Spacetime and Geometry · Problem 7.6

Cosmology — Sean Carroll

Physics — General Relativity · gravitational-radiation-head-on-collision

Problem

Two objects of mass

M

have a head-on collision at event

(0, 0, 0, 0)

. In the distant past,

t \to -\infty

, the masses started at

x \to \pm\infty

with zero velocity. (a) Using Newtonian theory, show that

x(t) = \pm(9Mt^2/8)^{1/3}

. (b) For what separations is the Newtonian approximation reasonable? (c) Calculate

h^{\mathrm{TT}}_{xx}(t)

(x, y, z) = (0, R, 0)