This exercise treats what is called hyperbolic motion. Suppose that, at any instant, a point mass m.

This exercise treats what is called
hyperbolic motion. Suppose that, at any instant, a point mass m has threevector
acceleration a = geˆ 1 in a system S in which m is instantaneously at rest,
where g is a given constant.

(a) Derive the following values for the
given fourvector dot products, w · w = g2 w · u = 0 u · u = −c2 (16.152)
where u is the velocity fourvector, and w is the acceleration fourvector.

(b) Consider a fixed system S relative to
which the mass m has threevector velocity v = v1eˆ 1.

Assume that S and
S are related by a standard Lorentz transformation. Prove that, relative to
this S system, the mass has velocity fourvector components