Schwarzschild Gravitational Redshift

In general relativity, a clock deeper in a gravitational field ticks more slowly than a clock further away. In the exterior Schwarzschild spacetime describing a non-rotating black hole, the ticking rate of a static clock at coordinate radius r compared to a clock at infinity is given by the lapse function:
lapse = √(1 - 1/r)
where r is given in dimensionless units relative to the Schwarzschild radius.

Experiment

You can use the interactive module to explore gravitational redshift between different static observers.

1. Select an Emitter radius of 10.
2. Select a Receiver radius of 3.
3. Observe that the frequency ratio is greater than 1, resulting in a negative redshift (blueshift), because the photon falls deeper into the gravitational well.