# General relativity a geometric approach

## General Relativity by Malcolm Ludvigsen

Starting with the idea of an event and finishing with a description of the standard big-bang model of the Universe, this textbook provides a clear, concise and up-to-date introduction to the theory of general relativity, suitable for final-year undergraduate mathematics or physics students. Throughout, the emphasis is on the geometric structure of spacetime, rather than the traditional coordinate-dependent approach. This allows the theory to be pared down and presented in its simplest and most elegant form. Topics covered include flat spacetime (special relativity), Maxwell fields, the energy-momentum tensor, spacetime curvature and gravity, Schwarzschild and Kerr spacetimes, black holes and singularities, and cosmology. In developing the theory, all physical assumptions are clearly spelled out and the necessary mathematics is developed along with the physics. Exercises are provided at the end of each chapter and key ideas in the text are illustrated with worked examples. Solutions and hints to selected problems are also provided at the end of the book. This textbook will enable the student to develop a sound understanding of the theory of general relativity, and all the necessary mathematical machinery.## Subscribe to RSS

Click here to close this overlay, or press the "Escape" key on your keyboard. European Journal of Physics , Volume 20 , Number 6. Get permission to re-use this article. Create citation alert. Journal RSS feed. Sign up for new issue notifications. General Relativity poses an interesting and exciting challenge for students, not the least part of which is the need for understanding at the same time subtle concepts in physics and in mathematics.

Editorial Reviews. Review. "This short, elegant book describes the major ideas of special and general relativity with unprecedented clarity and mathematical.

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General relativity GR , also known as the general theory of relativity or GTR is the geometric theory of gravitation published by Albert Einstein in and the current description of gravitation in modern physics. General relativity generalizes special relativity and refines Newton's law of universal gravitation , providing a unified description of gravity as a geometric property of space and time , or spacetime. In particular, the curvature of spacetime is directly related to the energy and momentum of whatever matter and radiation are present. The relation is specified by the Einstein field equations , a system of partial differential equations. Some predictions of general relativity differ significantly from those of classical physics , especially concerning the passage of time, the geometry of space, the motion of bodies in free fall , and the propagation of light. Examples of such differences include gravitational time dilation , gravitational lensing , the gravitational redshift of light, and the gravitational time delay.

General Relativity and Gravitation. An outline of recent applications of modern infinitedimensional manifold techniques to general relativity is presented. The uses, scope, and future of such methods are delineated. It is argued that the mixing of the two active fields of general relativity and global analysis provides stimulation for both fields as well as producing good theorems. The authors' work on linearization stability of the Einstein equations is sketched out to substantiate the arguments. Unable to display preview.

Starting with the idea of an event and finishing with a description of the standard big-bang model of the Universe, this textbook provides a clear and concise introduction to the theory of general relativity, suitable for final-year undergraduate mathematics or physics students. Throughout, the emphasis is on the geometric structure of spacetime, rather than the traditional coordinate-dependent approach. Topics covered include flat spacetime special relativity , Maxwell fields, the energy-momentum tensor, spacetime curvature and gravity, Schwarzschild and Kerr spacetimes, black holes and singularities, and cosmology. All physical assumptions are clearly spelled out and the necessary mathematics is developed along with the physics. Exercises are provided at the end of each chapter and key ideas are illustrated with worked examples.

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