulation of Newtonian cosmology. We recover the Buchert-Ehlers theorem for the general expansion law in Newtonian cosmology.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
