How can a blackhole be stabilized by adding to its angular momentum

Well, I suppose, but only in the sense that it is hard to change the direction of the axis of rotation.

A bicycle is also stabilized by the rotation of the tires. The faster the spin, the more torque is needed to turn or tip the wheels. (torque = rate of change of angular momentum, either in magnitude or direction)
Try Google - gyroscopic stabilization

ah - cute demo :

http://www.youtube.com/watch?v=az1_4WjadlU

Stabilizing a black hole by adding to its angular momentum is a concept known as the Penrose process. The Penrose process involves extracting energy from a spinning black hole by splitting an object (e.g., a particle) into two parts near the event horizon, where one part falls into the black hole while the other escapes.

Here's how the Penrose process contributes to stabilizing a black hole:

1. Angular momentum: A black hole gains angular momentum through accretion of matter or by merging with another spinning black hole. Spin is a measure of a black hole's rotational motion, just like how a planet or star can spin.

2. Ergosphere: The black hole's spinning motion creates a region surrounding it called the "ergosphere." In this region, objects can't remain stationary and are forced to rotate along with the black hole.

3. Superradiance: If an object (e.g., a particle or a wave) enters the ergosphere, it can extract energy and angular momentum from the black hole via a process known as "superradiance." This is possible due to a phenomenon in quantum mechanics called "negative energy states."

4. Particle splitting: Suppose an object with negative energy enters the ergosphere. Using the energy extracted from the black hole, the object can split into two parts, with one part falling into the black hole and the other part escaping through a process called "particle splitting."

5. Energy extraction: The escaped particle(s) can take away energy from the black hole, thereby reducing its mass and angular momentum. As a result, the black hole's spin decreases, leading to stabilization.

It is important to note that the Penrose process is a theoretical concept and currently has no practical application. Additionally, the process does not apply to all types of black holes, but only to rotating or "spinning" black holes (known as Kerr black holes).