Understanding quantum gravity is difficult. However, a much easier problem is understanding how quantum fields behave in the presence of strong gravity. This led in the 1960s and 1970s to a framework known as quantum field theory in curved spacetime. In this framework, we make the simplifying assumption that gravity is approximately classical. This allows us to obtain a classical spacetime (often described by general relativity) upon which we can describe the behavior of quantum fields. While this is not a take on what gravity is fundamentally like, this framework has proven to be fruitful in understanding better the interplay between quantum mechanical systems and gravity, hence giving us hints about what full quantum gravity should look like.
One of the first predictions of quantum field theory in curved spacetime was Hawking’s derivation of the so-called Hawking effect. In general relativity, a black hole is defined as the region of spacetime from which no signal can reach infinity, Chap. 12). As a consequence, it is impossible for anything to come out of a black hole. It was thus a surprise when Hawking showed that black holes can emit particles due to quantum effects. Furthermore, the particle emission happens in a thermal spectrum, with temperature inversely proportional to the black hole’s mass (in the case of a Schwarzschild black hole). Hence, in this sense, black holes can be understood as objects with a non-vanishing temperature once quantum effects are considered.
This result sparked interest in a topic now known as black hole thermodynamics, which studies the amazing similarities between thermodynamic systems and black holes. It was known before the discovery of the Hawking effect that black hole mechanics has laws quite similar to the laws of thermodynamics. For example, the area of a black hole behaves in a similar way to the entropy of a thermodynamic system. Namely, the area of a classical black hole can never decrease. In the quantum theory, the area of a black hole is allowed to decrease at the expense of the matter entropy outside the black hole increasing.
Soon after Hawking’s prediction came Unruh’s prediction of the Unruh effect. This is a similar effect but in a very different situation. One now considers flat spacetime (i.e. a spacetime with a vanishing gravitational field) and considers two observers: an inertial observer and an accelerating observer with constant acceleration. Unruh’s prediction is that in the same physical conditions in which the inertial observer sees no particles in spacetime, the accelerated observer sees a thermal distribution of particles, with temperature proportional to the acceleration.
Both of these predictions showcase a basic lesson from quantum field theory in curved spacetimes: the notion of particle should be seen as a useful interpretation, but not more than that. In particular, the concept of field is what is truly fundamental in the theory.
Notice how these predictions hint at behaviors we should expect from quantum gravity. For instance, reproducing the results of black hole thermodynamics (such as computing the entropy of a black hole) is a theoretical test of quantum gravity theories.
The following references discuss quantum field theory in curved spacetimes and black hole thermodynamics.