The Black Hole Universe

Is the Universe inside a black hole?

In memory of Jose Alberto Lobo (1953-2012)
What happens to an astronaut if it falls inside the Schwarzschild radius of a Black Hole? This was my first exam question in the General Relativity class back in 1985 when I was a 5 year undergraduate in Theoretical Physics. Alberto Lobo was our teacher and it was also his first exam. A few years later, in 2001, we started to work together in the detection of Gravitational Waves from Black Hole binaries. It was fun to start a new project and a new group within our Institute. But my interest soon shifted back into Cosmic maps. Alberto never left our hearts.

Big Bang, black holes and theories

What is a Black Hole?

During World War I (WWI), in 1915, Einstein published his new theory of Gravity (called General Relativity). From the trenches of WWI in Russia, Schwarzschild (1873-1916) sent a letter to Einstein with a solution to Einstein's new equations. This solution corresponds to a singular point of mass M in empty space, which could represent the solution for a star outside its radius R. But surprisingly, even for such a very simple case, the solution had something new that was never seen before in Newton's theory of Gravity. The Schwarzschild solution predicts that associated to its mass M, every object has a size defined by a radius R*, which equals two times its mass 2M, times G, Newton's constant over the square of the speed of light: R*=2GM/c^2. This is called the event horizon (also called Schwarzschild radius) and usually has a very small value compared to any other physical scales associated with the same mass. For all objects we know, like the Sun (R=700,000Km), the event horizon is much smaller (R*=3Km) than its actual size: R*<R. This means that the Schwarzschild solution is only valid for distances larger than the size of the objects r>R and is not valid for the inside r<R of the object (because it is not empty). So the Schwarzschild solution is only valid everywhere for a special type of hypothetical objects, which have a size smaller than the event horizon R<R*. Strictly speaking Schwarzschild solution is only valid for a point object, not for an object of finite size R. But in general, any object of size R<R* is called a Black Holes (BH). Are these objects real? Or just a result of using a mathematical simplification: can those objects be considered like singular points?

Our universe could have formed like the first stars: collapsing and exploding into a supernova (a Big Bang). The image on the left shows the Crab Nebula, a remnant of a supernova. This could be a small analog of our universe today, represented by a simulation (MICE) in the image on the right. Credits: NASA/ESA (left) and MICE (right).

Focus

Inside a Black Hole

What is inside the event horizon of a BH? Are they really empty inside as Schwarzschild solution? Everybody knows that BH are black because we can not look inside because nothing can come out of R*... But the opposite direction is possible:  people inside a BH can see us  (Interstellar)! The smaller the BH mass M (or R*) is, the larger is the density of the BH. You can think of a BH as an object that is so dense that the velocity needed to escape the gravitational attraction caused by its mass M is equal or larger than the speed of light.It seems impossible that people could live inside such a dense object... But we will see below that this is in fact possible!

We can't look inside R*, but we know that the inside can not be made of normal matter, like a very compact star. Not even White Dwarfs or Neutron stars  are compact enough....it has to be denser! In 1959, Hans Adolf Buchdahl, showed that the maximum density that matter (in a normal state) can have corresponds to an object that is always larger than a BH event horizon (exactly 9/8 larger than R*). This is the case under some reasonable assumptions like energy conservation and positive pressure. This seems to indicate that BH could not exist: nothing can be so dense!

Black Holes (BH) of very different sizes and masses (from stellar to galactic) have been detected and measured in astrophysical observations. By measuring the orbital velocity of objects around the BH (outside R*) we have been able to constrain their size and masses and there is no doubt that such BH objects exist (see the first actual image of a BH here). What is it that we are observing when we detect a BH and measure its mass M? This is still a mystery!

The BH mass, M, could in fact contribute to the mysterious Dark Matter( DM) in the universe. BH behave like DM because (even if they had regular matter inside) they only interact gravitationally with other forms of matter or radiation. They don't emit light (this is why they are called BH) or interact in other ways because of the event horizon R*. This behaviour is in fact the definition of DM! So understanding BH could also help us understand DM!

Recent Nobel Prize Awards have been given for the discovery of Gravitational Waves in colliding BHs, for the characterization of a massive BH in the centre of our galaxy (The Milky Way) and also for the theory of BH formation (By Roger Penrose). So what is going on? How can they give Nobel Prizes to something we don't even understand?

This has puzzled many scientists, specially Stephen Hawking  and his colleagues, because regular matter can (and it's been seen) to fall into a BH. Yet somehow BH can not be made of regular matter?? What happens to that matter (and the information that falls inside)? This all seems to be a big misunderstanding. Many theorists believe that this can only be explained with a new theory of Quantum Gravity that does not exist yet, but will tell us in the future what the BH singularity really means. Is this the only way forward?

What the laws of physics (General Relativity) that Buchdahl used really tell us is that on average the state of the fluid that is inside a Black Holes has to have negative pressure, similar to the so-called Dark Energy (DE), that is forcing our universe to accelerate. In fact, P. O. Mazur and E. Mottola  argued that the same DE repulsive force that causes cosmic acceleration could also prevent the BH collapse! So could a Black Hole be made of Dark Energy?

A Solution

In very recent research (see Further Reading below), it has been found that the inside of a BH could be dominated by a False Vacuum which is trapped together with matter and radiation that are expanding (or contracting) in a state very similar to that in the expanding Universe that we observe around us. We call this solution a Black Hole Universe (BHU). So there could be galaxies, stars, planets and other Black Holes inside any given Black Hole if it is large enough to hold them (i.e. if the mass is large enough).

These new ideas can be understood in terms of Classical Mechanics by noting that Newton's law of Gravity needs to be replaced by Newton-Hooke's law of Gravity which is composed of two opposing forces. One is the regular Newton law (inverse square law) and the other is Hooke's law, which acts like a centrifugal force (proportional to distance) that opposes Newton's law. When the two opposing gravitational terms are equal we are in a stable equilibrium (the same that gives rise to Kepler's planetary orbits). This happens at the event horizon, R*, which corresponds to a circular orbit in Kepler's law (Copernicus circular orbits around the Sun). Inside the BH centrifugal forces dominate, while the outside is governed by Newton's inverse square law. The equilibrium happens at the horizon R*.

This new classical BHU solution to the Black Hole problem only uses General Relativity. It does not need exotic, yet to be discovered, theories of Quantum Gravity, String Theory, Modify Gravity, SuperGravity or higher dimensions. It shows that BH could be made of regular matter that is expanding or contracting inside a False Vacuum. So, people can indeed live inside a BH (if it is large enough). What makes the BH look so dense is its False Vacuum and the mass M that we measured is not regular mass, but the mass associated to the False Vacuum energy according to Einstein's famous equation: E=M c^2.

Black Hole Universe (BHU)

So this solves the mystery of BHs, like the ones we observe in the sky. But this solution also opens a totally different new door. In fact, our Big Bang Universe is inside a very large BH! The larger the BH mass or size the smaller its density inside. This agrees with our Universe which is large and has a very low density! In fact, our universe is the only object, whose interior we know, that has the exact mass and density of a BH!

We have several observational evidences that this BHU solution could be the right one for our universe. For example the evidence that the universe's expansion is accelerating. The acceleration is presumably caused by some mysterious Dark Energy (DE) or Cosmological Constant . But in the BHU solution it turns out that this can be identified with a simple False Vacuum fluid that dominates the BH dynamics. This is why the BH interior has a fluid with negative pressure and explains why Buchdahl could not understand how a BH could exist as regular matter. An equivalent way to understand this, is that the cosmological constant really corresponds to the boundary condition at the event horizon of the BH. These ideas, which might look very exotic at first sight, solve many of the observational puzzles (or cracks) in the Big Bang model. Like the need for inflation, the observed cosmic acceleration and some recent discrepancies in cosmological measurements (see below). Maybe even Dark Matter. THE BHU universe solution could explain the whole Dark Cosmos.

The Big Bang Theory turns out to be an illusion that results from the fact that we are comoving observers with the expansion of matter and radiation inside our BHU. We see the space-time around us as homogeneous and isotropic, But in reality we are inside a Black Hole. The actual space-time (the larger Universe where our Black Hole lives, e.g. the Apollonial Universe) could be much larger and older than previously estimated...

What is outside our Black Hole

We have some observational evidence (and a picture!) of what the Outside of our Black Hole Universe looks like. This evidence comes from measuring the parameters of the CMB physics in our distant past. We find that these parameters vary in the sky according to the BHU predictions (which are slightly different from the Big Bang model predictions).

Cosmic acceleration is evidence that we are inside a Black Hole. Otherwise we should be decelerating. Some mechanism similar to Cosmic inflation, which is needed to understand the horizon problem in cosmic maps, provides further support to this idea. Current and upcoming observations of Cosmic maps of structure in the universe could provide additional evidence for the BHU by looking at the largest scales in the sky and comparing cosmological parameters at different times. So a BHU is not just a theoretical concept. It can be tested with current and new observations and explains some of the cracks of the Big Bang model.
This situation is reminiscent of the Island Universe where most eighteenth century scientist believed that the universe consisted only of the Milky Way (our own galaxy). It was later discovered (with technological improvements on Telescopes and instrumentation) that many other island Universes (other galaxies or nebulas) existed. They just were too faint to observe initially. The same way, our Big Bang is just one Black Hole Universe (BHU) and many others could exist (e.g Apollonial Multiverse). This is part of the The Copernican Revolution: not only our place is not the centre of the Solar system, or the centre of our galaxy or centre of our Big Bang. Our BHU is not the only one! We no longer know the age or size of the Universe as a whole. Only the values corresponding to our BHU. But we can actually see what is outside our BHU and we can therefore test if there are other BHU... Observational evidence will decide if these ideas are right.