General Relativity: An Introduction for Physicists · Problem 1.4

The spacetime of special relativity — Hobson, Efstathiou & Lasenby

Physics · relativistic-velocity-addition

Problem

An inertial frame

S'

is related to

S

by a boost of speed

v

in the

x

-direction, and

S''

is related to

S'

by a boost of speed

u'

in the

x'

-direction. Show that

S''

is related to

S

by a boost in the

x

-direction with speed

u

, where

u = c\tanh(\psi_v + \psi_{u'});

\tanh\psi_v = v/c

and

\tanh\psi_{u'} = u'/c