Complex Geometry and Mathematical Physics

This book, Complex Geometry and Mathematical Physics: Lorentzian Geometry and Field Equations (Book III-A), presents results from Lorentzian geometry (causality theory of spacetimes, submanifolds of Lorentzian manifolds, compact Lorentzian holonomy) and general relativity and gravitation theory. The first in a captivating series of three books, it demonstrates the bond between physics and geometry such as the mathematical structure of Maxwell’s equations predicting Minkowskian geometry, geodesic motion in the Newtonian limit, Kepler’s problem and Mercury’s perihelic shift, Morse theory for light rays). The book also includes discussion on certain quantum mechanical aspects (bending of light in quantum gravity) and the structure of Einstein’s (linearized) field equations in empty space or in the presence of matter. The other two books of the series are: Complex Geometry and Mathematical Physics: Classical and Quantum Singularities of Space-Times (Book III-B) Complex Geometry and Mathematical Physics: Complex Analysis versus General Relativity Theory (Book III-C) "Complex Geometry and Mathematical Physics" is part of the ampler book project "Differential Geometry, Partial Differential Equations and Mathematical Physics" by the same Authors, and aims to demonstrate the interaction between complex analysis and complex geometry on one hand, and general relativity and (quantum) gravity theory on the other, with an emphasis on the modern and contemporary trends of applying ideas from GRG theory to certain problems arising in complex analysis, such as the many pathologies of the Diederich–Fornæss worm domains.