Into the black hole

As written in my blog, black holes are ultimate sinks in the spacetime, and any information cannot escape beyond the event horizon of the black hole once dropped inside it. I want to open a bit what could be inside a black hole and emphasize that mentioned infinities do not describe the real world. By the "No Hair Theorem" a black hole has only three properties including mass, charge and angular momentum. When a particle drops to a black hole it has impact on these properties. For instance, a mass of the particle adds the mass of the black hole. However, the most of its information gets trapped in the event horizon, such as baryon number or polarization. As written in the previous blog, the event horizon encodes the maximum information density and entropy. The event horizon is a sphere which surface area is proportional to the mass of the black hole squared. If you were to double the mass, the surface area would get four times, and the occupied volume eight times larger. Thus the spatial curvature at the event horizon is enormous for low-mass black holes, but barely discernible for high-mass black holes. 

If were on Earth watching an astronaut approaching the event horizon we would actually never see reaching it. In the highly curved spacetime the time slows down relatively to us. It appears to us that photons from the astronaut will be emitted more and more slowly. As a consequence the astronaut rather fades out than reaches ever the event horizon. However, the astronaut perceives the crossing the event horizon in a finite amount of time. In case of the smallest black holes (a couple times of Sun mass) the curvature of the spacetime is so high that it has different gravitational impact on body parts which would cause tidal forces to spread the body before reaching the event horizon. On the other hand, tidal forces are much weaker for a super massive black hole (e.g in the center of our Milky Way galaxy) and it could be possible to cross the event horizon without further notice. When getting closer to the event horizon the astronaut will perceive time going faster and may watch the universe to rapidly age, perhaps even to its death. So while getting inside the event horizon the astronaut is still able to see outside but likely there is nothing to see anymore if universe faced the heat death in given infinite time. There is no way to get outside the event horizon or to send any messages out. At the event horizon the space and time swap roles meaning that for the part of space, there's only a single direction to the center and no way to stop or slow down or turn direction. Therefore the space will become unidirectional like the time in our normal world. While for the sake of time, the astronaut will be able to see the past and future of the location of black hole as the photons are already trapped inside the black hole and therefore we could observe all the directions of time present, past and future.

The field equations of the general relativity give four solutions for a black hole depending on if the black hole is rotating or having charge. Karl Schwarzschild in 1915, discovered a solution for a non-rotating and uncharged black hole, having a singularity in the center that is nothing but zero-dimensional point. This type of singularity would eventually crush any matter into infinite dense once captured to the black hole. In 1963, Roy Kerr found the solution for rotating uncharged black hole. In practice all known astrophysical objects have a non-zero angular momentum and are effectively zero charged. While a star collapses the resulting black hole inherits the same properties. Known as the frame-dragging effect, the rotating black hole drags the spacetime along it causing all particles approaching the black hole to rotate with it, forming an ergospehere around the event horizon. Interestingly, a rotating black hole gives two solutions for the event horizon, an inner and an outer horizon. The outer one marks the event horizon beyond the external observer cannot see, and thus the inner one is inaccessible. While being between the two horizons the astronaut cannot see inside the inner one before getting in it by the unidirectional way. The space and time swaps again at the inner horizon and the astronaut is able to move again in three direction and perceive time flowing normally. However, it is possible that the astronaut gets into another universe and is never able to get out of the inner horizon. The Kerr metric solution allows a one-dimensional ring singularity that is inside the inner horizon, spread along the equatorial plane of rotation. It is temporal or coordinate singularity and not like in the Schwarzschild solution, it is possible to eliminate it by selecting an appropriate coordinate system. Analogically, longitude is not uniquely defined at the poles on Earth, which is an artifact of the coordinate system chosen. Other difference is that the ring singularity is repulsive if not approached on its equatorial plane. Furthermore, by going through the singularity one gets to the different region of spacetime, from the region which would be reached by going around it. The singularity would lead to the region called as negative space, which would be interestingly another infinite spacetime. 

The interior of the inner horizon of the Kerr black hole is mathematical abstraction which probably does not reflect the reality. It has been expected that the interior is unstable, which could prevent the emergence of the ring singularity. For example, any gravitational wave hitting the blackhole could break the stability. In 2022, it was mathematically demonstrated that the equilibrium found by Kerr was stable. Kerr commented that there is no need nor proof that singularities form inside a rotating black hole. All the mass, charge, and angular momentum of a black hole is contained inside the inner horizon. All remains of matter, such as a collapsed star, co-rotate with the black hole inside the inner ergosphere which is a flattened sphere that touches the inner surface at the poles of the rotation axis. The size of the inner region varies dependent on how large the angular momentum is compared to the mass of the black hole. As a star collapses it spins faster and faster until the centrifugal force counterbalances the attractive gravitational forces. Kerr also mentioned that if the body is stellar sized then its density will be roughly similar to that of a neutron star. If it is super sized then it is quite possible that the perceived gravity will be earth like and so an astronaut could actually land on it.

While the general relativity allows spacetime singularities it is not believed they exist in reality, but it rather tells that the general relativity breaks down and we need more complete theory to explain extreme conditions in the black hole. In the Einstein–Cartan theory, first proposed in 1922, the minimal coupling between torsion and Dirac spinors generates a repulsive spin, which prevents gravitational singularity. Also in other quantum gravity theories it is expected that quantum effects would become dominant before singularity emerges. According to the loop quantum gravity, when reaching the Planck energy density, the spacetime causes a repulsive force before a singularity is formed. Furthermore, the collapse would turn to rebound till the black hole becomes a white hole. Because of time dilation in the extreme gravity the rebound would take easily the life time of the universe. In the string theory there is a fuzzball, which similarly eliminates the singularity. In 1935, Einstein and Rosen proposed that the collapsing matter reaches an enormous but finite density and rebounds, forming a regular Einstein–Rosen bridge called also as a wormhole. The wormholes are linked to the theory of eternal Schwarzschild blackholes. In theory it is possible that such non-rotating black holes were created in the birth of the universe and were stretched by the expansion of the spacetime. Thus a wormhole can connect black hole to a very distant white hole in the universe. However, it is not usable for a human to travel through it. It turns out that in the general relativity, the gravitational attraction of any normal matter passing through a wormhole acts to pull the tunnel shut. In 2017, physicists Ping Gao, Daniel Jafferis, and Aron Wall discovered a way to prop open wormholes with quantum entanglement—a kind of long-distance connection between quantum entities. The peculiar nature of entanglement allows it to provide the exotic ingredient needed for wormhole stability, however for microscopic wormholes. Recently, scientists from the California Institute of Technology developed a model of a traversable wormhole on the Google Sycamore quantum processing system. Even though the wormhole is tiny and not a real one, the publication raised wide discussion in many levels, and what it actually means for physics. First, the wormhole emerged like a hologram out of quantum bits of information, or “qubits,” which demonstrates the holographic principle, that posits a mathematical equivalence or “duality” between the two frameworks. It says the bendy spacetime continuum described by general relativity is really a quantum system of particles in disguise, as discussed in the previous blog. Second, by manipulating the qubits, the physicists then sent information through the wormhole. In addition to the teleported information, the model revealed other predictions of the wormhole theory.