# Kerr Black Hole Ergosphere

1. Feb 28, 2014

### Philosophaie

In a Kerr Black Hole there exists a region called the Ergosphere.

It is between the Event Horizon and a spheriod called the Static Limit.

The Event Horizon can be simplified to: $\Delta$ = 0.

The Static Limit can be simplified to: $g_{tt}$ = 0.

They yield two separate spheres the Static Limit being greater.

Is it theoretically possible to extract energy and mass from the black hole in this region?

Particles within this ergosphere must co-rotate with the inner mass if they are to retain their time-like character.

http://en.wikipedia.org/wiki/Ergosphere
Numerical relativity solving einstein's equations - baumgarte t w , shapiro s(isbn 052151407x)

Last edited: Feb 28, 2014
2. Feb 28, 2014

### George Jones

Staff Emeritus
3. Feb 28, 2014

### Philosophaie

The spin is restricted to the range 0 ≤ a/M ≤ 1 where a=J/M, M=G*Mass/c^2, G is Gravitational Constant and c is speed of light.

"The rotating black is stationary and axisymmetric, hence the spacetime possesses two Killing vectors $\delta_t$ and $\delta_\phi$".

I believe the Killing Vectors arise from the mixed components of the Metric?

Test particles moving in the field of a rotating black hole conserve their energy E = $−p_t$ and
axial component of angular momentum J = $p_\phi$.

Last edited: Feb 28, 2014