Yes. I think that it may well be possible to characterize a “Black Hole,” at least the very simplest one. In a recent publication it was noted that a model of the surface of “Black Holes” could only truly be explained if that surface were made up of minuscule “Black Holes!” one can combine this thought with the recent interest in considering the universe as having some basic structure. One instance in the recent Helium article on “Motion in a Matrix as a New Model….” In that article it was postulated that the basic fabric of the universe could be made up of “dots.” Let us consider these dots as the “Simplest Black Holes.”
There are a number of basic constants of the “Universe” known and basic laws. If we take our basic constants as “c,” the speed of light, and “h,” Planck’s constant, relating Energy to frequency, and as our basic formulas, the two energy formulas, E=mv^2, and E=hf, where “E” is in ergs, “h” is erg-sec, and “f” is cycles per second, we may be able to reach some conclusions about these little “Black Holes.” We will also need the momentum equation, P=mv, and some ideas from calculus.
If we “differentiate” the two energy equations, we obtain “dE/dt=mv, ” and “dE/dt=h.” These two “rate of change” equations, can be equated to form, “mv=h,” the form of a momentum equation. Either “m” or “v” has to be considered a variable, at some value their product will equal ” h.” If we guess that the maximum velocity of anything is “c,” we may consider, “m,” mass, as a variable, and “c” as a constant. Inserting the values of “h” and “c” and running out the mathematics for the various other ”constants” that would characterize our basic “Black Hole,” we obtain the following set of results:
h=6.63×10^-27 erg-sec. (A published value, rounded off.)
c=3.00×10^10 cm./sec. (A published value, rounded off.)
m=2.21×10^-37 g. (Found by running out the math. on “m=6.63×10^-27/3.00×10^10”; i.e inserting values in “mv=h.”)
f= 3×10^20 Hz, (This arises from solving “f=(mc^2/2)/h, with the previous three values inserted.)
l= 1×10^-10 cm. (This wave length, or cycle distance associated with the “mass,” arises from E=fl for which we have to have
E=1.985×10^-3 erg. previously solved for “E” from “E=mv^2, inserting our known values.)
r= 1.6×10-11 cm. (This radius of our tiny dot, is found by assuming that “l” is a cycle distance associated with “m” and is found
by dividing “l” by “2 Pi.” That is we are assuming that “l” is the circumference of a circle.
V= 6.7×10^-33 cc. (This “V,” for volume is from the formula for the volume of a sphere, 4/3(“Pi)r^3.)
d= 3.43×10^-4 g./cc. (This value, is, of course, “m/V.”)
The above calculations consider a fundamental Black Hole more or less as an isolated unit and the velocity being an angular velocity, with the mass being a component of that angular velocity. As angular velocity always has a component causing the spinning object to tilt. This would imply that there may well be two kinds of fundamental Black Holes with reversed directions of spin/tumble.
The Black Holes in the center of spiral galaxies appear likely to have a very directed vector so that they may show a very different mass/velocity relationship. Only at “c” can the constant “h” be used to evaluate mass.
The quality, “l.” could also be considered as the diameter of a vibrating entity. It may be that at the “ground-state vibrational energy” of an entity, the vibrational and rotational frequencies are identical with one vibration taking place during one rotation. A body would have to be vibrating to pass information.
Similar calculations to those above can be made for black holes of various masses and number of units. An interpretation of some of the data developed by the writer of the original article on “Motion in a Matrix…, ” q.v., whose ideas have inspired this, is that he may have, in that article, inadvertently determined some of the above values for a “Black Hole,” having a mass of one gram.
After the above was written it became clear that what was being defined above is what might be called a “Reference Basic Black Hole” which has a “mass” of 2.21 x 10-37 g. but which when one looks more closely would have within the defining equation of mv=h, a hidden situation which becomes clear if we evaluate mc=h at “c.” Dividing out “c,” we get “m” = 2.21×10^37. Since mass is in grams and the number, 2.21×10^-37 has the dimensions of gram-centimeters, i.e. a torque, what we really have left out on both sides is another division, by one centimeter. That is the equation is only valid if we consider that what has been called here “m” really is the combination of a force, m , acting at a torque arm of one centimeter.
Since the vector force and the torque arm are interchangeable, really are trying to talk about a “Reference Black Hole” which could have either a mass of 2.2l x 10^-27g. at a radius of 1 cm. or a mass of 1 gram. at 2.21 x 10^-37cm.