Welcome to the ergosphere

A black hole’s gravitational influence is a twisted – and twisting – thing, with many parts to it. We all know about the event horizon because of its wondrous ability to capture ‘even light’ within its envelope, keeping everything within trapped in absolute darkness for as long as the black hole lives. But beyond the event horizon, there is another region with equally – if not more – wondrous abilities that distorts the perception of reality in its own, unique ways. Since both their abilities are enabled by gravity, let’s begin there.

The gravitational force is actually an effect that objects seem to experience because of the shape of the spacetime continuum. All objects move on the continuum’s surface, and when the surface is bent, an observer sees the object moving as if on a curve. Such deformations are caused by massive bodies: the heavier a body, the more it bends the continuum around itself. So to the observer, it seems as if the heavy body is causing the lighter object to orbit itself.

The Moon orbits Earth because Earth’s mass has bent the spacetime continuum around itself. In effect, the Moon is simply moving on the continuum’s surface, and it seems to be circling around Earth because of the shape of the continuum in that region. Credit: Mysid/Wikimedia Commons, CC BY-SA 3.0

Depending on the mass of the deforming body, this effect can be felt across vast distances. For example, Pluto orbits the Sun at an average distance of 5.9 billion km. So Pluto’s average orbit indicates the deformation that an object as heavy as Pluto experiences due to the Sun (and other planets as well as the Kuiper belt) at that distance. According to the laws of Newtonian gravitation, the force’s strength falls off by the square of the distance. So if the force between two bodies is X at a distance of Y, it will be X/4 at a distance of 2Y (assuming the gravitational constant is the same at Y and 2Y). However, the strength never falls to zero unless the objects are infinitely far from each other.

Now, if Pluto wanted (for some fantastical reason) to exit its orbit, it would have to move at a certain velocity to escape it. Say it was the Death Star there instead of Pluto, and the Death Star has thrusters. It would have to fire those thrusters to accelerate itself to such an extent that its speed grows beyond the limit at which the Sun can hold Pluto there by its gravity.

The fundamental set up is the same when it comes to a black hole, but the numbers are more extreme. When you look at a black hole, you’re actually seeing its event horizon. The black hole’s gravitational pull itself emanates from a point at its centre called the singularity. This singularity deforms the spacetime continuum in unimaginable ways, although it becomes more and more imaginable the farther you get from the centre.

The event horizon is the distance at which the continuum is deformed in such a way that you’d have to travel faster than at the speed of light to escape it – i.e., if you were caught right at the event horizon, even travelling at exactly the speed of light will only keep you on the event horizon, and not let you zip off into space. (Put differently: this would allow us to work out the speed of light in a given universe using the rules of basic gravitational physics and the sizes of black holes in that universe.)

This is also why the event horizon is the thing you see when you see a black hole: it’s a literal horizon of events. Events occurring on one side can’t be seen on the other because the light that carries the information that you ‘see’ can’t cross it or return. This in turn should prompt the question whether there is a region of space around the black hole where its gravitational effects can be felt but which doesn’t demarcate ‘points of no return’. The answer is yes; it’s called the ergosphere.

The name itself casts a very utilitarian gaze upon the idea – that it’s the region of space from which you can extract work from the black hole – but it’s true. The ergosphere is the region wherein the spacetime continuum has been deformed by the black hole to such an extent that you can enter it and leave if you travelled fast enough (but less than at the speed of light). However, even if the black hole’s effects from the singularity to the event horizon are outright warped, and the event horizon itself is an important – albeit arbitrary – boundary, the black hole’s effects in the ergosphere are still mind-bending.

A part of this is due to an effect of rotating black holes called frame-dragging. Imagine you’re (an immortal elf) looking at Pluto orbiting the Sun from somewhere near Mercury, through a stationary window that’s between the orbits of Neptune and Pluto. If you keep looking through the window, you’ll see Pluto pass by once every 248 years. Apart from the fantasy elements, this scenario is also physically possible because the window is practically stationary. The part of the spacetime continuum on which it rests, so to speak, isn’t in motion itself due to the Sun’s rotation. That is, there is a negligible amount of frame-dragging.

But this wouldn’t be possible in the ergosphere of a rotating black hole. Say you’re just above the event horizon, looking through a window in the distance at an object orbiting the black hole at the inner edge of the ergosphere. Frame-dragging would absolutely prevent the window from being stationary, together with you and the object as well. This is because the black hole’s prodigious gravitational pull – i.e. prodigious deformation of the continuum – is such that it doesn’t just deform the continuum but also drags it along as it rotates, in the direction of its rotation, in a very pronounced way.

As a result of such frame-dragging, anything sitting on that part of the continuum also seems to be moved along even if it didn’t have any velocity in that direction to begin with. It would be as if looking at your friend walking west-east on a boat that’s moving east-west at the speed of light: for all practical purposes, she might as well be walking east-west! This is why a rotating black hole will force an object angling in towards the black hole’s ergosphere from the opposite direction to appear to switch and move along in the direction of its rotation.

The test particle, shown in red, first moves towards the ergosphere (in lilac) clockwise before frame-dragging forces it to seem to move anti-clockwise. Credit: Yukterez/Wikimedia Commons, CC BY-SA 4.0

Note the use of ‘appear’: the object won’t actually be forced to alter its direction towards that of the black hole’s rotation. However, the changing arrangement of spacetime in the region together with the light coming from the object towards the observer will make it seem that way.

If, by the effect of some compulsion, an object insists on appearing stationary inside the ergosphere, it can but there’s a catch. If it is inside the ergosphere but above the event horizon, the object has no option but to be frame-dragged. But just like the event horizon is the surface you’d travel for eternity if you travelled at the speed of light, the ergosphere also has a surface where you can avoid being frame-dragged if you were moving at the speed of light. This is simply called the ergosurface.

This image is one of the slides in a presentation prepared by Prof. Chris Reynolds, UMD
This image is one of the slides in a presentation prepared by Prof. Chris Reynolds, UMD

(Trivia: It’s possible to explain the effects of gravity outside the ergosurface using Newtonian physics. Inside it, however, you’ll need the theories of relativity.)

The location of both envelopes – the event horizon and the ergosurface – is determined by the speed of light. Their shapes are also determined by common factors: the black hole’s mass and angular momentum*. However, they aren’t affected similarly. For example, a non-rotating black hole will have a spherical event horizon but a rotating black hole will have an oblate event horizon. On the other hand, a non-rotating black hole will not have an ergosurface whereas a rotating black hole will have anything between an oblate and a pumpkin-shaped ergosurface.

Credit: Yukterez/Wikimedia Commons, CC BY-SA 4.0

These are just some of the reasons the shadow of the black hole at the centre of the M87 galaxy looked the way it did in the image composed by the Event Horizon Telescope (EHT). Aside from the way it was obtained (using techniques like VLBI), the image contains many distortions that originate from the black hole itself, so interpreting it isn’t a straightforward activity.

The EHT only recorded and studied radiation that could come away from the black hole, with a lot of matter accumulating beyond that point and falling into the hole. So what we’re looking at in sum is that hot and magnetised matter, all their radiation and the Doppler effects on them, the effects of the ergosphere frame-dragging them, and then the shadow of the event horizon.

The shadow (black) and event horizon and ergosphere (white) of a black hole rotating from left to right. At a = 0, the black isn’t rotating and at a = 1, it’s rotating maximally. Credit: Yukterez/Wikimedia Commons, CC BY-SA 4.0

The idea that you can extract work from within the ergosphere, thus giving the region its current name, can be traced to a few examples that different scientists have spelled out over the years. The three most-well-known examples are the Penrose mechanism, Hawking radiation, and the Blandford-Znajek process. The case of Hawking radiation is easiest to explain (only because it’s been done enough times in the popular press for one to be able to access it immediately), but understanding it provides insights into the Penrose alternative as well.

The vacuum of deep space isn’t a true vacuum: it contains some energy, including electromagnetic energy from distant stars, that is often transformed into a particle-antiparticle pair. That is, these particles are condensations of energy that pop into existence and pop back out as energy again (here’s a more detailed yet accessible primer) in a very short span of time. It’s possible that this process also happens near black holes simply because it can. And when it does, something strange follows.

If such a particle pair pops into existence right above the event horizon, one of them could fall into the black and the other will be pushed off into the ergosphere. This push-off happens because of the law of conservation of momentum, and the energy carried by the pushed particle will be a teeny, tiny bit transformed from the black hole’s mass. To a distant observer, it will look as if the black hole has just emitted a particle and lost a little bit of its mass to do so. Stephen Hawking and Jacob Bekenstein first predicted this phenomenon, since called Hawking radiation, in 1974. When this process happens over and over, over many eons, a black hole could possibly have lost all of its mass and evaporated completely into nothingness.

The British mathematical physicist Roger Penrose proposed a somewhat similar idea that was also relatively more practicable (and was used in the film Interstellar as well). As Suvrat Raju, a theoretical physicist at ICTS Bangalore, explained to me: Say an object – like a boulder – is thrown into the ergosphere. When it nears the event horizon, it is caused by a deliberate mechanism to break up into two pieces such that one piece falls into the event horizon in the direction opposite to the black hole’s rotation. As a result, the other would get accelerated in its journey through the ergosphere by a ‘kick’ from the black hole.

If orchestrated correctly, the kicked piece can emerge from the ergosphere with more energy than it had going in – energy provided by the black hole by converting some of its mass. Scientists have already worked out the average achievable energy gain in each Penrose mechanism attempt to be around 21%.

An explanatory video by Kurzgesagt

“In classical processes, one can never reduce the area of the black hole, but the Penrose process can reduce its mass,” Suvrat further told me. “The science fiction fantasy is that a sufficiently advanced civilisation could use rotating black holes for waste-disposal and even get some energy out in the process through the Penrose process.”

The Blandford-Znajek process is less crude and more… involved. Say a star got a bit too close to a black hole and is being shredded into bits that fall into orbit around the event horizon. Friction between these bits heats them up to a very high temperature, pushing them into a plasma state of matter. These bits also harbour electric and magnetic fields, and the electric and magnetic field lines pass through them even as they swirl around the monster and fall closer and closer.

At this point, let me quote the following coursework material, by Daniel Nagasawa, Stanford University in 2011:

The premise itself is that the material accreting around a black hole would probably be magnetised and increasingly so as the material gets closer to the event horizon. In fact, the magnetic field is so large that it will accelerate an electron to the point where it will begin to radiate gamma-rays, provided that the electron is not beyond the event horizon. In essence, the black hole acts as a massive conductor spinning in a very large magnetic field produced by the accretion disk, where there is a voltage induced between the poles of the black hole and its equator. The ultimate result is that power is dissipated by the slowing down of the rotation of the black hole…

To extract energy in this scenario, one way – as posited by user CapnTrippy on Everything2 – is to build a superconductor orbiting over the black hole’s poles such that it can intercept and carry away some of the current flowing from the equator to the poles, instead of letting it be deposited in the plasma in the ergosphere. Vis-à-vis the black hole itself, this electrical energy has two sources: its rotational energy and that imbibed by the plasma. Since a black hole can carry up to 29% of its total mass as its rotational energy, that’s also the maximum possible energy that can be extracted in this process. It’s not great but it’s still fantastic because black holes often weigh enough to be able to supply power for ages on end. According to Nagasawa,

… for a 108 solar mass black hole with a 1 T magnetic field, the power generated is approximately 2.7 × 1038 W. In perspective, the annual energy consumption of the world is estimated around … 5 × 1020 J. The example case presented produces more energy in a single second than the entire globe consumes in a year. While this is a bold claim to make, it is only an example case where not all the energy produced is extractable as usable energy. However, at that point, even a system which is less than 10-15 % efficient would be sufficient to supply enough energy to power the world for a full year.

The Blandford-Znajek process remains a subject of active research to this day. A part of this is thankfully because of a reason that has little to do with powering Earth: relativistic jets. These are extremely powerful and narrow beams of radiation travelling at nearly the speed of light that astronomers have observed in space. Astrophysicists believe that the Blandford-Znajek process and the Penrose mechanism can together explain how they’re formed and shot off from the poles of supermassive rotating black holes, and travel billions of kilometres. In fact, the galaxy CGCG 049-033, located 680 million lightyears from Earth, is thought to host a black hole weighing 2 billion solar masses that’s shooting jets a staggering 1.5 million lightyears into space.

So next time you read about black holes, don’t let the event horizon steal all the limelight (even literally). There’s action and drama above its surface as well, where things are still visible while behaving in strange ways, where a gallery of plasma, energy fields and a moving continuum exposes the black hole’s gravitational artwork to the full view of the universe. Just remember that what you see is not what you get.

*This is a result of the no-hair conjecture: that all properties of all black holes can be determined by their mass, charge and angular momentum alone. However, because gravity is 1036 times weaker than the electromagnetic force, black holes with significant charge are thought not to exist, leaving only the mass and the angular momentum to influence their physical surroundings.

Featured image: This artist’s concept illustrates a supermassive black hole weighing millions to billions of times the mass of our Sun. Credit: NASA/JPL-Caltech.

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Science writer and editor in Bangalore, India.