User:Agge1000/Sandbox

Black Hole parameters

For a stellar mass hole, the process in which a developing horizon settles into its asymptotically stationary form is of order 10^-5 sec, while for a supermassive hole of 10⁸ M₀ , it is thousands of seconds.

At the event horizon a falling observer cannot stop to be weighed. At the event horizon tidal stretching of an extended body is given by the gradient of the gravitational acceleration: 2GM/R_H³=c⁶/(4G²M²) .

In the case of a solar mass black hole the tidal stress (acceleration per unit length)at the horizon is on the order of : 3 x 10⁹(M/M₀)² sec^-2 : which is about about 10⁹ Earth gravities, enough to rip apart ordinary materials. For a supermassive hole, by contrast, the tidal force at the horizon is smaller by a typical factor 10^10-16 and would be easily survivable. However, at the central singularity, deep inside the event horizon, the tidal stress is infinite. In addition to its mass M, the Kerr spacetime is described with a spin parameter 'a' defined by the dimensionless expression a/M= cJ/GM² where J is the angular momentum of the hole. For the Sun (based on surface rotation) this number is about 0.2, and is much larger for many stars. Since angular momentum is ubiquitous in astrophysics, and since it is expected to be approximately conserved during collapse and black hole formation, astrophysical holes are expected to have significant values of a/M , from several tenths up to and approaching unity.

The value of a/M can be unity (an "extreme" Kerr hole), but it cannot be greater than unity. In the mathematics of general relativity, exceeding this limit replaces the event horizon with an inner boundary on the spacetime where tidal forces become infinite. Because this singularity is "visible" to observers, rather than hidden behind a horizon, as in a black hole, it is called a naked singularity. Toy models and heuristic arguments suggest that as a/M approaches unity it becomes more and more difficult to add angular momentum. The conjecture that such mechanisms will always keep a/M below unity is called cosmic censorship.

The inclusion of angular momentum changes details of the description of the horizon, so that, for example, the horizon area becomes Horizon area= 4πG²/c⁴[{M+(M²-a²)^1/2}²+a²]

This modification of the Schwarzschild (a=0) result is not significant until a/M becomes very close to unity. For this reason, good estimates can be made in many astrophysical scenarios with a ignored.