Ultracompact rotating gravastars and the problem of matching with Kerr spacetime

We study dynamics of a test charged particle moving in a weakly charged extreme Kerr throat. Dynamical equations of the particle motion are solved in quadratures. We show explicitly that the Killing tensor of the Kerr spacetime becomes reducible in the extreme Kerr throat geometry. Special types of motion of particles and light are discussed.

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Complete set of quasi-conserved quantities for spinning particles around Kerr

SciPost Physics ◽

10.21468/scipostphys.12.1.012 ◽

2022 ◽

Vol 12 (1) ◽

Author(s):

Geoffrey Compère ◽

Adrien Druart

Keyword(s):

Linear Order ◽

Conserved Quantities ◽

Killing Tensor ◽

Kerr Geometry ◽

Spinning Particles ◽

Kerr Spacetime ◽

Killing Tensors ◽

Mixed Symmetry ◽

Constants Of Motion ◽

Complete Set

We revisit the conserved quantities of the Mathisson-Papapetrou-Tulczyjew equations describing the motion of spinning particles on a fixed background. Assuming Ricci-flatness and the existence of a Killing-Yano tensor, we demonstrate that besides the two non-trivial quasi-conserved quantities, i.e. conserved at linear order in the spin, found by Rüdiger, non-trivial quasi-conserved quantities are in one-to-one correspondence with non-trivial mixed-symmetry Killing tensors. We prove that no such stationary and axisymmetric mixed-symmetry Killing tensor exists on the Kerr geometry. We discuss the implications for the motion of spinning particles on Kerr spacetime where the quasi-constants of motion are shown not to be in complete involution.

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Quasilocal momentum and angular momentum in Kerr spacetime

Classical and Quantum Gravity ◽

10.1088/0264-9381/8/4/014 ◽

1991 ◽

Vol 8 (4) ◽

pp. 697-701 ◽

Cited By ~ 12

Author(s):

G Bergqvist ◽

M Ludvigsen

Keyword(s):

Angular Momentum ◽

Kerr Spacetime

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Exact Axially Symmetric Solution inf(T)Gravity Theory

Advances in High Energy Physics ◽

10.1155/2014/857936 ◽

2014 ◽

Vol 2014 ◽

pp. 1-9 ◽

Cited By ~ 1

Author(s):

Gamal G. L. Nashed

Keyword(s):

Vacuum Solution ◽

Gravity Theory ◽

Kerr Metric ◽

Radial Coordinate ◽

Lorentz Transformations ◽

Axially Symmetric ◽

Field Equations ◽

Tetrad Field ◽

Kerr Spacetime ◽

Euler’S Angles

A general tetrad field with sixteen unknown functions is applied to the field equations off(T)gravity theory. An analytic vacuum solution is derived with two constants of integration and an angleΦthat depends on the angle coordinateϕand radial coordinater. The tetrad field of this solution is axially symmetric and the scalar torsion vanishes. We calculate the associated metric of the derived solution and show that it represents Kerr spacetime. Finally, we show that the derived solution can be described by two local Lorentz transformations in addition to a tetrad field that is the square root of the Kerr metric. One of these local Lorentz transformations is a special case of Euler’s angles and the other represents a boost when the rotation parameter vanishes.

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