Gravitation according to general relativity remains singularly challenging to understand from first principles in relation to the other forces in Nature. On the other hand, it describes a broad range of phenomena in cosmology and astrophysics, some of which are well constrained by observations of the galaxy redshifts, the cosmic microwave background [338], supermassive black holes in galactic nuclei, radio-pulsars in neutron star–neutron star binaries [297], and, possibly in the near future, binary mergers, that should ultimately lead to new insights on its origin.

Geometrically, general relativity is built on the Riemann tensor as discussed in Chapter 3, which describes spacetime in terms of two-surfaces for which the Planck scale – the smallest length scale in Nature – introduces a unit of area. The event horizons of black holes are null-surfaces that carry entropy [77] and temperature by virtue of their radiation properties [276]. For macroscopic black holes, the entropy represents a large, hidden phase space of an underlying structure of spacetime and matter. It is tempting to think of low energy manifestations in the real world also without black holes, such as Newton's law between two ordinary point particles [625].