Physical frames along circular orbits in stationary axisymmetric spacetimes

Bini, Donato; Cherubini, Christian; Geralico, Andrea; Jantzen, Robert T.

doi:10.1007/s10714-007-0587-z

Cited by 7 publications

(4 citation statements)

References 31 publications

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“…where ζ is the rapidity in the local inertial frame defined by and N = 1 tt N ϕ = g tϕ g ϕϕ (7) subject to the constraint u ν u ν = −1 as stated in [5], where N is the lapse function and N ϕ is the nonvanishing component of the shift vector field. This is not however a geodesic, so an external force must be applied to the particle to counter the gravitational field.…”

Section: Kerr-newman Distortionmentioning

confidence: 99%

Einstein-Podolsky-Rosen correlation in Kerr-Newman spacetime

Said

Adami

2010

Phys. Rev. D

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The EPR correlation has become an integral part of quantum communications as has general relativity in classical communication theory, however when combined an apparent deterioration is observed for spin states. We consider appropriate changes in directions of measurement to exploit full EPR entanglement for a pair of particles and show that it can be deduced only up to the outer even horizon of a Kerr-Newman black hole, even in the case of freely falling observer.

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Section: Kerr-newman Distortionmentioning

confidence: 99%

Einstein-Podolsky-Rosen correlation in Kerr-Newman spacetime

Said

Adami

2010

Phys. Rev. D

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“…one considers the solutions which describe deviations from that geodesic due to the spin-curvature force alone. The spin evolution equations (2) just represent parallel transport along the original circular geodesics, which leads to a simple rotation of the spin components (Sθ, γ −1 K Sφ) in the r-φ plane within the local rest space of the circular geodesics [22]. These equations are explicitly…”

Section: Introductionmentioning

confidence: 99%

Spin-geodesic deviations in the Schwarzschild spacetime

Bini¹,

Geralico²,

Jantzen³

2010

Gen Relativ Gravit

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The deviation of the path of a spinning particle from a circular geodesic in the Schwarzschild spacetime is studied by an extension of the idea of geodesic deviation. Within the Mathisson-Papapetrou-Dixon model and assuming the spin parameter to be sufficiently small so that it makes sense to linearize the equations of motion in the spin variables as well as in the geodesic deviation, the spin-curvature force adds an additional driving term to the second order system of linear ordinary differential equations satisfied by nearby geodesics. Choosing initial conditions for geodesic motion leads to solutions for which the deviations are entirely due to the spin-curvature force, and one finds that the spinning particle position for a given fixed total spin oscillates roughly within an ellipse in the plane perpendicular to the motion, while the azimuthal motion undergoes similar oscillations plus an additional secular drift which varies with spin orientation.Comment: 16 pages, 3 figures; published versio

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“…A useful class of observers in the following discussion are the "zero angular momentum observers" (ZAMO) [5,8]. They are orthogonal to the constant time spacelike hypersurfaces and their orthonormal frame in the case we are considering here, described in terms of the coordinates in (2.19) is…”

Section: Considerations On Rigidly Rotating Dustmentioning

confidence: 99%

Rigid rotation in GR and a generalization of the virial theorem for gravitomagnetism

Astesiano

2022

Gen Relativ Gravit

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In this work we study the properties of rigidly rotating neutral dust solutions in general relativity. This class of solutions gained relevance recently due to applications to the dynamics of spiral galaxies. We show that this class could be interpreted as a “rigid body” in general relativity and we analyze the different properties respect to the rigidly rotating disk in special relativity: for example, the general relativistic counterpart shows no Doppler effect for a light signal emitted and received from any two points at rest respect to the “rigid body”. This effect can be important to test the validity of the assumed model for our galaxy. In the second part we approach the problem from a low energy expansion perspective and we write down a generalization of the virial theorem for stationary spacetimes. The non-Newtonian contributions can lead to a re-weighting of dark matter in galaxies.

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Physical frames along circular orbits in stationary axisymmetric spacetimes

Cited by 7 publications

References 31 publications

Einstein-Podolsky-Rosen correlation in Kerr-Newman spacetime

Einstein-Podolsky-Rosen correlation in Kerr-Newman spacetime

Spin-geodesic deviations in the Schwarzschild spacetime

Rigid rotation in GR and a generalization of the virial theorem for gravitomagnetism

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