« Does space and time still exist in a black hole? »Sandy Rucheton asks us on our page Facebook. This is our question of the week. To answer, (re)discover our article originally published in below magazine Les Indispensables de Sciences et Avenir n°209 (dated April/June 2022) et entitled « Journey to the center of a black hole: make the film Interstellar is this realistic? »
A black hole, a machine where time and space no longer exist?
One of the adventures of the film Interstellar (2014) sees astronaut Joseph Cooper approaching Gargantua, the central black hole of an imaginary galaxy. He easily passes the disk of matter that surrounds the star and plunges beyond what is called his event horizon, the threshold of the region that surrounds it from which nothing can escape, not even light. Cooper is then pushed towards the center of the celestial object, which Christopher Nolan, the director, describes as a machine in which time and space no longer exist…
A realistic scenario? Maybe or maybe not. Because, heated to millions of degrees, the disk of matter that generally orbits such supermassive black holes emits deleterious X-rays. « Unless this disk has been fed on external matter for years. million years, which is unlikely, Cooper would surely be fried before going any further! comments Alain Riazuelo, researcher at the Paris Institute of Astrophysics. However, the film is right about one point: Cooper I would not feel the effect of the inevitable tidal forces. »
“The space between the horizon and the center is therefore… empty”
Tidal forces are the effects due to the differential attraction of points on a solid: for example, the Moon attracts the nearer side of our planet more than its center, and even more than the opposite point. The Earth is stretched in the direction of the Earth-Moon axis. In the case of a black hole, the force of this effect causes the body that approaches it to stretch, a phenomenon that physicist Stephen Hawking called spaghettification. If it’s a black hole of one to ten solar masses, the problem is quickly resolved: tidal effects tear any body apart long before it reaches the event horizon.
On the other hand, near the horizon of a 225 million solar mass black hole like Gargantua, tidal forces are still little felt, because their intensity varies inversely proportional to the square of the central mass. Cooper can cross the horizon without even realizing it! « It’s like writing a checksmiles Alain Riazuelo. You will only become aware of the charge after you have received your bank statement. » The signals that Cooper will be able to emit will be increasingly weaker as he gets closer to the horizon. Beyond this limit no photon will be able to reach it and the astronaut will become forever invisible to the eyes of an external observer. However, he can still receive messages.
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For the hero ofInterstellar, followed by a dizzying fall towards the heart of the star. In reality, it would have been different. « Nothing can’t resist the immense attraction of downtowndescribes Éric Gourgoulhon, director of research at the Meudon observatory. Everything falls very fast towards him. The space between the horizon and the center is therefore…empty. »
After that ? Mystery. What happens at the center remains an enigma. Because black holes remain one of the most puzzling curiosities of our Universe. More massive ones like Gargantua, which are found in the center of galaxies, formed at the same time as their host galaxy. Those whose mass is between 1 and 10 solar masses are the final form of a massive star at the end of its life. When it explodes as a supernova, its nucleus contracts so much that no nuclear force can hold the atoms together. The heart collapses irreparably. « According to the equations of general relativity, developed by Albert Einstein in 1915, the collapse results in a locus of infinite density and curvature, what mathematicians call a singularity, » recalls Éric Gourgoulhon.
The black hole, an eternal celestial object?
This place can have different forms depending on the sophistication of the models. The simplest – but the least realistic! – is a static black hole that does not swallow matter. It is said of Schwarzschild, from the name of the German physicist who first put forward the hypothesis. In this case, the center of the black hole is a point of infinite density. A much more realistic description can be attributed to the New Zealander Roy Kerr and the American Ezra Newman who, in 1963 for the former and in 1965 for the latter, considered the case of a rotating black hole with an electric charge other than zero, a proposition which, however, also has a flaw: it assumes that the black hole was not created and does not receive matter. In short, that it is eternal.
In this model, the singularity is no longer a point but a ring – a theory that will give rise to the craziest ideas, such as « wormholes », tunnels connecting two points in space-time, or the transition from one universe to another . Approaching this ring is very difficult, because the closer to the center, the higher the rotational speed. And with it the centrifugal forces that tend to repel the approaching particle. Then comes an area, the Cauchy horizon, where centrifugal forces prevail. Anything that comes close is thrown out. It’s an impassable wall of radiation. In the case of our interstellar astronaut, »Cooper would therefore have to receive an infinite amount of radiation in an infinitely short time. »assures Alain Riazuelo.
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However, none of these models allow physicists to get rid of the singularity. Which is a problem for them, because they don’t know how to juggle endless features. Furthermore, they acknowledge that their description of the black hole’s center is wrong, because it is based only on the theory of general relativity, which cannot be applied to these extreme densities. Particle physics then reigns supreme, described by quantum mechanics, a probabilistic theory. According to Alain Riazuelo’s calculations, for a solar mass black hole, these quantum effects occur 10-24 second before reaching the singularity.
Time travel ?
To reconcile these two enemy sisters of physics, some astrophysicists have been trying since the 1960s to develop string theory, in which particles are no longer punctual but resemble strings, in one dimension. Others, like Carlo Rovelli or Aurélien Barrau, construct a loop theory of quantum gravity, in which space-time is granular. The size of the smallest element is therefore the Planck scale, i.e. 10-35 meter, length at which the theory of gravitation ceases to apply. Since spacetime is no longer continuous as in general relativity, it is no longer a singularity of infinite density. However, it remains to build a predictive theory and verify it with more tests. Will Cooper be able to travel through time, as Christopher Nolan thinks? Perhaps ! Then he would join Buzz Lightyear »to infinity and beyond« .
The shapes of the black hole
For an external observer, the black hole is bounded by its event horizon: beyond this limit no object, not even a photon, can get out. This horizon has an almost spherical shape: the faster the black hole rotates, the flatter this sphere becomes. Its radius is proportional to the mass of the central object. For a solar-mass black hole, it measures 3 kilometers. For Gargantua, of 225 million solar masses, that would be 775 million kilometers. On the scale of the Solar System, it would encompass everything up to Jupiter!
Also, inside the black hole, space is completely disturbed. Indeed, the curvature of space-time is extreme there: the notion of distance from the center is no longer relevant. « It’s like a bottle seen from abovewarns Carlo Rovelli, professor at the University of Aix-Marseille. The outside observer only sees the cap, while the internal volume is much larger. » This notion of volume needs to be handled with caution, because it only applies to objects that are static with respect to each other. However, in a black hole, everything falls towards the center… Everything is therefore in motion.
A black hole is bounded by its event horizon (in blue), below which no particles can emerge. Its other layers depend on its rotation speed. For a static black hole (top), the center is a point of infinite density (red). For a black hole rotating at half the speed of light (middle) or 90% of the speed of light (bottom), the dot turns into a ring and we notice another horizon, the Cauchy horizon, on which particles they stumble due to enormous centrifugal forces. Credits: RT CAVALCANTI, SAGEMANIFOLDS PROJECT