An outstanding open issue in our quest for physics beyond Einstein is the unification of
general relativity (GR) and quantum physics. Loop quantum gravity (LQG) is a leading …

The goal of this review is to present an introduction to loop quantum gravity—a background-
independent, non-perturbative approach to the problem of unification of general relativity …

The problem of describing the quantum behavior of gravity, and thus understanding
quantum spacetime, is still open. Loop quantum gravity is a well-developed approach to this …

The fact that one can associate thermodynamic properties with horizons brings together
principles of quantum theory, gravitation and thermodynamics and possibly offers a window …

Recent advances in classical machine learning have shown that creating models with
inductive biases encoding the symmetries of a problem can greatly improve performance …

This article reviews the present status of the spin-foam approach to the quantization of
gravity. Special attention is payed to the pedagogical presentation of the recently-introduced …

Quantum gravity is expected to be necessary in order to understand situations in which
classical general relativity breaks down. In particular in cosmology one has to deal with …

Applications of Riemannian quantum geometry to cosmology have had notable successes.
In particular, the fundamental discreteness underlying quantum geometry has led to a …

Over the past three decades, black holes have played an important role in quantum gravity,
mathematical physics, numerical relativity and gravitational wave phenomenology …

We calculate the black-hole entropy in loop quantum gravity as a function of the horizon
area and provide the exact formula for the leading and sub-leading terms. By comparison …