The relativistic acceleration addition theorem

Mishra, Lokanath

doi:10.1088/0264-9381/11/7/001

Cited by 6 publications

(10 citation statements)

References 4 publications

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“…This enables one to define trajectories for which the curvature vanishes identically as "relatively straight" with respect to the ordinary or corotating Fermi-Walker total spatial covariant derivative. Relative motion for which this is true may be called the case of purely linear relative acceleration (for each type), examined recently in the static case by Rindler and Mishra 31,32 and the present authors. 30 On the other hand, if the longitudinal relative acceleration vanishes, as it does for the case of constant relative speed in the ordinary and corotating cases, one has the case of purely transverse relative acceleration, the case studied extensively for circular orbits by Abramowicz et al in the static case [3][4][5][6][7][8][9] and by Abramowicz and coworkers in the stationary Kerr spacetime and stationary axisymmetric spacetimes.…”

Section: Relative Acceleration: Longitudinal and Transverse Partsmentioning

confidence: 85%

The Intrinsic Derivative and Centrifugal Forces in General Relativity: I.

Bini

Carini

Jantzen

1997

Int. J. Mod. Phys. D

177

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Everyday experience with centrifugal forces has always guided thinking on the close relationship between gravitational forces and accelerated systems of reference. Once spatial gravitational forces and accelerations are introduced into general relativity through a splitting of spacetime into space-plus-time associated with a family of test observers, one may further split the local rest space of those observers with respect to the direction of relative motion of a test particle world line in order to define longitudinal and transverse accelerations as well. The intrinsic covariant derivative (induced connection) along such a world line is the appropriate mathematical tool to analyze this problem, and by modifying this operator to correspond to the observer measurements, one understands more clearly the work of Abramowicz et al who define an "optical centrifugal force" in static axisymmetric spacetimes and attempt to generalize it and other inertial forces to arbitrary spacetimes. In a companion article the application of this framework to some familiar stationary axisymmetric spacetimes helps give a more intuitive picture of their rotational features including spin precession effects, and puts related work of de Felice and others on circular orbits in black hole spacetimes into a more general context.

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Section: Relative Acceleration: Longitudinal and Transverse Partsmentioning

confidence: 85%

The Intrinsic Derivative and Centrifugal Forces in General Relativity: I.

Bini

Carini

Jantzen

1997

Int. J. Mod. Phys. D

177

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“…In the particle mechanics description by S w , the mass m, the momentum p and γ-factor are dependent on v 0 , eqs. (38,43,42). In order to have this dynamical dependency in γ, it is required to use the GMLT with effective frame velocity u − w, i.e.…”

Section: Photon Dynamicsmentioning

confidence: 99%

“…However a transformation of acceleration is well known for Fermi and Schwarzschild coordinates. A number of specific acceleration transformation laws in GRT were described by Mishra and Rindler [54,43] and more generally using generic coordinates by [5] and, [12] for static observers (a coordinate-free space-time decomposition of a covariant expression):…”

Section: Relativistic Acceleration Transformationsmentioning

confidence: 99%

A Spatially-VSL Gravity Model with 1-PN Limit of GRT

Broekaert

2008

Found Phys

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In the static field configuration, a spatially-Variable Speed of Light (VSL) scalar gravity model with Lorentz-Poincaré interpretation was shown to reproduce the phenomenology implied by the Schwarzschild metric. In the present development, we effectively cover configurations with source kinematics due to an induced sweep velocity field w. The scalar-vector model now provides a Hamiltonian description for particles and photons in full accordance with the first Post-Newtonian (1-PN) approximation of General Relativity Theory (GRT). This result requires the validity of Poincaré's Principle of Relativity, i.e. the unobservability of 'preferred' frame movement. Poincaré's principle fixes the amplitude of the sweep velocity field of the moving source, or equivalently the 'vector potential' ξ of GRT (e.g.; S. Weinberg, Gravitation and cosmology, 1972), and provides the correct 1-PN limit of GRT. The implementation of this principle requires acceleration transformations derived from gravitationally modified Lorentz transformations. A comparison with the acceleration transformation in GRT is done. The present scope of the model is limited to weak-field gravitation without retardation and with gravitating test bodies. In conclusion the model's merits in terms of a simpler space, time and gravitation ontology -in terms of a Lorentz-Poincaré-type interpretation-are explained (e.g. for 'frame dragging', 'harmonic coordinate condition').

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“…Mishra [1] has recently presented some relations (the "transformation law" and the "addition law" for accelerations) between cinematical observations on particles in one-dimensional motion in a general relativistic static spacetime, as performed by accelerated observers in this spacetime. From his general relativistic addition law Mishra obtains, in particular, the formula a = γ −2 g (see equation (11) in [1]) for the local proper-time relative 3-acceleration a (Mishra's "physical acceleration") of a relativistic particle in one-dimensional free fall in any static gravitational field, relative to a preferred non-linear static reference frame ( g stands for the acceleration when the "physical" relative velocity v is zero; γ −2 = (1 − v 2 ) in units in which c = 1).…”

Section: Introductionmentioning

confidence: 99%

“…From his general relativistic addition law Mishra obtains, in particular, the formula a = γ −2 g (see equation (11) in [1]) for the local proper-time relative 3-acceleration a (Mishra's "physical acceleration") of a relativistic particle in one-dimensional free fall in any static gravitational field, relative to a preferred non-linear static reference frame ( g stands for the acceleration when the "physical" relative velocity v is zero; γ −2 = (1 − v 2 ) in units in which c = 1).…”

Section: Introductionmentioning

confidence: 99%

The static spacetime relative acceleration for general free fall and its possible experimental test

Bunchaft

Carneiro

1998

Class. Quantum Grav.

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Mishra has recently established, using a generic static metric, the relative local proper-time 3-acceleration of a test-particle in one-dimensional free fall relative to a static reference frame in any static spacetime. In this paper, on the grounds of gravitoelectromagnetism we establish, in a covariant spacetime form, the relative 4-acceleration for the general free fall, indicating its canonical representation with its 3-space cinematical content. Then we obtain the relation between this representation and the very known expression for the relative free fall acceleration in Fermi coordinates. Taking this into account, it is shown that an experiment with relativistic beams in a circular accelerator, modelled by Fermi coordinates, recently proposed by Moliner et al, can test the here established covariant result and, therefore, can also verify Mishra's formula. This possibility of experimental verification, besides its intrinsic importance, can answer a recent inquire by Vigier, related to his recent proposal of derivation of inertial forces.

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The relativistic acceleration addition theorem

Cited by 6 publications

References 4 publications

The Intrinsic Derivative and Centrifugal Forces in General Relativity: I.

The Intrinsic Derivative and Centrifugal Forces in General Relativity: I.

A Spatially-VSL Gravity Model with 1-PN Limit of GRT

The static spacetime relative acceleration for general free fall and its possible experimental test

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