Uniform acceleration in general relativity

Friedman, Yaakov; Scarr, Tzvi

doi:10.1007/s10714-015-1966-5

Cited by 29 publications

(37 citation statements)

References 13 publications

(50 reference statements)

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“…Let us examine the case of constant proper acceleration, a = a 0 constant. In our view this constancy will correspond to Einstein's intuitive definition of uniform acceleration [6].…”

Section: A Constant Proper Accelerationmentioning

confidence: 81%

“…Our definition excludes the uniform circular motion (see Appendix A), for which κ 2 > κ 1 , with both κ 2 and κ 1 constants. Let us comment that our definition is much more restrictive than that used in [6], inspired in [11]. In [6] the observer with constant proper acceleration (uniform acceleration) is defined by the constancy of the first, second and third curvature invariants (in a 4 dimensional Minkoswki spacetime), and it is understood that in higher dimensions the definition will include the constancy of the new curvature invariants that may appear.…”

Section: Discussionmentioning

confidence: 99%

“…Let us comment that our definition is much more restrictive than that used in [6], inspired in [11]. In [6] the observer with constant proper acceleration (uniform acceleration) is defined by the constancy of the first, second and third curvature invariants (in a 4 dimensional Minkoswki spacetime), and it is understood that in higher dimensions the definition will include the constancy of the new curvature invariants that may appear. Of course it is all a matter of definition, but we would like to point out that with our definition, for whatever dimension of the Minkowski spacetime, there is always a frame of reference in which the motion will at most be three dimensional (κ 3 = 0).…”

Section: Discussionmentioning

confidence: 99%

See 2 more Smart Citations

Observers with constant proper acceleration, constant proper Jerk, and beyond

Pons

Palol

2019

Gen Relativ Gravit

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We discuss in Minkowski spacetime the differences between the concepts of constant proper n-acceleration and of vanishing (n + 1)-acceleration. By n-acceleration we essentially mean the higher order time derivatives of the position vector of the trajectory of a point particle, adapted to Minkowski spacetime or eventually to curved spacetime. The 2-acceleration is known as the Jerk, the 3-acceleration as the Snap, etc. As for the concept of proper n-acceleration we give a specific definition involving the instantaneous comoving frame of the observer and we discuss, in such framework, the difficulties in finding a characterization of this notion as a Lorentz invariant statement. We show how the Frenet-Serret formalism helps to address the problem. In particular we find that our definition of an observer with constant proper acceleration corresponds to the vanishing of the third curvature invariant κ 3 (thus the motion is three dimensional in Minkowski spacetime) together with the constancy of the first and second curvature invariants and the restriction κ 2 < κ 1 , the particular case κ 2 = 0 being the one commonly referred to in the literature. We generalize these concepts to curved spacetime, in which the notion of trajectory in a plane is replaced by the vanishing of the second curvature invariant κ 2 . Under this condition, the concept of constant proper n-acceleration coincides with that of the vanising of the (n + 1)-acceleration and is characterized by the fact that the first curvature invariant κ 1 is a (n − 1)-degree polynomial of proper time. We illustrate some of our results with examples in Minkowski, de Sitter and Schwarzschild spacetimes.1 From now on, by constantly accelerated observer we mean the observer with constant proper acceleration.Proper in the sense of being described in the instantaneous frame comoving with the observer. 2 We learn in [4] that "This terminology goes back to a 1932 advertisement of Kellogg's Rice Crispies which 'merrily Snap, crackle, and pop in a bowl of milk' ". Here our use of these concepts is unrelated to the standard use in cosmology as higher order time derivatives of the scale factor in the Friedmann-Lemaitre-Robertson-Walker (FLRW) metric

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“…Let us examine the case of constant proper acceleration, a = a 0 constant. In our view this constancy will correspond to Einstein's intuitive definition of uniform acceleration [6].…”

Section: A Constant Proper Accelerationmentioning

confidence: 81%

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Observers with constant proper acceleration, constant proper Jerk, and beyond

Pons

Palol

2019

Gen Relativ Gravit

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“…For treatments of uniformly accelerated motion in the theory of relativity, see, for instance, Refs. [19][20][21][22][23].…”

Section: Accelerated Systemmentioning

confidence: 99%

Conformal Symmetry, Accelerated Observers, and Nonlocality

Mashhoon

2019

Symmetry

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The acceleration transformations form a 4-parameter Abelian subgroup of the conformal group of Minkowski spacetime. The passive interpretation of acceleration transformations leads to a congruence of uniformly accelerated observers in Minkowski spacetime. The properties of this congruence are studied in order to illustrate the kinematics of accelerated observers in relativistic physics. The generalization of this approach under conformal rescaling of the spacetime metric is examined.

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“…For example, Rindler used the relation between Lorentzian circles and uniformly accelerated motion in Minkowski spacetime to determine hyperbolic motion in General Relativity [21,22]. Covariant definition of the UAM and its explicit solutions were investigated by Friedman and Scarr [23,24]. The notion of the UAM was analyzed in detail by giving its novel geometric characterization by Fuente and Romero [25].…”

Section: Uniform Motion Of Spacelike Sabban Magnetic Curves On the S 2mentioning

confidence: 99%

A New Version of Spherical Magnetic Curves in the De-Sitter Space S 1 2

Baş

2018

Symmetry

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This paper presents a new type of spacelike magnetic curves associated with the Sabban vector field defined in the Minkowski space. In this approach, some geometrical and physical features of the moving charged particle corresponding to the spacelike magnetic curves are identified. An entire characterization is developed for spacelike spherical magnetic curves, denoting particularly the changes of their energy with respect to time, the influence of the magnetic force on them, and the existence condition for the uniformity of these curves.

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Uniform acceleration in general relativity

Cited by 29 publications

References 13 publications

Observers with constant proper acceleration, constant proper Jerk, and beyond

Observers with constant proper acceleration, constant proper Jerk, and beyond

Conformal Symmetry, Accelerated Observers, and Nonlocality

A New Version of Spherical Magnetic Curves in the De-Sitter Space S 1 2

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