The information in the information paradox is the variables that mathematical projections are using to describe the object; mass, color, density, structure, position, velocity and number of "atoms". The holographic principle appears to have sub layers per object solution ..not just large volumes of space. Every object has its own mathematical object associated with it.

Entanglement is when multiple quantum waves use the same complex mathematical object. All quantum behavior is using complex numbers with uncertainty.

The holographic principle is based on the projection of mathematical objects from a higher mathematical dimension to 3D representation with "physical" properties.

I question if living objects have associated math objects.

Is entropy and EM radiation the keys to making a mathematical projection become physical?

Is quantum information entropy and why it is on the surface area of the event horizon?

Is entropy quantum information in a mathematical projection?

If entropy makes mathematical projections physical, are physical objects passing the event horizon of a black hole still physical?

pittsburghjoe:

As always, you raise valid and intriguing questions especially about images on the event horizon of a black hole.

It appears that language is entirely inadequate to describe the situation you describe. There is an underlying assumption that there is a unique time that can be synchronized across events. Reality as described by General Relativity is just not like that.

As viewed from a distance objects appear red-shifted and time-dilated as they appear to approach the event horizon. They effectively appear to disappear as they appear to take an infinite time to reach the horizon. They never quite get there. Nothing ever appears to “pass through”.

As viewed from a distance the Black Hole retains all the properties that are still observable of material that “fell in”, namely mass, charge, and spin. There are some technical issues to do with “information” that are unresolved and probably cannot be resolved until a theory satisfactorily uniting Relativity and the smallest Quantum effects is created.

Additionally, subatomic particles may be created near the black hole, akin to those who blink in and out of a vacuum as a result of its inherent vacuum energy, due to the massive energy contained within the black hole. With this in mind, this process is how the physicist Stephen Hawking proposed that a black hole, over time if left alone and it no longer ingests mass, could evaporate.

As viewed from an object falling in, nothing very special happens at the event horizon, and the object reaches the putative singularity at the centre in a finite proper time*, that is time as measured by clocks moving with the object itself.

As viewed by an observer at the event horizon, again nothing very special happens as the infalling object whizzes by. But you are observing things in highly curved space-time so observations are not quite that simple. Indeed even the phrase “at the event horizon” has its issues because there is an ingoing horizon that is distinct from the outgoing horizon.

Black holes can even have an electric charge if they eat up too many protons and not enough electrons (or vice versa). But in practice this is very unusual, since these charges tend to be so evenly balanced in the universe. And then even if the black hole somehow picked up a charge, it would soon be neutralized by producing a strong electric field in the surrounding space and sucking up any nearby charges to compensate.

A large class of spherically symmetric static extremal black hole spacetimes possesses a stable null photon sphere on their horizons. For the extremal Kerr–Newman family, the photon sphere only really coincides with the horizon in the sense clarified by Doran. The condition under which a photon orbit is stable on an asymptotically flat extremal Kerr–Newman black hole horizon has recently been clarified; it is found that a sufficiently large angular momentum destabilizes the photon orbit, whereas an electrical charge tends to stabilize it. We investigated the effect of a negative cosmological constant on this observation, and found the same behavior in the case of extremal asymptotically Kerr–Newman–AdS black holes in

-dimensions. In

-dimensions, in the presence of an electrical charge, the angular momentum never becomes large enough to destabilize the photon orbit.

These charged black holes are called "Reissner-Nordstrom black holes" or "Kerr-Newman black holes" if they also happen to be spinning.

Additionally, there exists a radius at which even photons of light can have a circular orbit about a black hole. But the circling photons are subject to a few constraints. First, the photons must keep to their trajectories very precisely, since the photon sphere is really just a very precise, spherically symmetric radius at which objects moving at the speed of light (i.e. only photons) can orbit a black hole. If a photon interacts with another photon and changes its trajectory it can easily get flung out of the system or plunge into the black hole. So it is important to note that the orbiting photons are not stable in this orbit for very long!

The nature of the photon sphere depends on the spin of the black hole. The easiest case is for a non-rotating hole: here the radius of the photon sphere is 1.5 times the radius of the event horizon (2GM/c^2). Things get a bit more complex if the black hole is spinning: then there are actually two photon spheres-- one that rotates with the hole (closer in), and one that rotates in the opposite direction as the hole (further out). The faster the hole spins, the more distance exists between the two photon spheres. So photons with the right trajectory that orbit in the same direction as the black hole are temporarily stable in the inner photon sphere, and photons with the right trajectory that orbit in the opposite direction are temporarily stable in the outer photon sphere. It also helps if the photons in question come in on equatorial trajectories with respect to the black hole... things get a bit more complex if they don't.

Material infalling to the accretion would have a darker interior than the static case, which is due to the Doppler effect of the infalling matter. Different quintessence state parameters would change the positions of the photon spheres of the image.

In reality geometrically thick and optically thin accretion may occur. For geometrically thick and optically thin-disk accretion, the observed appearance of the shadow will have significant difference from that of geometrically thin and optically thin accretion. Because in this case the brightness at each impact parameter is an integrated volume emissivity along the line of sight. Therefore, the observed appearance of the shadow is a complex function of the emission profile and the shape of the emitting region. It has been found that, for geometrically thick emission, the lensing ring would provide a more significant feature in the observed appearance than in the thin-disk case. Besides, in the Universe black holes often exist as rotating objects. Therefore, extending the static quintessence black hole solution to a Kerr-Newman like solution is a natural extension.

The redshift factor for the infalling accretion is related to the velocity of the accretion, that is,

𝑔=𝑘𝛽𝑢𝛽o𝑘𝛾𝑢𝛾e,g=kβuoβkγueγ, in which 𝑘𝜇=𝑥𝜇˙kμ=xμ˙ is the four-velocity of the photon, 𝑢𝜇o=(1,0,0,0)uoμ=(1,0,0,0) is the four-velocity of the static observer, and 𝑢𝜇eueμ is the four-velocity of the accretion under consideration, given by 𝑢𝑡e=1𝑓(𝑟),𝑢𝑟e=−1−𝑓(𝑟)‾‾‾‾‾‾‾‾√,𝑢𝜃e=𝑢𝜓e=0.uet=1f(r),uer=−1−f(r),ueθ=ueψ=0.

The four-velocity of the photon has been obtained previously from Eqs. (

2.8) to (

2.10). From these equations, we know that 𝑘𝑡=1/𝑏kt=1/b is a constant, and 𝑘𝑟kr can be inferred from the equation 𝑘𝛼𝑘𝛼=0kαkα=0, that is,

𝑘𝑟𝑘𝑡=±1𝑓(𝑟)1−𝑏2𝑓(𝑟)𝑟2‾‾‾‾‾‾‾‾‾‾‾√,krkt=±1f(r)1−b2f(r)r2, in which the ++/− corresponds to the case that the photon gets close to/away from the black hole. Where the redshift factor can be simplified as

𝑔=1𝑢𝑡𝑒+𝑘𝑟/𝑘𝑒𝑢𝑟𝑒,g=1uet+kr/keuer, which is different from the static accretion case.

Profiles of the specific intensity *I*(*b*) cast by an infalling spherical accretion, viewed face-on by an observer near the cosmological horizon. We set 𝑀=1M=1, 𝑎=0.05a=0.05, 𝑤=−0.5w=−0.5 (top row) and 𝑤=−0.7w=−0.7 (bottom row) as two examples.
In addition, the proper distance is defined by d𝑙p=𝑘𝛾𝑢𝛾ed𝑠=𝑘𝑡𝑔|𝑘𝑟|d𝑟,dlp=kγueγds=ktg|kr|dr,

See where

*s* is the affine parameter along the photon path 𝛾γ. With regard to the specific emissivity, we also assume that it is monochromatic, so that Eq. (

4.2) is still valid. Integrating Eq. (

4.1) over the observed frequencies, we obtain 𝐼∝∫𝛾𝑔3𝑘𝑡d𝑟𝑟2|𝑘𝑟|.I∝∫γg3ktdrr2|kr|.

Now we will investigate the shadow of the quintessence black hole numerically with infalling accretion. Note that there is an absolute sign for 𝑘𝑟kr in the denominator. Therefore, when the photon changes the direction of its motion, the sign before 𝑘𝑟kr should also change. For different state parameters

*w*, the observed intensity with respect to

*b* are shown in the figure above, in which the top row is for 𝑤=−0.5w=−0.5 while the bottom row is for 𝑤=−0.7w=−0.7. From the figure above, we find that, as

*b* increases, the intensity will increase as well to a peak 𝑏=𝑏𝑝ℎb=bph; after the peak it drops to smaller values. This behavior is similar to that in the static accretion. We can also observe the effect of

*w* on the intensity and find that the intensity increases as the value of

*w* increases, i.e., the intensity for 𝑤=−0.5w=−0.5 is stronger than 𝑤=−0.7w=−0.7. The two-dimensional image of the intensity is shown on the right column in the figure above. We see that the radii of the shadows and the locations of the photon spheres are the same as in the static case. That means the motion of the accretion does not affect the radii of the shadows and the locations of the photon spheres. However, different from the static accretion, the central region of the intensity for the infalling accretion is darker, which can be accounted for by the Doppler effect. In particular, near the event horizon of the black hole, this effect is more obvious.

See:

https://link.springer.com/article/10.1140/epjc/s10052-020-08656-7#Fig1
See:

https://iopscience.iop.org/article/10.1088/1361-6382/aa95ff
See:

http://imagine.gsfc.nasa.gov/docs/ask_astro/black_holes.html
See:

https://www.quora.com/If-objects-appear-to-freeze-as-they-enter-a-black-hole-wouldnt-the-event-horizon-appear-to-be-packed-with-everything-that-has-ever-passed-through?share=1
Dark energy can escape a black hole, if its found there, no matter what size the black hole is and no matter how close the dark energy is to the center of the black hole. This is because dark energy is not affected by gravity at all.

Dark energy is what causes the universe to expand faster and faster, and this means that it actually has an effect opposite gravity's, since gravity pulls things together. So, while gravity causes things like stars, planets and black holes to be attracted to each other and become physically closer, dark energy makes everything in the universe become more distant because it makes space stretch itself bigger and bigger.

For this reason, it is the only thing in the universe, as far as we know, that is not affected by supermassive black holes.

There is also enough matter in a galaxy, so that the matter within the galaxy is not affected by the expansion of the universe. You can visualize this as the gravity of the galaxy holding it together, but really it's more fundamental than that. The rate of the expansion of the universe depends on the amount of matter (and dark energy) in the universe. If you just consider a tiny fraction of the universe which just includes a galaxy and total the matter in that region, it's more than enough to have already stopped the expansion in that region.

Dark energy effect on a black hole.
See:

http://curious.astro.cornell.edu/about-us/86-the-universe/black-holes-and-quasars/general-questions/427-is-dark-energy-affected-by-black-holes-intermediate
* Proper time: proper time along a

timelike world line is defined as the

time as measured by a

clock following that line. It is thus independent of coordinates, and is a

Lorentz scalar. The proper time interval between two

events on a world line is the change in proper time. This interval is the quantity of interest, since proper time itself is fixed only up to an arbitrary additive constant, namely the setting of the clock at some event along the world line.

The proper time interval between two events depends not only on the events but also the world line connecting them, and hence on the motion of the clock between the events. It is expressed as an integral over the world line (analogous to

arc length in

Euclidean space). An accelerated clock will measure a smaller elapsed time between two events than that measured by a non-accelerated (

inertial) clock between the same two events. The

twin paradox is an example of this effect.

The dark blue vertical line represents an inertial observer measuring a coordinate time interval

*t* between events

*E*1 and

*E*2. The red curve represents a clock measuring its proper time interval

*τ* between the same two events.

By convention, proper time is usually represented by the Greek letter

*τ* (

tau) to distinguish it from

coordinate time represented by

*t*. Coordinate time is the time between two events as measured by an observer using that observer's own method of assigning a time to an event. In the special case of an inertial observer in

special relativity, the time is measured using the observer's clock and the observer's definition of simultaneity.

The concept of proper time was introduced by

Hermann Minkowski in 1908, and is an important feature of

Minkowski diagrams**.

See:

https://en.wikipedia.org/wiki/Proper_time
** A Minkowski spacetime diagram is a geometric representation of motions in spacetime. The vertical axis is usually plotted as the time axis. Any point in spacetime is called a world point, and a series of worldpoints representing the motion of some object is called a world line. If ct is used for the time axis, then light on a Minkowski diagram will always travel at 45° to the time axis (either right or left at 45° in a one spatial direction Minkowski diagram, along the surfaces of a 45° cone - called the light cone - in a dual spatial dimension Minkowski diagram.

Fig. 1 Spatial contraction of object

When there is no movement between the object's rocket (B in red) and the observer's rocket (A in blue) they are both one unit in length. In fig 1 the object is passing the observer with a speed of 0.6c. The observer measures that the object's rocket (in red) has contracted to 1/g = 0.8 its original length. The relativity factor g (gamma) = 1/(1-v2/c2) ½.The observer's rocket (blue) is one unit long on any of its lines of simultaneity (any horizontal line). The object's rocket (red) is 0.8 units long on any of the observer's lines of simultaneity and shown at several different times. This illustrates the spatial contraction (the SC arrow).

See: https://discover.hubpages.com/education/Using-the-Minkowski-Diagram-
Any individual event is uniquely represented by some point P. The description of this event is described in the S frame by the coordinates (x, ct) and in the S' frame by the coordinates (x', ct'). If the origins of S and S' are chosen so as to coincide at ct = ct' = 0, then the relation between (x, ct) and (x', ct') is contained in the Lorentz transformations. The world line of a light signal starting out at x = 0, ct = 0, is a bisector of the angle between the axes. This holds good in both the S and S' frames.

See:

http://bingweb.binghamton.edu/~suzuki/ModernPhysics/2_Minkowski_spacetime_diagram.pdf
Black holes remain an enigma in so many ways. Will the image of an object remain on the singularity after the object has fallen through it? Are the infalling objects affected by the photon spheres? Infalling objects effectively appear to disappear as they appear to take an infinite time to reach the horizon, but they never quite get there. As viewed from a distance the Black Hole retains all the properties that are still observable of material that “fell in”, namely mass, charge, and spin.

Hartmann352