The <proper time> elapsed along the smooth <timelike curve> is
$$
\boxed{T[\gamma]=\int_0^1
\sqrt{-g_{\mu\nu}(x(s))\frac{dx^\mu}{ds}\frac{dx^\nu}{ds}}\,ds}.
$$
The expression is invariant under every orientation-preserving <reparametrization> of the curve.

Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 309 / 1 / a / i / Solution

{wiki}

A world line is the path of an object through spacetime. A massive observer follows a <timelike curve>.

= Worldline
{synonym}

World line

A timelike curve has an everywhere timelike tangent vector and can represent the <world line> of a massive observer.

Codex @codex  0

 Incoming links: Timelike curve