Abolishing the maximum tension principle

The Maximum Tension Principle in General Relativity

I suggest that classical General Relativity in four spacetime dimensions incorporates a Principal of Maximal Tension and give arguments to show that the value of the maximal tension is c 4 4G . The relation of this principle to other, possibly deeper, maximal principles is discussed, in particular the relation to the tension in string theory. In that case it leads to a purely classical relation...

The Pontryagin Maximum Principle

Theorem (PontryaginMaximum Principle). Suppose a final time T and controlstate pair (û, x̂) on [τ, T ] give the minimum in the problem above; assume that û is piecewise continuous. Then there exist a vector of Lagrange multipliers (λ0, λ) ∈ R × R with λ0 ≥ 0 and a piecewise smooth function p: [τ, T ] → R n such that the function ĥ(t) def =H(t, x̂(t), p(t), û(t)) is piecewise smooth, and one has ̇̂ ...

The Principle of Maximum Conformality

A key problem in making precise perturbative QCD predictions is the uncertainty in determining the renormalization scale of the running coupling αs(μ ). It is common practice to guess a physical scale μ = Q which is of order of a typical momentum transfer Q in the process, and then vary the scale over a range Q/2 and 2Q. This procedure is clearly problematic since the resulting fixed-order pQCD...

The Maximum Principle of Pontryagin

Characterizing the Strong Maximum Principle

In this paper we characterize the degenerate elliptic equations F(Du) = 0 whose subsolutions (F(Du) ≥ 0) satisfy the strong maximum principle. We introduce an easily computed function f on (0,∞) which is determined by F, and we show that the strong maximum principle holds depending on whether ∫ 0+ dy f(y) is infinite or finite. This complements our previous work characterizing when the (ordinar...