Quantum Gravity 248.2: Why the Riccati Equation Applies to Black Hole Infinite Force and Infinite Energy

From Osher Doctorow

By the way, I meant to type "infinite" rather than finite in the title
of the previous post.

The "topper" or "punch line" to the force-kinetic-energy-momentum
equation of the previous posting is the rather remarkable fact that
the proper equation to use for a collapsing star is the Riccati
Differential Equation, for an "astonishing" reason: the Riccati
Differential Equation, unlike almost all relevant equations of
physics, describes expansion-contraction rather than tangential
motion. A black hole represents a collapsing/collapsed star of a
certain minimal mass. Neither the Schrodinger equation of Quantum
Mechanics nor the Einstein Equation(s) of GR represent expansion-
contraction, being essentially either tangential or neither, whether
along a geodesic or whatever.

Remember that expansion-contraction of a body occurs simultaneously in
(usually infinitely) many directions in space, which we can take to be
roughly Euclidean, unlike tangential motion which has one direction
and only one direction at each time in most scenarios. That is to
say, a body moving straight ahead or along a curved line either has a
bunch of parallel tangents (more or less) or its c.g. or c.m. can be
taken as its single "representative" tangent for most purposes. This
is not so for an expanding or contracting body, which loses entirely
its motion if its c.g. or c.m. were taken as representing its
expansion-contraction, and which in fact can expand or contract
differently in infinitely many if not all different directions, both
in magnitude and direction.

The simplest expansion-contraction motion is exponential expansion-
contraction-growth, which is a special case of the Riccati
Differential Equation dy/dt = By. The different directional expansion-
contractions can be represented by simultaneous Riccati equations. If
expansion-contraction is "supply-limited", then the exponential
equation is replaced by another Riccati equation, the Logistic
Differential Equation, dy/dt = ky(1 - y) = ky - ky^2 = By - By^2, k =
b, normalized.

Osher Doctorow
.

Relevant Pages

  • Re: Distinct linear orderings on Z
    ... Tangents to functions as a measure of sizes ... minus the tiny fraction of infinite subsets of N. The function? ... from the numeric members of one set to the numeric members of another. ...
    (sci.math)
  • Re: expanding universe
    ... if we reverse expansion through time we get ... contraction, so at some point we must arrive at a single point, ... So if the universe is to ever contract to a single point, ... Not infinite, just unbounded and all-inclusive. ...
    (talk.origins)
  • Re: expanding universe
    ... if we reverse expansion through time we get ... contraction, so at some point we must arrive at a single point, ... So if the universe is to ever contract to a single point, ... Not infinite, just unbounded and all-inclusive. ...
    (talk.origins)
  • Re: Does Light Travel ?
    ... so this infinite length contraction and infinite time dilation ... Animals are divided into vertebrates and invertebrates. ...
    (sci.physics.relativity)