Mass and Angular Momentum of Black Holes An Overlooked Effect of General Relativity Applied.pdf

Chinese Journal of Astronomy and Astrophysics manuscript no. A (LT X: aschenbach˙2005˙01.tex; printed on February 5, 2008; 10:24) E Mass and Angular Momentum of Black Holes: An Overlooked Effect of General Relativity Applied to 6 0 the Galactic Center Black Hole Sgr A∗ 0 2 r B. Aschenbach ⋆ a M Max-Planck-Institut f¨ur Extraterrestrische Physik, P.O. Box 1312, Garching, 85741, 8 Germany 1 v 3 Received 2006 month day; accepted 2006 month day 9 1 3 0 Abstract I report the discovery of a new effect of General Relativity which 6 0 is important to understand very rapidly rotating (Kerr) black holes. The / h orbital velocity of a test particle is no longer a monotonic function of the p - orbit radius when the spin of the black hole is 0.9953, but displays a local o r minimum-maximum structure for radii smaller than 1.8 gravitational radii. t s a There the rate of change of the orbital velocity per radius unit equals the : v radial epicyclic frequency and is exactly one third of the polar epicyclic i X frequency, suggesting a 3:1 resonant oscillatory motion of the particle. If r a associated with the most recently observed quasi-periods the mass of the supermassive black hole Sgr A∗ in the centre of the our Galaxy is determined 6 to 3.3 ×10 M⊙ , and the spin is 0.99616. Key words: Galaxy: center - X-rays: general - black hole physics - X-rays: individuals - Sgr A∗ 1 INTRODUCTION The classical problem of a test particle orbiting a rotating black hole has long been solved (Bardeen et al. 1972). Stable circular orbits exist down to a minimal orbital radius r, the innermost marginally stable circular orbit. As for Newt