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The Riemann Hypothesis as a Stability Principle

  The Riemann Hypothesis can be reformulated as an infinite sequence of explicit positivity tests. This is not a proof. It turns a statement about complex zeros into inequalities that can be calculated, falsified at finite order, and compared with operator or physical models.   The completed zeta function is $$\xi(s)=\frac12s(s-1)\pi^{-s/2}\Gamma\left(\frac{s}{2}\right)\zeta(s),$$ with $$\Xi(t)=\xi\left(\frac12+it\right).$$ The function $\Xi$ is even and real on the real axis. A nontrivial zero $\rho=\beta+i\gamma$ corresponds to $$t_\rho=\gamma-i\left(\beta-\frac12\right).$$ Therefore $$t_\rho\in\mathbb R \quad\Longleftrightarrow\quad \beta=\frac12,$$ and hence $$\boxed{\mathrm{RH}\quad\Longleftrightarrow\quad\text{every zero of }\Xi\text{ is real}.}$$ Folding the Zeros Because $\Xi$ is even, write $$\Xi(t)=\sum_{n\ge0}c_nt^{2n}.$$ Now define $$G(z)=\frac{\Xi(i\sqrt z)}{\Xi(0)}.$$ Although this contains $\sqrt z$, the even expansion makes $G$ entire: $$G(z)=...
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Is there a Maximum Power Limit in General Relativity?

Yes!
Also, it is not the 'Planck Power' (despite what you might have read in Misner, Thorne and Wheeler, P.980).  The existence of black hole horizons implies a maximum luminosity (power) limit in General Relativity. Not even gravitational waves can escape a black hole. Consider an (almost) black hole made of light (this is called a Kugelblitz) sphere of radius
\begin{equation}
\notag
R \geq \frac{2Gp}{c^3}
\end{equation}  which is filled with photons with a total mass-energy of momentum $p$ times speed of light $c$ \begin{equation}
\notag
E=p \ c
\end{equation} the shortest time which the entire sphere can release its energy is its light-crossing time: 
\begin{equation}
\notag
t=R/c
\end{equation}  with average power (luminosity) 
$$
P = \frac{E}{t} \leq \frac{p \ c^2}{R}$$
So $$P_{max}=\frac{c^5}{2G}\approx 1.8\times10^{52} \ W$$  This is maximum power in GR, for a compact, casually connected emitter. 
 
i.e. is not already enclosed by a horizon, releases an energy E from a region of radius R, and does so on no less than the regions light-crossing time. 
 
You might be tempted to call this half a 'Planck Power' but there is no $\hslash$ in this expression, it is purely classical. This is why you won't see an equation for 'Planck Power' in wiki 
Source: Cardoso (2018)
 
OK, so what if there is a maximum power limit in GR? Well, for one it means that even in classical GR, a lab-scale Kugelblitz cannot be formed. From this paper, to overcome Schwinger dissipation (which is quantum) to form one with a 1m radius would require a power of  around $P_{req}=10^{84}\ W$. This is greater than our derived maximum power! 
 
To get an energy density low enough to avoid triggering the vacuum breakdown (Schwinger effect) to build a Kugelblitz that doesn't blow itself up via quantum effects, you would need to construct a sphere of light larger than our Sun. Getting  $P_{max}$ watts of power coherently focused across a region 2 million kilometres wide is...effectively impossible.

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