General Relativity: An Introduction for Physicists · Problem 5.6

Special relativity revisited — Hobson, Efstathiou & Lasenby

Physics · uniformly-accelerated-spaceship-4-acceleration

Problem

Show that the 4-acceleration of the spaceship in Exercise 5.5 is given by

[a^\mu] = \left(a\sinh\frac{a\tau}{c},\, a\cosh\frac{a\tau}{c},\, 0,\, 0\right).

Hence show that

a^\mu a_\mu = a^2

and that the magnitude of the spaceship's 3-acceleration in its own instantaneous rest frame is also

a