VULNERABLE..! (BLACK HOLE ENERGY EXTRACTION || Penrose process)

This post specifically pertains to Blackhole energy extraction(Penrose superradiance).

As known, Black Holes are something which gulps almost everything(except hypothetical space-like objects). This means Black holes comprise a lot of energy in different forms. But, is any of that energy useful?. Fortunately, a long time ago scientists hypothesised two methods(one by Misner in 1968 and other by Penrose in 1971) which are theoretically possible to extract energy from a black hole. 

To start with, it is important to know what a black hole comprises.

COMPONENTS OF A BLACK HOLE

1). Accretion disk: The outermost component containing dust and superheated gases which revolve at very high speed in the form of an inward spiral

producing electromagnetic radiation.

2). Stable orbit: This is the orbit where objects with mass are safe to revolve around the black hole.

3).Relativistic jets: These are jets of particles and radiation released by the black hole with speeds close to the light.

4).Photon sphere: This is a layer containing photons with high thermal energy travelling in straight lines.

5).Event Horizon: This is the radius(also known as Schwarzschild radius) at which matter cannot escape the black hole's gravity

6).Singularity: This is the point at which the matter is condensed to infinite density and very less is known about this point.

Moving on to next step, Schwarzschild’s solution of the Einstein vacuum equations represents the gravitational field exterior to a spherically symmetrical body. In Schwarzschild’s coordinates, the metric(or the equation of space-time) is given as 

Here general relativistic units are taken, i.e. c=1, G=1

For In shorters, watch this youtube video

 

Though the equation seems complex and derivation of this is much more complex, all we need to focus on is where the equation breaks or tends to infinite. At r=2m the metric breaks down, and this is referred to as the Schwarzschild’s radius. It is assumed that the observer(going into) does not encounter tidal forces(space-time singularity)-which will destroy him/her. Other possibility is that the observer will enter some region that is not described/covered by the above metric. A probable guess for that metric would be replacing t with an advanced time parameter v given by

And hence metric takes the form(which encompasses the whole range of 0<r<infinity)

Misner process

Now getting onto energy extraction, Misner process requires a whole galaxy of 2^N black holes each of mass m. The method is to somehow bring them together in pairs and allow them to spiral each other. And during this spiralling, some fraction K of mass-energy content is radiated in the form of gravitational energy, and hence the resulting black hole has a mass of 2m(1-K). The energy of these gravitational waves is collected. 

As this seems highly practical, another method is proposed by Penrose.

Penrose process

Penrose process suggests a slightly different way of extracting rotational energy from a rotating black hole. It is assumed that somehow an advanced civilisation could build a stable structure S outside of the black hole. From S, a mass is slowly released until point L, which is a stable orbit and we can recover the mass, and hence energy is extracted, which is equal to the mass lowered. But that is not enough because mass is just converted to energy. To tackle this, there can be another S* built, which is rotating slightly, and from there a mass can be lowered beyond L. Finally the mass is dropped through

H, but in such a way that its energy content, as measured from S, is negative. Thus, the inhabitants on S will be able to extract energy by lowering masses.

Is total energy conserved?

It is general to think that whether Energy is conserved in the total process?. Yes, the total energy is conserved. The mass lowered will get more energy than its mass eqvivalence because some of the black hole's angular momentum is converted to energy and hence black hole rotates a bit slower than before. And so rotational energy is extracted by the mass lowered.

Later in 1971, Zel'dovich converted this idea of rotational superradiance from rotating black hole to a normal rotating absorber, like a metallic cylinder, and showed that it would amplify incident electromagnetic radiation if the following condition is satisfied

where Ω  is the rotation rate of the absorber, l is the order of the orbital angular momentum and ω is the incident wave frequency.

So to satisfy the above condition with l=1 it is required to have the rotation speeds Ω in Giga Hz to Pico Hz, which is 100-1000Hz faster than the available mechanical motors. So it is much difficult to illustrate it experimentally. 

Thanks to the physche of the scientists who solved this problem using intelligently different approach.

But that's the idea for another Sci-Hole story.