I'm reading the Gravity Hartle book (ed.2003) and I'm having trouble with the question in the last part of Example 5.9 - Frequency Measured by an Accelerating Observer. More specifically the problem is to consider an observer staying on the bridge of a starship following the accelerated worldline described by $$t(\sigma)=a^{-1} \sinh(\sigma), \;\;\;\;\;\;\;\;\;\; x(\sigma)=a^{-1} \cosh(\sigma)$$ where $a$ is a constant, $\sigma$ is a parameter ranging from $-\infty$ to $+\infty$, $x$ and $t$ are the usual coordinates of a flat spacetime ($c=1$ units). The reader is asked to explain why this observer when looking at a field of stars, will see them for only a limited period of proper time of order $1/a$, where the observer proper time $\tau$ is given by the relation $$d\tau^{2} = dt^{2} - dx^{2} = (a^{-1}\,d\sigma)^{2}$$
$\begingroup$
$\endgroup$
Add a comment
|