Comment on  A remark on the mass angular-momentum relation in the double-Kerr solution

Euler derived equations for rigid body rotations in the body reference frame and in the stationary reference frame by considering an infinitesimal part of the rigid body.Another derivation is possible, and it is widely used: transforming torque-angular momentum relation to the body reference frame.However, their equivalence is not shown explicitly.In this work, for a rigid body with different moments of inertia, we calculated Euler equations explicitly in the body reference frame and in the stationary reference frame and torque-angular momentum relation.We also calculated equations of motion from Lagrangian.These calculations show that all four of them are equivalent.

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Carter constant and angular momentum

International Journal of Modern Physics D ◽

10.1142/s0218271817501802 ◽

2017 ◽

Vol 27 (01) ◽

pp. 1750180 ◽

Cited By ~ 2

Author(s):

Sajal Mukherjee ◽

K. Rajesh Nayak

Keyword(s):

Angular Momentum ◽

Kerr Solution ◽

Newtonian Mechanics ◽

Axially Symmetric ◽

Missing Link ◽

Symmetric Spacetimes ◽

Dipolar Potential ◽

Carry Over ◽

Definition Of ◽

Special Case

We investigate the Carter-like constant in the case of a particle moving in a nonrelativistic dipolar potential. This special case is a missing link between the Carter constant in stationary and axially symmetric spacetimes (SASS) such as Kerr solution and its possible Newtonian counterpart. We use this system to carry over the definition of angular momentum from the Newtonian mechanics to the relativistic SASS.

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Rotating bodies; the Kerr metric

10.1093/oso/9780192895646.003.0019 ◽

2021 ◽

pp. 260-273

Author(s):

Andrew M. Steane

Keyword(s):

Black Hole ◽

Angular Momentum ◽

Kerr Black Hole ◽

Kerr Metric ◽

Kerr Solution ◽

Limit Surface ◽

Generic Properties ◽

Rotating Body ◽

Particle Orbits ◽

Rotating Bodies

Spacetime around a general rigidly rotating body is discussed, and the Kerr solution explored in detail. First we obtain generic properties of stationary, axisymmetric metrics. The stationary limit surface and ergoregion is defined. Then the Kerr metric is presented (without derivation) and discussed. Horizons and limit surfaces are obtained, and the overall structure of the Kerr black hole deduced. The mass and angular momentum is extracted. Equations for particle orbits are obtained, and their properties discussed.

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