Dec 12, 2016 · In this series of articles I am going to discuss the key properties of the spacetime geometry described by Schwarzschild's solution..

Dec 19, 2016 · In fact, Schwarzschild coordinates are not a single coordinate chart on this spacetime; each of the four regions, I, II, III, and IV, has its own Schwarzschild coordinate …

Dec 28, 2022 · Much of that familiarity probably derives from the fact that the Schwarzschild solution describes a black hole. However, for some reason, much less attention is paid to the …

Oct 21, 2009 · Homework Statement I'm having problems seeing how the transformation to Eddington-Finkelstein in the Schwarzschild geometry works. Any help would be great! …

Dec 29, 2017 · A Short Proof of Birkoff’s Theorem derived the Schwarzschild metric in units of G = c = 1: (1) d s 2 = (1 2 M r) d t 2 + (1 2 M r) 1 d r 2 + r 2 d θ 2 + r 2 sin 2 θ d ϕ 2 and I used …

Oct 6, 2021 · The theory of geodesic congruences is extensively covered in many textbooks (see References); what follows in the introduction is a brief summary.

Apr 16, 2011 · I have been reading about black holes and am intrigued by the fact that when you use schwarzschild coordinates to describe a particle free falling radially into a black hole, it …

Dec 27, 2017 · To show how concentric spheres in the space of Schwarzschild spacetime are spaced farther apart than their flat space counterparts, one often sees circles replacing …

Feb 25, 2025 · Calculating the volume of a black hole using the Schwarzschild metric presents challenges due to the nature of the coordinates involved. The integral derived for volume …

Dec 17, 2016 · At the end of part 1, we looked at the form the metric of the Schwarzschild geometry takes in Gullstrand-Painleve coordinates: d s 2 = (1 2 M r) d T 2 + 2 2 M r d T d r + d …