Black Holes: Physics and Astrophysics - Stellar-mass, supermassive and   primordial black holes
  I present an elementary primer of black hole physics, including its general relativity basis, all peppered with astrophysical illustrations. Following a brief review of the process stellar collapse to a black hole, I discuss the gravitational redshift, particle trajectories in gravitational fields, the Schwarzschild and Kerr solutions to Einstein's equations, orbits in Schwarzschild and in Kerr geometry, and the dragging of inertial frames. I follow with a brief review of galactic X-ray binary systems with known black holes, stressing the QPO phenomenon in particular.   I then discuss the evidence from AGN for the existence of supermassive black holes in galaxy nuclei, as well as evidence for such black holes in ordinary galaxy nuclei. I use the free motion of gas parcels to illustrate aspects of accretion disks around black holes, showing how to calculate energy efficiency and surface emissivity of disks, and the rate of black hole spin-up. I recall the primary methods for black hole mass determination, the correlation of black hole mass with the stellar velocity dispersion of its neighborhood, and implications for the origin of supermassive black holes. Finally, I consider the formation of primordial black holes, and calculation of their mass spectrum at present in the case of scale invariant primordial inhomogeneities. 
Jacob D. Bekenstein