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

$c$

$\begin{equation} \notag E=p \ c \end{equation}$ that leave after a time

$\begin{equation} \notag t=R/c \end{equation}$ with average power (luminosity)

$\begin{equation} \notag P = \frac{E}{t}=\frac{p \ c^2}{R}=\frac{c^5}{2G} \end{equation}$ This is maximum power in GR, regardless of the nature of the system. 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? It leads you to think about other possible conjectures, like...maximum tension, acceleration and so on. And in the end, all these roads lead toward contemplating the nature of quantum gravity. Stay tuned!

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Remarks on the cosmological constant and minimal acceleration

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$T_{dS}$ . It is the minimum possible temperature of the Universe, and, it is not absolute zero (zero Kelvins). Numerically

$T_{dS} \approx 2.4 \times 10^{-30}K$ , the universal minimum (black body) `absolute cold' local temperature of the future dS state. As a comparison, in 2020 the NASA Cold Atom lab was able to cool an atom to a record low

$\sim 2 \times 10^{-7}K$ . Now, in any theory one may think of temperature as an energy, and from the semi-classical Unruh relationship, temperature

$\sim$ acceleration. Therefore:

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In a previous post we introduced the idea that our current Universe has boundary conditions. Classical 1+1 dS space-time visualized as basketball hoop, with the up/down slam-dunk direction being the time dimension, and the hoop circumference the space dimension. We also showed a diagram similar to Figure 1 below. Except here, we are once again thinking about the future dS state . Figure 1 . For an observer at O inside the cosmic event horizon (CEH) with radius

$l_{\Lambda}$ , the universe can be divided into two sub-vacuums,

$(A)$ inside the CEH, and

$(B)$ , outside. The horizon surface

$\Sigma$ has entanglement entropy

$S_{dS}$ and rest energy

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A 2021 paper by Zurek applied a random walk argument to a black hole horizon. Credit, Zurek, 2021 Zurek called this a blurring of the horizon (a fuzzy, or uncertain horizon), and also went through some equivalent derivations, which basically supported the idea this length scale is the quantum uncertainty in the position of the BH horizon, aka a dynamic quantum width of an event horizon (a concept which would therefore also apply to the universe's own CEH). The Bekenstein-Hawking entropy gives the number of quantum degrees of freedom that can fluctuate. Below, we step out our own cosmic de-Sitter derivation of the random walk argument, obtaining the same result as Zurek did, so its certainly correct!

$\begin{equation} \Delta x^2 =2 DT \end{equation}$ In this equation,

$\Delta x$ is the position uncertainty,

$D$ is the Einstein diffusion coefficient and

$T$ is the time between measurements (aka the relaxation time). So, lets look at the Einstein diffusion co...

What have electrons, black holes and Clifford Algebra ever done for us?

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