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Full-Text Articles in Physics
Rainich-Type Conditions For Perfect Fluid Spacetimes, Dionisios Krongos, Charles G. Torre
Rainich-Type Conditions For Perfect Fluid Spacetimes, Dionisios Krongos, Charles G. Torre
Research Vignettes
In this worksheet we describe and illustrate a relatively simple set of new Rainich-type conditions on an n-dimensional spacetime which are necessary and sufficient for it to define a perfect fluid solution of the Einstein field equations. Procedures are provided which implement these Rainich-type conditions and which reconstruct the perfect fluid from the metric. These results provide an example of the idea of geometrization of matter fields in general relativity, which is a purely geometrical characterization of matter fields via the Einstein field equations.
Vector Spaces (Appendix B), Charles G. Torre
Vector Spaces (Appendix B), Charles G. Torre
Foundations of Wave Phenomena
Throughout this text we have noted that various objects of interest form a vector space. Here we outline the basic structure of a vector space. You may find it useful to refer to this Appendix when you encounter this concept in the text.
Taylor’S Theorem And Taylor Series (Appendix A), Charles G. Torre
Taylor’S Theorem And Taylor Series (Appendix A), Charles G. Torre
Foundations of Wave Phenomena
Taylor’s theorem and Taylor’s series constitute one of the more important tools used by mathematicians, physicists and engineers. They provides a means of approximating a function in terms of polynomials.
References And Suggestions For Further Reading (Appendix C), Charles G. Torre
References And Suggestions For Further Reading (Appendix C), Charles G. Torre
Foundations of Wave Phenomena
References and Suggestions for Further Reading (Appendix C)
Perihelion Precession In General Relativity, Charles G. Torre
Perihelion Precession In General Relativity, Charles G. Torre
Charles G. Torre
This is a Maple worksheet providing a relatively quick and informal sketch of a demonstration that general relativistic corrections to the bound Kepler orbits introduce a perihelion precession. Any decent textbook will derive this result. My analysis aligns with that found in the old text "Introduction to General Relativity", by Adler, Bazin and Schiffer. The plan of the analysis is as follows. * Model the planetary orbits as geodesics in the (exterior) Schwarzschild spacetime. * Compute the geodesic equations. * Simplify them using symmetries and first integrals. * Isolate the differential equation expressing the radial coordinate as a function of …