ABSTRACT
This chapter studies how and why an apparent (gravitational) horizon manifests itself in the Friedmann-lemaitre-Robertson-Walker spacetime and, in one of the most important consequences of the role it plays in cosmology. It investigates whether this redshift is due to a third form of time dilation, distinct from the better known gravitational and kinematic versions in other applications of general relativity, or whether it is merely a combination of the two, often called a ‘lapse’ function. Our exposition includes the fact that the gravitational horizon in cosmology coincides with what is commonly called an ‘apparent’ horizon in general relativity. The chapter demonstrates pedagogically that the best way to understand such features is to invoke and utilize the theorem of George David Birkhoff. A gravitational horizon appears for the observer outside the star when its radius shrinks sufficiently for the escape speed at the surface to equal or exceed the speed of light.
