Students are often not exposed to the main ideas of general relativity until relatively late in their education, due to the mathematical complexity of the theory. In particular, the Einstein field equation is generally presented in a way that obscures its geometrical meaning under a thicket of indices. I will show an index-free geometrical approach to the equation that is suitable for students unfamiliar with tensor calculus. This approach can be used to derive some important consequences of the Einstein equation, including the Newtonian limit and the Friedmann equation.

In addition, I will argue that the cosmological redshift should be interpreted as a Doppler shift, and not as an effect of the “stretching of space” as it is often described. The latter description reinforces misconceptions about cosmology and relativity.