All Spacetimes Beyond Einstein
by Frederic P. Schuller
Publisher: arXiv 2011
Number of pages: 44
Which geometries on a smooth manifold (apart from Lorentzian metrics) can serve as a spacetime structure? This question is comprehensively addressed from first principles in eight lectures, exploring the kinematics and gravitational dynamics of all tensorial geometries on a smooth manifold that can carry predictive matter equations, are time-orientable, and allow to distinguish positive from negative particle energies.
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by A. A. Logunov - arXiv
In the framework of the special theory of relativity, the relativistic theory of gravitation is constructed. The energy-momentum tensor density of all the matter fields (including gravitational one) is treated as a source of the gravitational field.
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This book goes back to the work of the philosophers and astronomers of two thousand years ago; and it extends to that of Einstein, whose work laid the foundations for our present-day ideas about the nature of space itself.
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The first six lectures are devoted to Special Relativity, and the remaining ones to Einstein's General Relativity and Gravitation Theory and to relativistic Electromagnetism. Due attention is given to the critically conceptual side of the subject.
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Contents: the special theory of relativity, vectors and tensors in special relativity, conceptual basis of general relativity, curved space time and general relativity, Einstein's field equations, Schwarzschild's solution.