Skip to main content

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_{max} = \frac{E}{t}=\frac{p \ c^2}{R}=\frac{c^5}{2G} \approx 1.8\times10^{52} \ W
\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? 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.

Comments

Post a Comment

Popular posts from this blog

Blurring the horizon - the quantum width of the cosmic event horizon

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 went through derivations supporting the idea that this length scale is the quantum uncertainty in the position of the black hole horizon: a dynamic quantum width of an event horizon. This is a concept which fundamentally applies to the Universe's own Cosmic Event Horizon (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. To do this, let $l_{\Lambda}$ represent the generalised de Sitter horizon scale. Due to the holographic UV/IR correspondence, this scale manifests dually: at the fundamental microscopic limit as $l_{UV} = 2L_p$, and at the macroscopic cosmological limit as $l_{IR} = c/H$. By mapping between these conformal boundaries, we can derive the limits of the...
Post a Comment
Read more

De Sitter Horizons One Radius to Rule Them All

  As we know , de Sitter spacetime is a one-parameter thermodynamic system : every state variable is a power of the single horizon radius $l_\Lambda$. This has profound consequences for thermodynamics, information theory, and quantum chaos.     Key results: Smarr relation: $M = (D-1)TS$ (exact for all $D \geq 3$) First law: $dM = (D-2)T dS$ (exact for all $D$) Extended first law $dM = TdS + VdP$ fails except at $D=4$ (numerical coincidence) Pressure ratio: $|\Delta P|/|P_{vac}| = 2/D$ (exact) Ruppeiner metric: $g^{Rupp}_{VV} > 0$ (1D state-space curvature, not stability) Heat capacity: $C_P = -(D-1)S < 0$ (thermal instability) Classical fidelity: $F = 2/(D+1) \approx 2/D$ (asymptotic) Elastic analogy for $D=3$ explains why extended first law fails All results follow from one scale: $\kappa = 1/l_\Lambda$ 1. Setup and Natural Units Converting to SI Units When restoring physical constants: $$\begin{align} S &= \frac{k_B A c^3}{4 G \hbar}\ T &= \frac{\h...
Post a Comment
Read more

Our cosmic event horizon on a string

In this post, we introduced the idea that in the presence of a positive cosmological constant, there is a minimum (local) mass $m_{GR}$   McDormand swinging a cosmic light-like mass-energy $m_{GR}$, with a "cosmic string" of radius $l_{\Lambda}$, giving a centripetal force $F_{local}=m_{GR} \ c^2/l_{\Lambda}$.    Let's think about that string for a bit. In fact, a great number of physicists have spent their entire careers tied up unraveling string theory . For a classical string, which lives in D = 10 dimensions, associated with Nambu-Goto action, the the string tension $T_G$ is a local force, or energy per unit length (dimensions $MLT^{-2}$): \begin{equation} \notag T_G = \frac{1}{2\pi \alpha \prime} \end{equation}$\alpha \prime$ is the Regge slope parameter, set here with dimensions of inverse force.  The wavelength of the stringy mass-energy standing wave (such that it does not interfere with itself), is the circumference of the circle, and we know it moves...
Post a Comment
Read more