By Torsten Fließbach

Dieses Buch gibt eine Einf?hrung in die Allgemeine Relativit?tstheorie, additionally in Einsteins relativistische Theorie der Gravitation. Zu den behandelten Anwendungen der Theorie geh?ren Experimente im Sonnensystem, Gravitationswellen, Sterne und der Kosmos. Die Darstellung bewegt sich auf dem Niveau einer Kursvorlesung in Theoretischer Physik, additionally auf einem f?r das Thema eher einfachen Niveau. In der vorliegenden five. Auflage sind erstmals Musterl?sungen f?r die ?ber forty gestellten Aufgaben enthalten. Stimmen zu fr?heren Auflagen: "Dieses Buch ist eine gelungene Einf?hrung in die Allgemeine Relativit?tstheorie. Es ist vor allem jenen Studenten der Theoretischen Physik zu empfehlen, die an den physikalischen Grundprinzipien dieser Theorie und an deren durchsichtiger mathematischer Darstellung interessiert sind." Prof. Dr. H.-H. v. Borzeszkowski, Technische Universit?t Berlin "Das Buch zeichnet sich durch hervorragende Stoffauswahl, klare Gliederung, guten didaktischen Aufbau und ansprechende Darstellung aus." Prof. Dr. U. Heinz, Universit?t Regensburg "Ein Lehrbuch, das jedem Studenten (oder Wissenschaftler), der sich in die artwork einarbeiten m?chte, unbedingt empfohlen werden kann." Priv.-Doz. Dr. H.-R. Berger, Technische Universit?t Chemnitz

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In this limit, we αβ retain only the dominant, r −1 term in hN , and we approximate Eq. (165) by αβ hN = 4G rc4 ∞ =0 (−1) ! M ∂L τ αβ (τ, x )x L d 3 x + O(r −2 ) . (167) The dependence of τ αβ on x j is contained in τ = t − r/c, so, using the fact for any function f (τ ) that ∂j f = −c−1 ∂j r(df/dτ ) = −c−1 nj (df/dτ ), we find that Eq. c M τ αβ (τ, x )x L d 3 x + O(r −2 ) . (168) Gravity: Newtonian, Post-Newtonian, and General Relativistic 47 αβ This is a multipole expansion for the potential hN , in which each -pole moment αβ L 3 L = M τ x d x is differentiated -times with respect to τ .

The constancy of ι and Ω is related to the spherical symmetry of the problem, which fixed the direction of L and the orbital plane. The constancy of ω is a very important property of a Keplerian orbit: it ensures that the orientation of the orbit within its plane stays fixed, that the position of the pericenter does not move, and when the orbit is bound, that the orbit retraces itself after each orbital cycle. The constancy of ω is the result of a hidden, dynamical symmetry of Kepler’s problem, associated with the specific 1/r nature of the gravitational potential; the symmetry does not exist for other potentials.

Suppression of this enormous Newtonian effect in order to detect the possible effect of general relativistic frame-dragging (∼ 30 milliarcseconds per year) is a major challenge. The chapter “Fundamental Physics with the LAGEOS Satellites” by R. Peron, addresses how this suppression has been carried out in analysing data from the LAGEOS I and II satellites. 1 Mathematics of Curved Space-Time The foundation of general relativity is the space-time metric gαβ , which connects the arbitrary coordinates x α = (ct, x j ) used to label events in space-time to physical 32 C.

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