Quantum gravity aims to reconcile the principles of general relativity, which describes gravity as a curvature of spacetime, with the principles of quantum mechanics, which governs the behavior of matter at the atomic and subatomic level.

Black holes are important in quantum gravity because they represent extreme environments where the effects of gravity are strongest and the principles of quantum mechanics must be taken into account.

In the classical theory of general relativity, matter that falls into a black hole is compressed into a singularity, which is a point of infinite density and curvature. However, quantum gravity suggests that this singularity may not exist and that matter may instead be spread out over a region of spacetime known as a black hole horizon.

Hawking radiation is a theoretical prediction in quantum gravity that black holes emit thermal radiation due to quantum vacuum fluctuations near their event horizons. This radiation is named after physicist Stephen Hawking, who first proposed its existence.

The Bekenstein-Hawking entropy is a theoretical result in quantum gravity that relates the entropy of a black hole to its surface area. This relationship has profound implications, as it suggests that black holes have a finite temperature and that they obey the laws of thermodynamics.

The AdS/CFT correspondence is a theoretical conjecture in quantum gravity that relates a theory of gravity in a higher-dimensional spacetime to a conformal field theory in a lower-dimensional spacetime. This correspondence has been used to gain insights into the nature of black holes and other gravitational phenomena.

Quantum entanglement is a phenomenon in which two particles become correlated in such a way that the state of one particle cannot be described independently of the other, even when they are separated by a large distance. This phenomenon has been proposed as a possible explanation for the paradox of black hole evaporation, which suggests that information can be lost when matter falls into a black hole.

The firewall paradox is a theoretical problem in quantum gravity that arises when trying to reconcile the principles of quantum mechanics with general relativity near the event horizon of a black hole. The paradox suggests that an observer falling into a black hole would encounter a firewall of high-energy particles, which would destroy the observer before they could reach the singularity at the center of the black hole.

The holographic principle is a theoretical conjecture in quantum gravity that states that the information contained in a volume of spacetime can be encoded on its boundary. This principle has profound implications for our understanding of the nature of spacetime and the relationship between gravity and other forces.

String theory is a theoretical framework in physics that attempts to unify all the fundamental forces of nature, including gravity, into a single theory. String theory suggests that the fundamental constituents of the universe are not point-like particles, but tiny, vibrating strings. These strings can vibrate in different ways, giving rise to different types of particles and forces.

Loop quantum gravity is a theoretical framework in quantum gravity that attempts to describe spacetime as a network of interconnected loops. These loops are thought to be the fundamental building blocks of spacetime, and they can be used to describe the behavior of matter and energy in a quantum gravitational context.

Causal dynamical triangulation is a numerical technique used to study the behavior of quantum gravity. It involves discretizing spacetime into a network of four-dimensional simplices, or building blocks, and then using Monte Carlo simulations to evolve the system over time. This technique has been used to study a variety of phenomena in quantum gravity, including black hole formation and evaporation.

Asymptotic safety is a theoretical framework in quantum gravity that suggests that gravity becomes non-perturbative at very high energies. This means that the usual perturbative methods used to study quantum gravity break down, and new techniques are needed. Asymptotic safety has been proposed as a possible way to solve the problem of quantum gravity and to develop a unified theory of all the fundamental forces.

The black hole information paradox is a theoretical problem in quantum gravity that arises when trying to reconcile the principles of quantum mechanics with general relativity near the event horizon of a black hole. The paradox suggests that information can be lost when matter falls into a black hole, which would violate the fundamental principles of quantum mechanics.