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Curvilinear motion characterizes the movement of a particle or object along a curved path, notably evident when envisioning a car navigating a winding road. If the car starts at point A, its position vector is established within a fixed frame of reference, where the ratio of the position vector to its magnitude signifies the unit vector pointing in the position vector's direction.
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The Motion of Point Particles in Curved Spacetime.

Eric Poisson1, Adam Pound1, Ian Vega1

  • 1Department of Physics, University of Guelph, Guelph, Ontario Canada N1G 2W1.

Living Reviews in Relativity
|February 10, 2017
PubMed
Summary

This review details how charged particles and masses move in spacetime, experiencing self-forces due to their own radiation. These forces, including radiation reaction, alter their motion from simple geodesics.

Area of Science:

  • Theoretical physics
  • General relativity
  • Electromagnetism

Background:

  • Particles in spacetime generate radiation, losing energy.
  • Particle fields create self-forces, deviating motion from geodesics.
  • Calculating self-forces is complex due to field singularities.

Purpose of the Study:

  • To review the motion of point scalar charges, electric charges, and masses in background spacetimes.
  • To develop mathematical tools for deriving equations of motion.
  • To address the challenges of self-force calculations and radiation reaction.

Main Methods:

  • Developing the theory of bitensors.
  • Constructing coordinate systems around particle world lines.
  • Utilizing Green's functions in curved spacetime.

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  • Deriving equations of motion for point particles and extended bodies.

    • Main Results:

    • Self-forces include conservative and dissipative (radiation reaction) terms.
    • Singular parts of the field contribute to inertia, not force.
    • Regular fields are responsible for the self-force and radiation reaction.
    • Work done by self-force equals energy radiated.

    Conclusions:

    • The review provides a comprehensive derivation of equations of motion for various point particles.
    • It offers an alternative method for extended bodies, addressing issues in general relativity.
    • The work clarifies the nature of self-forces and radiation reaction in curved spacetimes.