This book addresses the latest advances in general relativity research, including the classical world and spinor formalisms; keys to understanding gravity; the continuum mechanics of space-time; new evidences on matter without energy-stress tensor; a new approach to study gravitational stability of the solutions to the Einstein equations; Mond theory; polynumbers field theory; the algebra, geometry and physics of hyperland; S2-like star orbits near the galactic center in RN and Yukawa gravity; geodesic analysis in multidimensional gravity models; and the collapsing of general relativity and the singularity in the event of the Big Bang and black holes.

These lecture notes are intended for starting PhD students in theoretical physics who have a working knowledge of General Relativity. The four topics covered are: Surface charges as conserved quantities in theories of gravity; Classical and holographic features of three-dimensional Einstein gravity; Asymptotically flat spacetimes in four dimensions: BMS group and memory effects; The Kerr black hole: properties at extremality and quasi-normal mode ringing. Each topic starts with historical foundations and points to a few modern research directions.

Papers from the Discussion Conference on Recent Advances in General Relativity, held at the U. of Pittsburgh, May 1990, survey the interacting fields of classical general relativity, astrophysics, and quantum gravity. Some of the remarks made following the invited papers are also included. The conference also included three workshops on classical g

Following the approach of Lev Landau and Evgenii Lifshitz, this book introduces the theory of special and general relativity with the Lagrangian formalism and the principle of least action. This method allows the complete theory to be constructed starting from a small number of assumptions, and is the most natural approach in modern theoretical physics. The book begins by reviewing Newtonian mechanics and Newtonian gravity with the Lagrangian formalism and the principle of least action, and then moves to special and general relativity. Most calculations are presented step by step, as is done on the board in class. The book covers recent advances in gravitational wave astronomy and provides a general overview of current lines of research in gravity. It also includes numerous examples and problems in each chapter.

Einstein's general theory of relativity — currently our best theory of gravity — is important not only to specialists, but to a much wider group of physicists. This short textbook on general relativity and gravitation offers students glimpses of the vast landscape of science connected to general relativity. It incorporates some of the latest research in the field. The book is aimed at readers with a broad range of interests in physics, from cosmology, to gravitational radiation, to high energy physics, to condensed matter theory. The pedagogical approach is "physics first": readers move very quickly to the calculation of observational predictions, and only return to the mathematical foundations after the physics is established. In addition to the "standard" topics covered by most introductory textbooks, it contains short introductions to more advanced topics: for instance, why field equations are second order, how to treat gravitational energy, and what is required for a Hamiltonian formulation of general relativity. A concluding chapter discusses directions for further study, from mathematical relativity, to experimental tests, to quantum gravity. This is an introductory text, but it has also been written as a jumping-off point for readers who plan to study more specialized topics.

This book is aimed at students making the transition from a first course on general relativity to a specialized subfield. It presents a variety of topics under the general headings of gravitational waves in vacuo and in a cosmological setting, equations of motion, and black holes, all having a clear physical relevance and a strong emphasis on space-time geometry. Each chapter could be used as a basis for an early postgraduate project for those who are exploring avenues into research in general relativity and who have already accumulated the required technical knowledge. The presentation of each chapter is research monograph style, rather than text book style, in order to impress on interested students the need to present their research in a clear and concise format. Students with advanced preparation in general relativity theory might find a treasure trove here.

This book introduces the general theory of relativity and includes applications to cosmology. The book provides a thorough introduction to tensor calculus and curved manifolds. After the necessary mathematical tools are introduced, the authors offer a thorough presentation of the theory of relativity. Also included are some advanced topics not previously covered by textbooks, including Kaluza-Klein theory, Israel's formalism and branes. Anisotropic cosmological models are also included. The book contains a large number of new exercises and examples, each with separate headings. The reader will benefit from an updated introduction to general relativity including the most recent developments in cosmology.