This volume guides early-career researchers through recent breakthroughs in mathematics and physics as related to general relativity. Chapters are based on courses and lectures given at the July 2019 Domoschool, International Alpine School in Mathematics and Physics, held in Domodossola, Italy, which was titled "Einstein Equations: Physical and Mathematical Aspects of General Relativity". Structured in two parts, the first features four courses from prominent experts on topics such as local energy in general relativity, geometry and analysis in black hole spacetimes, and antimatter gravity. The second part features a variety of papers based on talks given at the summer school, including topics like: - Quantum ergosphere General relativistic PoyntingRobertson effect modelling Numerical relativity Lengthcontraction in curved spacetime Classicality from an inhomogeneous universe Einstein Equations: Local Energy, Self-Force, and Fields in General Relativity will be a valuable resource for students and researchers in mathematics and physicists interested in exploring how their disciplines connect to general relativity.

Sergio Luigi Cacciatori is an Associate Professor at the Department of Science and High Technology at the University of Insubria in Como, Italy. His research interests regard Theoretical and Mathematical Physics with particular interests in General Relativity, Quantum Field Theory, Supergravity and Superstring Theories and Analogue Gravity. He is author of more than 100 publications of scientific articles and founder of the Domoschool, the International Alpine School of Mathematics and Physics in Domodossola, Italy.Alexander Kamenshchik is a Full Professor at the Department of Physics and Astronomy at the University of Bologna. His research interests regard Theoretical and Mathematical Physics and involve Classical and Quantum Cosmology, unification models for dark matter and dark energy, Tachyonic models, initial conditions in Quantum Cosmology, Mathematical Methods for Perturbative Cosmology. He is author of more than 200 scientific articles. In 2017 he was awarded by the Russian Academy of Sciences with the A.A. Friedmann Prize for the cycle of works "New directions in cosmology of the early and modern Universe".