RAR. Gravitation And Cosmology Weinberg PdfThe Einstein field equations EFE ; also known as Einstein's equations comprise the set of 10 equations in Albert Einstein 's general theory of relativity that describe the fundamental interaction of gravitation as a result of spacetime being curved by mass and energy. Similar to the way that electromagnetic fields are determined using charges and currents via Maxwell's equations , the EFE are used to determine the spacetime geometry resulting from the presence of mass—energy and linear momentum, that is, they determine the metric tensor of spacetime for a given arrangement of stress—energy in the spacetime. The relationship between the metric tensor and the Einstein tensor allows the EFE to be written as a set of non-linear partial differential equations when used in this way. The solutions of the EFE are the components of the metric tensor. The inertial trajectories of particles and radiation geodesics in the resulting geometry are then calculated using the geodesic equation. As well as obeying local energy—momentum conservation, the EFE reduce to Newton's law of gravitation where the gravitational field is weak and velocities are much less than the speed of light. Exact solutions for the EFE can only be found under simplifying assumptions such as symmetry.
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The amount of preknowledge required and how mathematical the course is or should be is discussed here. Note that this is a master level theoretical physics course and the difficulty level is adjusted to that. It can be taken by bachelor students in their third year but tends to be rather hard at that level.
Einstein field equations
You bet! There are dozens of superb, up-to-date books on various aspects of relativity theory. Most of these are currently in print and widely available through university libraries and organizations such as Amazon. In addition, several classic books have recently come back into print. It is not an exaggeration to say that there has probably never been a better time to shop around for books on relativity! In what follows I offer a sort of "consumer's guide" which I hope will help readers choose the book or books best suited to their needs.
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