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16933 results

Page 17 of 847

  • 5 - Gravitational Waves and Radiation

  • Joel Franklin, Reed College, Oregon
  • Book:
    An Introduction to Gravity
    Published online:
    04 May 2024
    Print publication:
    11 April 2024, pp 173-210

  • Summary

    Gravitational plane waves and their detection start the chapter off in parallel with electromagnetic plane waves and their detection. Geodesic deviation is reviewed and allows for a brief introduction to LIGO. The stress tensor source of radiation (and therefore, at least local, plane waves) and its conservation of energy and momentum are tied to the radiation solution of the linearized form of Einstein’s equation. A highlight is the role of gauge freedom in making gravitational plane waves physically relevant (by gauge fixing to reveal the underlying plus and cross polarizations). Power loss to gravitational radiation is discussed in the linearized limit by comparison with electric quadrupole radiation.

  • 4 - Vacuum Solutions and Geodesics

  • Joel Franklin, Reed College, Oregon
  • Book:
    An Introduction to Gravity
    Published online:
    04 May 2024
    Print publication:
    11 April 2024, pp 136-172

  • Summary

    Spherical symmetry for a metric is defined and used to build a two-function ansatz. The Schwarzschild spacetime emerges as the solution to Einstein’s equation with, and we see how the Newtonian potential is related to the linearized Schwarzschild metric. The lightlike and spacelike geodesics of the metric are explored using exact, approximate, and numerical approaches. Many of the usual experimental tests are covered in detail: perihelion precession, bending of light, and time dilation, for example. The structure of the singularities in the Schwarzschild spacetime is studied using Eddington–Finkelstein and Kruskal–Szekeres coordinates. At the end of the chapter, the Kerr spacetime is introduced, and students are invited to explore its geodesics.

Page 17 of 847