Quantum field theory in curved spacetime gave birth to an area nowadays known as black hole thermodynamics (BHT). Within BHT, black holes are understood as thermodynamical objects, with non-vanishing temperature and entropy, which are originated by quantum effects. In particular, the second law of thermodynamics must be patched to also consider the entropy contained in black holes, hence leading to the generalized second law: the sum of the entropies of black holes and of matter outside black holes can never decrease. When considering these ideas, we can learn that nature seems to bind the maximum amount of entropy that can fit in a certain spacetime region.
The entropy of a black hole is proportional to its area. Thus, when an object is dropped into a black hole, its area must increase by an amount equal to or larger than the total entropy of the object. These sorts of considerations lead to the so-called entropy bounds, which bind the amount of entropy a given object can contain. Hence, they bound the amount of information that can be stored in a region of spacetime, typically by the area surrounding it. This leads to the notion that information must be somehow stored in spacetime surfaces and to the clue that this principle should be trivially implemented in a full theory of quantum gravity. Since storing information on a surface is the working principle behind holograms, this is known as the holographic principle. It invites us to think of the world as a hologram.
The most famous realization of this result is the AdS/CFT conjecture, which prescribes that certain theories in the bulk of a specific spacetime are equivalent to other theories on the boundary at infinity of the same spacetime. The spacetime considered in this case is the anti-de Sitter (AdS) spacetime and variations of it. Nevertheless, holography goes beyond AdS. For example, it is possible to encode information about quantum field theories in asymptotically flat spacetimes (i.e., spacetimes that are roughly flat at infinity) at the boundary at infinity of the spacetime. While no duality is prescribed, one still has a holographic correspondence in the sense that the amount of information in the bulk of spacetime is limited by the boundary.
An interesting development in these topics is the quantum focusing conjecture (QFC). This conjecture states that gravity is always attractive once the notion of “attractive” is appropriately reinterpreted to take quantum effects into account. The classical equivalent of this result, known as the Raychaudhuri focusing theorem, is an important component of the proofs of many theorems in classical general relativity. Hence, the QFC may allow to generalize these results to scenarios in which quantum mechanics plays a significant role. Furthermore, it implies the Bousso bound—a completely covariant entropy bound—and the quantum null energy condition. Both of these results are consequences to non-gravitational physics derived from gravitational considerations, and hence they may lead us to fundamental aspects of the interplay between gravity and quantum field theory.
The following references discuss entropy bounds and holography in general spacetimes.