Fractal escapes in Newtonian and relativistic multipole gravitational fields

Alessandro P. S. de Moura, Patricio S. Letelier

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We study the planar motion of test particles in gravitational fields produced by an external material halo. Both the Newtonian and the general-relativistic dynamics are examined, and in the relativistic case the dynamics of both massive and massless particles are investigated. The halo field is given in general by a multipole expansion; we restrict ourselves to multipole fields of pure order, whose Newtonian potentials are homogeneous polynomials in cartesian coordinates. A pure n-pole field has n different escapes, one of which is chosen by the particle according to its initial conditions. We find that the escape has a fractal dependency on the initial conditions for n>2 both in the Newtonian and the relativistic cases for massive test particles, but with important differences between them. The relativistic motion of massless particles, however, was found to be regular for all the fields we could study. The box-counting dimension was used in each case to quantify the sensitivity to initial conditions which arises from the fractality of the escape route.
Original languageEnglish
Pages (from-to)309-320
Number of pages12
JournalPhysics Letters A
Volume266
Issue number4-6
DOIs
Publication statusPublished - 28 Feb 2000

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gravitational fields
multipoles
escape
fractals
halos
Cartesian coordinates
boxes
counting
polynomials
poles
routes
expansion
sensitivity

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Fractal escapes in Newtonian and relativistic multipole gravitational fields. / de Moura, Alessandro P. S.; Letelier, Patricio S.

In: Physics Letters A, Vol. 266, No. 4-6, 28.02.2000, p. 309-320.

Research output: Contribution to journalArticle

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