The Motion of Point Particles in Curved Spacetime

By E. Poisson, A. Pound, I. Vega. Living Reviews in Relativity, 2003

750 citations recorded by the source corpus.

This review is concerned with the motion of a point scalar charge, a point electric charge, and a point mass in a specified background spacetime. In each of the three cases the particle produces a field that behaves as outgoing radiation in the wave zone, and therefore removes energy from the particle. In the near zone the field acts on the particle and gives rise to a self-force that prevents the particle from moving on a geodesic of the background spacetime. The self-force contains both conservative and dissipative terms, and the latter are responsible for the radiation reaction. The work done by the self-force matches the energy radiated away by the particle.The field’s action on the particle is difficult to calculate because of its singular nature: the field diverges at the position of the particle. But it is possible to isolate the field’s singular part and show that it exerts no force on the particle — its only effect is to contribute to the particle’s inertia. What remains after subtraction is a regular field that is fully responsible for the self-force. Because this field satisfies a homogeneous wave equation, it can be thought of as a free field that interacts with the particle; it is this interaction that gives rise to the self-force.The mathematical tools required to derive the equations of motion of a point scalar charge, a point electric charge, and a point mass in a specified background spacetime are developed here from scratch. The review begins with a discussion of the basic theory of bitensors (Part I). It then applies the theory to the construction of convenient coordinate systems to chart a neighbourhood of the particle’s word line (Part II). It continues with a thorough discussion of Green’s functions in curved spacetime (Part III). The review presents a detailed derivation of each of the three equations of motion (Part IV). Because the notion of a point mass is problematic in general relativity, the review concludes (Part V) with an alternative derivation of the equations of motion that applies to a small body of arbitrary internal structure.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

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Citations in the corpus

Gravitational memory, BMS supertranslations and soft theorems (2014, neutral): “J H E P 0 1 ( 2 0 1 6 ) 0 8 6 and the leading corrections are related to Rabcd = Rμνρσe μ ae ν b e ρ ce σ d [24, 25] where the Riemann tensor is evaluated along the geodesic γ(τ).”
Black hole perturbation theory and gravitational self-force (2021, methodology): “[148, 156] cover the foundations of self-force theory, and Ref.”
Physics, Astrophysics and Cosmology with Gravitational Waves (2009, methodology): “This field is reviewed by two separate Living Reviews [292, 319].”
Essentials of blackfold dynamics (2009, methodology): “(9)This, however, is a somewhat formal statement due to the appearance of gravitational self-force divergences on the worldvolume that must be dealt with carefully [18].”
The Effective Field Theorist's Approach to Gravitational Dynamics (2016, background): “Not surprisingly, since in the self-force problem one does not expand in a small velocity parameter [404], this program has been extended to (very-)high PN order (21.”