**Articles & Reviews**

###### Authored by RSF Research Staff

# Planck Stars: Quantum gravity research ventures beyond the event horizon.

In the last section of one of our articles dealing with the so called *information loss paradox* of black hole physics - Stephen Hawking Goes Grey – we included a quick description of the cutting-edge work of two astrophysicist Carlo Rovelli and Francesca Vidotto describing what they came to call Planck Stars, which is gaining much interests in the popular press.

The *information loss paradox* is such a hot-bed of theoretical modeling right now because it suggests that either our theory of quantum physics or our model of black holes is flawed or at least incomplete (the most likely case being both/and, as is usually the solution to seeming paradoxes, which results from either/or thinking). Additionally, and perhaps most importantly, it is also recognized with some prescience that resolving the *information loss paradox* will hold the key to a holistic description of quantum gravity, and therefore be a major advance towards a unified field theory of physics.

The paradox, as formulated, arises from considerations of the ultimate fate of the information that falls into a black hole: does it disappear as it falls into the singularity in the middle? As well, what happens to the information of a black hole when it evaporates to nothing due to Hawking radiation (a mechanism described by Hawking in the 70’s where black holes slowly radiate their energy or mass)? But why are physicists talking about information and what do they mean by that? There are a number of characteristics that describe the state of matter and energy, and this is thought to be the information content of matter. Much of this information is the same data one would give to describe your own state – such as your relative position (where are you at?), your velocity (are you moving or are you stationary?), etc… these states are therefore information. As a result, there is an equivalence between information and energy. If a black hole loses all of its energy, then all of the information about all of the particles that fell in it would be lost as well. Of course the disappearance of information would be a violation of conservation laws of energy, which states that no energy/information can be destroyed.

Haramein has always contended that the information paradox problem is artificially generated by the incomplete understanding of black hole radiation, in which the virtual particles of the vacuum fluctuations are not only extracting energy from the black hole but as well feeding energy or information into the black hole in a continuous feedback, which we experience as the gravitational and electromagnetic fields.

**Planck Stars**

Nevertheless, assuming that the evaporation of black holes occurs, astrophyisicists Carlo Rovelli and Francesca Vidotto have offered perhaps one of the most palatable solutions thus far to this seeming paradox (notwithstanding Leonard Susskind’s wormhole solution, which we commented on in the article Firewalls and Cool Horizons)– and quite possibly a major advance in our model of black holes in general. The team, in their publication entitled *Planck Stars*, demonstrate how a gravitationally collapsing object may not be crushed down to a point of zero-dimension (no kidding), but instead will reach a point of metastable equilibrium when the volume reaches a specifc mass-energy density. Imagine what would happen if the mass of 14 of our Sun’s were compressed into a space the size of an atomic nucleus, what force would be needed to compress it further? According to Rovelli and Vidotto an equilibrium is achieved as the extreme inward force of gravity is balanced by a powerful repulsive force from the quantum vacuum energy density.

Normally quantum gravity is only described at the extremely small size of the Planck diameter (~10^{-33} cm). Such as in the theory of loop quantum gravity, where space itself, similar to atomic structure, has a discrete spacetime quantities like filaments, woven together in spin networks, the evolution of which is called spinfoam. Although Rovelli and Vidotto primarily utilize Planck values, they suggests that quantum gravitational phenomena can become relevant at sizes much large than planckian. The reason being that although the volume of a gravitationally collapsing mass is much larger than the Planck diameter, the energy of the Planck density of a centimeter cubed of space is extremely large (~10^{93} grams per centimeter cubed), and since quantum-graviational pressure is the direct result of energy density – a quantum-gravitational repulsive force will occur at a relatively large size to balance out the crushing inward force of gravitational collapse. This quantum pressure is predicted to occur at sizes around the subatomic scale (on the order of 10^{-10} – 10^{-14} cm). Therefore, according to their calculations, a collapsing black hole would stop and “bounce” back when it reaches, what turns out to be, the approximate size of a proton (a fact not mentioned by the authors), which is still some 20 orders of magnitude larger than the Planck length. In the section below we will discuss the formalism utilized by Rovelli and Vidotto that are variations of equations (volumes, surfaces, lengths) found in Haramein’s paper Quantum Gravity and the Holographic Mass, and the relationship of the Planck Star framework with his proton mass solution.

**Back to the Future**

In terms of a Planck Star, a mass that has been compressed to this density would no longer satisfy the classical Einstein equations (not withstanding Haramein’s holographic Schwarzschild solution) – general relativity once again meets quantum theory. Immediately some physicists would be throwing up their hands and yelling that this could not be physically relevant, as a black hole of that diameter would nearly immediately explode in a burst of high energy gamma rays (because of the relationship of the rate of Hawking radiation to the size of a black hole – the smaller a black hole, the more energy it radiates). However, what is being neglected in such a scenario (which has been a criticism that was as well applied to Haramein’s model of subatomic blackholes) is the relativistic effects of such a highly compacted mass. It is known that at the event horizon of any black hole – no matter its size – the extreme curvature of space-*time* causes local inertial frames (spaces adjacent to the event horizon) to experience a time dilation factor. It’s not just space that warps and bends under gravity and acceleration, but time as well. Said simply, from an external observer’s point of view, time appears to crawl to almost a halt near the event horizon of a black hole because of the acceleration approaching relativistic speeds, or if you’d like, the speed of light.

Therefore, the *proper *time of a Planck star (the time experienced in the frame of reference of the Planck Star itself) is very short (assuming that Hawking radiation is real), however from an external observer's perspective the radiation of a Planck Star before the “bounce” is extremely long. From it’s own time frame, it basically collapses very close to the Planck density and then rapidly experiences a “bounce” in which it radiates all of its information back into the Universe – saving us from the dreaded loss of information. The team demonstrates how long a Planck star would be around to an outside observer. Taking a black hole with a mass around 10^{15} grams (close to what could be considered a primordial black hole, which we will describe shortly) it will have a radius of approximately 10^{-14} centimeters (about the proton radius), then the calculated time dilation factor is approximately 14 billion years – or about the length of time the Universe is thought to have been around! Therefore, these objects *appear *amazingly stable. As a side note, if you could survive the extreme gravitational tidal forces, getting into the frame of reference of a Planck star would be a fast track trip to the future – you would essentially immediately be transported to the distant, distant future of the evolution of that star, something cool to think about.

**The Baby Universe**

Now, considering the early Universe Rovelli and Vidotto demonstrate that it may not have been emerging from a point of singularity as previously believed, but rather from the “bounce” of a Planck Star reaching the Planck density and therefore giving an alternative explanation to the so-called Big Bang and giving a source of energy (the vacuum energy density) to the reason the Universe is inflating. At the planckian density, the Universe was such a high temperature that even subatomic particles could not form. In this extremely high mass-energy density, it is theorized that all over the Universe small clusters of this plasma soup could have collapsed down to form black holes. These are called primordial black holes, and are theorized to possibly be distributed all throughout space even today, and were probably the progenitors of the supermassive black holes the reside at the heart of most galaxies. Since an atomic-scale primordial black hole would have a bounce-cycle of about 14 billion years, using the parameters calculated by Vidotto and Rovelli for the time dilation – some of these primordial black holes would just now be starting to experience their “quantum bounce”, from our perspective (even though in their proper time it occurred 14 billion years ago!). Rovelli and Vidotto suggests that we may be able to detect these events, by intercepting high energy gamma rays from space. Therefore, according to them, these high energy gamma rays may hold actual empirical evidence of quantum gravity.

**The Haramein Factor**

However, Rovelli and Vidotto not knowing of the Haramein holographic solution were unaware that there is already empirical evidence of quantum gravity. That is that Haramein’s prediction of the proton radius based on the Planck density of the vacuum, which to this day stands as the most accurate prediction of the latest proton measurement, and which is the only theoretical model (including the standard model) which predicts it accurately, is empirical evidence of the Planck quantum vacuum fluctuations having real and measurable effects, namely forming the proton in this case (this is why Rovelli and Vidotto came up with a very similar radius for their Planck Star). Haramein extracts the correct radius of the proton by demonstrating that gravity, not only at the quantum scale but as well at the cosmological scale, is fundamentally the result of the Planck information granular structure of spacetime producing the gravitational force we experience as black holes, and applies it to the quantum scale to show that the so-called confining force that binds the protons together in the nuclei is in fact quantum gravity miss-labeled as the strong force. Therefore, the structure of atoms themselves is empirical evidence of quantum gravity from vacuum fluctuations being a fundamental player in the creation of our world, from cosmological genesis as demonstrated by Rovelli and Vidotto to the structure and forces of all of the material world. This is why the Planck Star calculations eventually led them to the scale radius of in the vicinity of a proton.

As mentioned in our earlier article Hawking goes Grey *“In fact, the formulism utilized by Rovelli and Vidotto is extremely relevant as equations 3, 4, 8 and 9 in **their paper** are all basic variations of equation 19 in Haramein’s **Quantum Gravity and the Holographic Mass paper**, given there as: r=2ℓ(m/m _{ℓ}) where ℓ is the Planck length and m_{ℓ} is the Planck mass… Both approaches are geometric in nature, and both describe different aspects of the dynamics of space-time driven by the quantum resolution.” *Therefore, Rovelli and Vidotto arrive to the same formulism as Haramein from a completely different path, in their case curvature, where Haramein came from the discrete pixilation holographic structure of spacetime. In any case, the two are like pieces of a puzzle fitting together to give us a deeper understanding of universal evolution and creation.

Yet, although the team of astrophysicists arrived to a Planck Star in the region of the radius of a proton, it didn’t necessarily occur to them that the Planck Density in this volume when the “bounce” would occur is equivalent to the cosmological constant energy density of the vacuum in the rest of the Universe, which is currently thought to be the source of expansion of the Universe. Therefore, the apparent stability of the proton, or in their case the Planck Star, is not only due to time dilation, but also an equilibrium state between the internal Planck density quantum gravitational pressure of the proton and the cosmological energy density of the vacuum confining it.

The utilization of Haramein's equations from *Quantum Gravity and the Holographic Mass*, ostensibly arrived at independently by Rovelli and Vidotto, demonstrate the power of the Holographic Mass approach in describing dynamics that involve quantum gravity.

By: Resonance Science Foundation Research Team

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