We consider global properties of gravitomagnetism by investigating the gravitomagnetic field of a rotating cosmic string. We show that although the gravitomagnetic field produced by such a configuration of matter vanishes locally, it can be detected globally. In this context we discuss the gravitational analogue of the Aharonov-Bohm effect.

Holonomy and loop variables are presented for the spacetime of a torsion line defect in (2+1)-dimensional spacetime immersed on a (3+1)-dimensional spacetime. The metric considered has a teleparallel counterpart presented earlier by Letelier (Class. Quantum Grav. (1995)). In this letter we show that the (2+1)-dimensional torsion defect given by Letelier metric does not appear only in teleparallel (Weitzenbock) spacetime, but also in Riemann-Cartan (RC) spacetime. Since here the space off the torsion defect is not teleparallel, torsion appears only through curvature effects and maybe detected off the torsion lines.

Global aspects of gravitomagnetism

Holonomy and torsion defects in (2 + 1)D spacetime

Non-universal topological quantum computation models, such as the
Majorana fermion-based Ising anyon model, have to be supplemented with
an additional non-topological noisy gate in order to achieve
universality. Here we endeavour to remedy this using an Einstein­—Cartan
analog gravity picture of scalar fields. Specifically, we show that the
analog gravity picture enables unitary transformations to be realized in
two distinct ways: (i) via space-time holonomy and (ii) as gravitational
time dilation. The non-abelian geometric phases are enabled by
gravitational interactions, which are mediated by the spin-connection.
We analytically compute its matrix elements as a function of the scalar
field density distribution. This density can be regarded as the
gravitating distribution of matter in an analog universe. We show via
explicit calculations that there exists an infinite set of
asymptotically flat analog gravitational fields, each of which
implements a unique unitary transformation, that render the interactions
topological. We emphasise the generality of this result by asserting
that such gravitational gates could potentially be implemented in a
broad range of real systems modeled by scalar field with an acoustic
metric.

Topological quantum computation using analog gravitational holonomy and time dilation

The classical theory of fields

PrefaceChart of Main Topics1A First Tour12Einstein Geometrodynamics133Tests of Einstein Geometrodynamics874Cosmology, Standard Models, and Homogeneous Rotating Models1855The Initial-Value Problem in Einstein Geometrodynamics2696The Gravitomagnetic Field and Its Measurement3157Some Highlights of the Past and a Summary of Geometrodynamics and Inertia384Mathematical Appendix403Symbols and Notations437Author Index445Subject Index of Mathematical Appendix455Subject Index461Fundamental and Astronomical Constants and Units493

Global aspects of gravitomagnetism

Citations

Holonomy and torsion defects in (2 + 1)D spacetime

Topological quantum computation using analog gravitational holonomy and time dilation

References

The classical theory of fields

Gravitation and Inertia

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