The Galactic Black Hole Falcke

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69) In terms of the original Schwarzschild coordinates we have2 r˜ = t˜ = r r t − 1 exp cosh 2m 4m 4m t r r sinh − 1 exp . 72) in these Kruskal–Szekeres coordinates (t˜, r˜ , θ, φ), behaves regularly at the gravitational radius r = 2m. 72) into the Einstein equation (via computer algebra), then we see that it is a solution of it for all r > 0. 71) yield r r . 73) − 1 exp r˜ 2 − t˜2 = 2m 2m Thus, the transformation is only valid for regions with |˜r | > t˜. However, we can find a set of transformations which cover the entire (t˜, r˜ )-space.

100) Thus, in a special frame, we have the same tidal accelerations as in the Newtonian case. Accordingly, the gravitational field of a spherically symmetric body in Newton’s 3D theory is very naturally embedded into Einstein’s 4D theory. 8 Computer algebra As a typical example, we will demonstrate how to obtain the exterior Schwarzschild solution by means of the computer algebra system Reduce and its package Excalc for applications in differential geometry. When Reduce is called, it prompts the user for input.

Preuss. Akad. Wiss. Berlin 189–96 ¨ [20] Schwarzschild K 1916 Uber das Gravitationsfeld einer Kugel aus inkompressibler Fl¨ussigkeit nach der Einsteinschen Theorie Sitzungsber. Preuss. Akad. Wiss. Berlin 424–34 34 The Schwarzschild black hole: a general relativistic introduction [21] Will C M 2001 The confrontation between general relativity and experiment Living Rev. Relativity 4 4 [Online article]: cited on 17 Nov 2001. http://www. org/Articles/Volume4/2001-4will/ Chapter 2 The Milky Way: structure, constituents and evolution Susanne Huttemeister ¨ Ruhr-Universit¨at Bochum, Germany After having learned, in chapter 1, about an idealized relativistic star, we now turn to the Milky Way which consists of about 1011 stars and has a diameter of about 105 light years.

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