Acceleration of particles to high energy via gravitational repulsion in the Schwarzschild field

Abstract

Gravitational repulsion is an inherent aspect of the Schwarzschild solution of the Einstein-Hilbert field equations of general relativity. We show that this circumstance means that it is possible to gravitationally accelerate particles to the highest cosmic ray energies. *

Comment on “Acceleration of particles to high energy via gravitational repulsion in the Schwarzschild field” by C. H. McGruder III

“…The last expression should be compared with Drumaux's equation (1). The sign of acceleration (15) changes to the opposite when r < α.…”

“…In a recent paper [1], McGruder III discussed the radial motion of massive particle emitted at some point outside the horizon of Schwarzschild field, and then outgoing to infinity. If at the starting point the particle obeys the condition dr dt > c √ 3 (1 − α r ), the geodesic equation implies d 2 r dt 2 > 0 (see Eq.…”

“…2 we show the incorrectness of McGruder's conclusion for all arrival velocities: velocity of the particle incoming to infinity always is less than its initial velocity. Since the confusion around this point 2 has a centenary history [6,7], and continues to the present day [1,[8][9][10][11][12], we believe that a self-contained presentation of this result could be of interest.…”

Near-Horizon Geodesics for Astrophysical and Idealised Black Holes: Coordinate Velocity and Coordinate Acceleration

“…where ǫ is a constant (effectively the energy per unit rest mass; ǫ = 1 corresponds to dropping a particle at rest from spatial infinity; ǫ > 1 corresponds to dropping a moving particle from spatial infinity; ǫ < 1 corresponds to a gravitationally bound particle, dropped at rest from some finite radius). 1 In spherical symmetry this Killing conservation law can be written as…”

Comment on "Acceleration of particles to high energy via gravitational repulsion in the Schwarzschild field" [Astropart. Phys. 86 (2017) 18-20]

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Comments are due on a recent paper by McGruder III (2017) in which the author deals with the concept of gravitational repulsion in the context of the Schwarzschild-Droste solution. Repulsion (deceleration) for ingoing particles into a black hole is a concept proposed several times starting from Droste himself in 1916.

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