I remind that I defined generalized limit of arbitrary function. The limit may be an infinitely big value.
It allows to define derivative and integral of an arbitrary function.
I also defined what are solutions of partial differential equations where such infinities (instead of e.g. real numbers or complex numbers) are defined.
You may see in my book that for the simple differential equation y'(x) = -1/x2 we can consider either in a sense arbitrary generalized solutions or generalized solutions with a “pseudodifferentiable” derivative. The first one gives an arbitrary value in the zero point and the second a fixed real value in zero point. See the book for more details.
If we would instead consider the general relativity Einstein equations, we would probably get the following (not yet checked):
- We require the solutions to be pseudodifferentiable in time (or rather, timelike intervals).
- We do not require the solutions to be pseudodifferentiable in space(or rather, spacelike intervals).
- Then in the singularity point there would form during time of black hole forming a certain value with an infinite structure in the center which is determined by the values of the variables while the hole was forming but is not a function of the characteristics of the already form black hole.
If that hypothesis is true, we have a solution to the black hole information paradox: the center of a black hole holds not a hole but an infinite value containing the information of how the hole was formed. This value is a constant, but does not depend on the “dead” form of an already formed black hole, rather it contains the information of how the hole was formed.
It’s a very interesting hypothesis. Just write a publication on this topic, unless I do it before you. Win a Nobel prize.