(a) Show that the embedding surface of Eq. (26.48) is a paraboloid of revolution everywhere outside the...
Question:
(a) Show that the embedding surface of Eq. (26.48) is a paraboloid of revolution everywhere outside the star.
(b) Show that in the interior of a uniform-density star, the embedding surface is a segment of a sphere.
(c) Show that the match of the interior to the exterior is done in such a way that, in the embedding space, the embedded surface shows no kink (no bend) at r = R.
(d) Show that, in general, the circumference/(2π) for a star is less than the distance from the center to the surface by an amount of order one sixth the star’s gravitational radius, M/3. Evaluate this amount analytically for a star of uniform density, and numerically (approximately) for Earth and for a neutron star.
Step by Step Answer:
Modern Classical Physics Optics Fluids Plasmas Elasticity Relativity And Statistical Physics
ISBN: 9780691159027
1st Edition
Authors: Kip S. Thorne, Roger D. Blandford