Free Fall and Self-Force: an Historical Perspective

Abstract

Free fall has signed the greatest markings in the history of physics through the leaning Pisa tower, the Cambridge apple tree and the Einstein lift. The perspectives offered by the capture of stars by supermassive black holes are to be cherished, because the study of the motion of falling stars will constitute a giant step forward in the understanding of gravitation in the regime of strong field. After an account on the perception of free fall in ancient times and on the behaviour of a gravitating mass in Newtonian physics, this chapter deals with last century debate on the repulsion for a Schwarzschild black hole and mentions the issue of an infalling particle velocity at the horizon. Further, black hole perturbations and numerical methods are presented, paving the way to the introduction of the self-force and other back-action related methods. The impact of the perturbations on the motion of the falling particle is computed via the tail, the back-scattered part of the perturbations, or via a radiative Green function. In the former approach, the self-force acts upon the background geodesic; in the latter, the geodesic is conceived in the total (background plus perturbations) field. Regularisation techniques (mode-sum and Riemann-Hurwitz z function) intervene to cancel divergencies coming from the infinitesimal size of the particle. An account is given on the state of the art, including the last results obtained in this most classical problem, together with a perspective encompassing future space gravitational wave interferometry and head-on particle physics experiments. As free fall is patently non-adiabatic, it requires the most sophisticated techniques for studying the evolution of the motion. In this scenario, the potential of the self-consistent approach, by means of which the background geodesic is continuously corrected by the self-force contribution, is examined.

Deformation of horizons during a merger

“…We then studied the deformation of the event and apparent horizons as the particle approaches the black hole (FIGS. [3][4][5][6].…”

The Influence of Vacuum Electromagnetic Fluctuations on the motion of Charged Particles

“…(38) is right, then the existence of the limit value of 2 y shows that the conventional uniformly accelerating motion can not be strictly realized in the real world, and the radiation reaction originated from the vacuum fluctuations could solve the puzzles associated with this motion, such as whether or not charges uniformly accelerated radiate with respect to inertial observers and the problems associated with a freely falling charge in a gravitation field etc. [Dewitt & Brehme, 1960;Singal, 1995Singal, , 1997Lyle, 2008;Spallicci, 2010]. As seen in section 3, uniformly accelerating motion has an intimate relationship with the Unruh effect.…”

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

“…As it was repeatedly pointed out by Spallicci [2][3][4], in the particular case 1 of a particle that reaches infinity at zero velocity V ∞ = 0, the incorrectness of this reasoning follows from the old work of Drumaux [5], and the confusion arises due to identification of coordinate quantities dr dt and d 2 r dt 2 with velocity and acceleration of the particle in local environment. In Sect.…”

“…* Electronic address: alexei.deriglazov@ufjf.edu.br † Electronic address: wguzman@fisica.ugto.mx 1 Initial unrenormalized velocity of such a particle will be above the critical value only if it started its motion in the region α < r < 3α. 2 Detailed history of the subject can be found in [3].…”

“…The notions of unrenormalized and semi-renormalized velocities/accelerations have been extensively discussed in the literature[3,[13][14][15] 4. We stress that the definition of space and time intervals between two events in general relativity is not a matter of agreement, but follow from detailed analysis of the notion of simultaneous events using the null geodesics[16,17].…”