On an analytical solution of the optimum trajectory problem in a gravitational field

ABSTRACT The gravitational field of a galaxy group or cluster slows down the Hubble stream and turns its speed to zero at some radius R0. We offer an exact analytical relation between R0 and the mass of the group.

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Analytical solution from vector potentials for the gravitational field of a general polyhedron

Celestial Mechanics and Dynamical Astronomy ◽

10.1007/s10569-014-9588-x ◽

2014 ◽

Vol 121 (1) ◽

pp. 17-38 ◽

Cited By ~ 30

Author(s):

John T. Conway

Keyword(s):

Gravitational Field ◽

Analytical Solution ◽

Vector Potentials

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Many accelerating distorted black holes

The European Physical Journal C ◽

10.1140/epjc/s10052-021-09693-6 ◽

2021 ◽

Vol 81 (10) ◽

Author(s):

Marco Astorino ◽

Adriano Viganò

Keyword(s):

Black Holes ◽

General Relativity ◽

Black Hole ◽

Gravitational Field ◽

Analytical Solution ◽

Inverse Scattering ◽

Inverse Scattering Method ◽

Scattering Method ◽

Schwarzschild Black Hole ◽

Hole Configuration

AbstractAn analytical solution of four-dimensional General Relativity, representing an array of collinear and accelerating black holes, is constructed with the inverse scattering method. The metric can be completely regularised from any conical singularity, thanks to the presence of an external gravitational field. Therefore the multi-black hole configuration can be maintained at equilibrium without the need of strings or struts. Some notable subcases such as the accelerating distorted Schwarzschild black hole and the distorted double C-metric are explicitly presented. The Smarr law and the thermodynamics of these systems is studied. The Bonnor–Swaminarayan and the Bičák–Hoenselaers–Schmidt particle metrics are recovered, through appropriate limits, from the multi-black holes solutions.

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A one-dimensional self-gravitating stellar gas

Symposium - International Astronomical Union ◽

10.1017/s0074180900105261 ◽

1966 ◽

Vol 25 ◽

pp. 46-48 ◽

Cited By ~ 2

Author(s):

M. Lecar

Keyword(s):

Gravitational Field ◽

Phase Space ◽

Motion Picture ◽

Space Distribution ◽

Two Dimensional ◽

One Dimensional ◽

Phase Space Distribution ◽

Dimensional Phase Space ◽

The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

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