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Chapter 6: Gravitational Sources

Chapter 6: Gravitational Sources

pp. 211-246

Authors

, Reed College, Oregon
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Extract

The solutions so far have all be “in vacuum,” away from sources. In this chapter, we study gravity “in material.” For comparison, we review the continuum form of Newton’s second law and think about Newtonian gravitational predictions for, for example, hydrostatic equilibrium. Then we develop the relativistic version of those equations directly from Einstein’s equation with various source assumptions (spherical symmetry, perfect fluid) and obtain the interior Schwarzschild solution. Cosmology is another example of working “in material,” and we briefly review the Robertson–Walker starting point and solutions both with and without a cosmological constant. At the end of the chapter, spacetimes requiring exotic sources, including the Ellis wormhole and Alcubierre warp drive, are described.

Keywords

  • fluid dynamics
  • Navier–Stokes
  • Euler’s equations
  • stellar interior
  • cosmology
  • cosmological constant
  • worm hole
  • Alcubierre warp drive
  • interior Schwarzschild solution
  • Robertson–Walker

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