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This chapter provides the derivation of the equations of motion of the test particles and light rays in a general curved spacetime. The path or the differential equation of the curve having an external length, i.e., path of extremum distance between two points is called the geodesic equation.
Along the way, the metric and the notion of causal structure are explained, and it is shown that the geodesic equation can reproduce the equations for motion of an object in Newtonian gravity. Keywords: causal structure, geodesic equation, geodesics, light cone, metric, Minkowski space, Newtonian limit, spacetime. Subject.
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The general theory of relativity, together with the necessary parts of the theory of invariants, is dealt with in the author’s book Die Grundlagen der allgemeinen Relativitätstheorie (The Foundations of the General Theory of Relativity) — Joh. Ambr. Barth, 1916; this book assumes some familiarity with the special theory of relativity. v
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Twelve comprehensive and in-depth reviews, written by a team of leading international experts, together present an up-to-date overview of key topics at the frontiers of these areas, with particular emphasis on the significant developments of the last three decades.
general relativity are derived. A wide range of applications to physical situations follows, and the conclusion gives a brief discussion of classical field theory and the derivation of general relativity from a variational principle. Written for advanced undergraduate and graduate students, this approachable
Geodesics in Schwarzschild space-time are treated in detail: the precession of the perihelion of Mercury; the bending of light by the Sun; Shapiro time delay; black holes and the event horizon. Gravitational waves and gravitational lensing are also covered. Keywords.
Relativity textbooks. From early undergraduate to graduate courses, Cambridge has a relativity textbook at the right level. http://www.cambridge.org/physics/relativity. Gravity from the Ground Up. An Introductory Guide to Gravity and General Relativity. Bernard F. Schutz. Max-Planck-Institut für Gravitationsphysik, Germany. Advance praise: ‘...
