A Possible Physical Interpretation of How A Universe Can Exist Within a Black Hole Using Holographic Conjecture and Four Radii

UPDATE (April 29, 2010): Sean Carroll weighs in on this subject: here
and
Lubos Motl's response to Sean, here.


Recent papers by Paul Frampton and Erik Verlinde which can be traced back to Ted Jacobsen and many others including Gerardus 't Hooft and Leonard Susskind regarding the Holographic Conjecture, Stephen Hawking and Jacob Bekenstein regarding Black Hole Thermodynamics, Juan Martin Maldacena and colleagues and their work in AdS/CFT, Alan Guth and Cosmological Inflation Theory, and Lee Smolin with his Fecund Universes "Cosmological Natural Selection" Theory, have led me to the following thoughts.

Is it at all possible that there is a physical interpretation to the Holographic conjecture (as Sir Roger Penrose calls it) enough to promote it to a "principle"? That is to say, can our Universe actually reside (as Frampton et. al. maintain) inside of a Black Hole? Possibly. Here is my idea:

First, for qualitative and future mathematical quantitative purposes, let's define four radii from the center of a Black Hole, thus:

Concerning the Four Radii, we then define their relationship in a Black Hole of a certain size to be:

R1>R2>R3>R4 (1.1)

R1 = The Schwarzschild Radius (for a stationary Black Hole), aka the Event Horizon, and the only part of the Black Hole visible to outside observers.

R2 = The outer surface of a Black Hole.

R3 = The average mass radius of the Black Hole. The mass between R2 and R3 = the mass between R3 and R4, so it is not at the midpoint between them because of geometry.

R4 = The Interior Surface of the Black Hole. A Universe is postulated to exist between R4 and the center of the hole. We therefore consider the sphere defined by R4 to be the 2D Holographic boundary that defines the 3D (with gravity) Universe within.

For small Black holes, let us assume

R4 = 0 (1.2)

That is to say, R4 is the center of the hole, and so no Universe resides therein. Frampton estimates the Black Hole in which we reside to be on the order of R1 = 30 Billion light years across.

If so, there must be a time t > t naught (the time of the formation of the Black hole via Supernova collapse) when a Black hole with m = or greater than a certain critical mass m sub-c (for critical and very large mass) required to create a Universe therein is achieved, thus changing (Calculus, anyone?) R4 = 0 to R4 >0, and the universe begins, via a "Big Bang."

What could possibly possess a Black Hole to do so without "divine intervention", that is to say: naturally?

My contention is that for this to be possible, that no matter can compress itself smaller than quark-gluon plasma (see Brookhaven and their wonderful current results for reference), and therefore something has to give.

What I believe gives is radius R3. It expands because it has no other choice, being the mass equilibrium point (sort of a spherical center-of-mass of the hole), and as it expands, it draws R4 away from the center of the Black Hole.

We must then ask ourselves: what "fills" the "vacuum" in the region, the "region" being the volume between R=0 and our new (and expanding) R4?

Well, that most basic of Sciences that is Physics has already provided the answer, hasn't it? Virtual particles (in the form of quarks/anti-quarks and gluons), stimulated by the quantum fluctuations of the nearly perfect but not quite perfect surface that is the expanding sphere defined by R4.

Thinking further: the black hole in which we reside will eventually evaporate, when the four radii become one, when:

R1=R2=R3=R4 (1.3)

This is when I posit (speculate) that "The Big Rip" demise of our Universe will occur. Fortunately for us, the larger the hole, the longer the evaporation, so if someone would care to check my numbers, I feel we are hundreds of trillions of years away from that event. Phew.

I eagerly await comments, both pro and con. I would much prefer to be right than wrong, but if I'm wrong then Pfft!, so be it. There are so many wonderful Unknowns in our Universe to explore and our time is finite and limited; I see no purpose in pursing dead ends, other than to learn they lead nowhere in order to back up and pursue greater knowledge.

Sincerely,

Steven A. Colyer
Cosmological Thermodynamicist, apparently

April 18-19, 2010

P.S. Thanks to:
- Tomasso Dorigo and Johannes Koelman at their wonderful blogs for making me aware of the current situation, and their post repliers as well.
- Sabine Hossenfelder and Stefan Scherer and their wonderful blog BackReAction for keeping us up to date on Quantum Gravity issues.
- Peter Woit/Columbia Math Dept. and Lubos Motl/Umbrella Corporation for their blogs, in spite of their way too-heavy moderation, for keeping the discussion going. Not all blogs are Democratic, but fine, nor are all Nations. Yet.
And saving the very best for last:
- Phil Warnell who gave me comfort that in the end, the Logic of Aristotle is most supreme, and that I was not the only person to think so.

A merger of 2 black holes. May this never happen to us.