Einstein Gravity

This book serves two main purposes: firstly, it shows, in a simple way, how the possible existence of an extra-spatial dimension would affect the predictions of four-dimensional General Relativity, a model known as the Brane world; secondly, it explains, step-by-step, a new technique called Minimal Geometric Deformation, which was introduced for the purpose of solving the correspondingly modified Einstein field equations. This method gave rise to the Gravitational Decoupling in General Relativity, which is widely used to solve the Einstein field equations in various contexts.

Beyond Einstein’s Gravity is a graduate level introduction to extended theories of gravity and cosmology, including variational principles, the weak-field limit, gravitational waves, mathematical tools, exact solutions, as well as cosmological and astrophysical applications. The book provides a critical overview of the research in this area and unifies the existing literature using a consistent notation. Although the results apply in principle to all alternative gravities, a special emphasis is on scalar-tensor and f(R) theories.

Many of us have experienced the same; fallen and broken something. Yet supposedly, gravity is the weakest of the fundamental forces; it is claimed to be 10-15 times weaker than electromagnetism. Still, every one of us has more or less had a personal relationship with gravity.

Einstein's theory of gravitation is perhaps one of the best-established theories ever conceived. However, it is based on the hypothesis that space-time carries curvature alone, leaving torsion out. Because torsion is a natural part of the most general geometric background in which Einstein gravity is built, it is all too natural that the torsional completion of gravity should be considered. Constructing an underlying stage in which both curvature and torsion are present, the fact that curvature couples with energy suggests that torsion may couple with spin, which is the other conserved quantity in quantum field theory. Torsion-gravity with spinning matter is, therefore, a complete and self-consistent setting for modern physics, with potential applications wherever spin effects may be important, stretching from quantum mechanics to the standard models of particle physics and early cosmology. However, this fact is not as present in today's literature as it might be. The scope of the present collection of papers is to consolidate the wisdom of various experts in the field so as to clarify the present status of torsion in gravity and spin in quantum field theory.

This book reviews various modified gravity models, including those with modifications in the pure gravitational sector; those involving extra fields, that is, scalar-tensor and vector-tensor gravity theories; gravity models with Lorentz symmetry breaking; and nonlocal gravity models. The authors discuss both classical and quantum aspects of these theories. The book is unique in bringing together all the current alternatives to Einstein gravity in one source and serves as an excellent starting point for graduate students and other newcomers seeking an overview.