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The Horizon Quantum of Area

  Several independent semiclassical arguments converge on $$\boxed{\Delta A=8\pi l_{\mathrm{Pl}}^2}, \qquad l_{\mathrm{Pl}}^2=\frac{G\hbar}{c^3}$$ I got interested in this reading the 2018 paper  Bekenstein, I, and the quantum of black-hole surface area . Even though I disagree with Hod, its a great paper.  Honourable mentions also go to:   The Physical Interpretation of the Spectrum of Black Hole Quasinormal Modes , 2008  The Off-Shell Black Hole , 1994     On Black Hole Spectroscopy via Adiabatic Invariance , 2012 An Analytical Computation of Asymptotic Schwarzschild Quasinormal Frequencies , 2003  Asymptotic Black Hole Quasinormal Frequencies , 2003  1. Horizon Action Near any nonextremal horizon, imaginary time turns the normal geometry into a plane: $$ds_E^2\simeq d\rho^2+\rho^2d\Theta^2+\cdots.$$ Smoothness requires one horizon cycle: $$\oint d\Theta=2\pi.$$ The gravitational action identifies the momentum conjugate to $\The...
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Remarks on the cosmological constant and minimal acceleration

As Lineweaver explained, because our Universe is expanding at an accelerating rate, our Universe has a cosmic event horizon (CEH).    Its an event horizon Jim, but not as we know it...Image credit: DALL.E2 by SR Anderson Events beyond the CEH will never be observed. The CEH is also the source of de Sitter radiation, which has a specific temperature $T_{dS}$. 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:   \begin{equation} \notag E_{dS} = T_{ds} \ k_B= \frac {\hslash a}{2\pi c} \end{equation} What we g...
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Blurring the horizon - the quantum width of the cosmic event horizon

A  paper by Zurek applied a random walk argument to a black hole horizon. Credit, Zurek, 2021 Zurek  ( Snowmass White Paper: Observational Signatures of Quantum Gravity )  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, giving us the exact phenomenological signature Zurek found: $$\Delta x^2 = 2DT$$ In this equation, $\Delta x$ is the position uncertainty, $D$ is the Einstein diffusion coefficient, and $T$ is the time between measurements (the relaxation time). Einstein Diffusion Coeffici...
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The Cosmic Strange Metal

      Strange metals, quantum spin liquids, and SYK-like systems share a striking transport pattern: no quasiparticles, strong collective dynamics, Planckian relaxation, near-minimal viscosity, and maximal chaos. Their characteristic data are $$\frac{\eta}{s}=\frac{\hbar}{4\pi k_B}, \qquad \lambda_L=\frac{2\pi k_BT}{\hbar}, \qquad \tau_P=\frac{\hbar}{k_BT}.$$ The claim is not that the three-dimensional de Sitter bulk is literally a strange metal. The sharper claim is: $$\boxed{\text{The de Sitter stretched horizon belongs to the same transport universality class as a Planckian strange metal.}}$$ The correspondence applies to the horizon membrane, not to bulk spacetime. Membrane Paradigm and the KSS Value In the membrane paradigm, an event horizon behaves for exterior observers as a stretched viscous membrane with transport coefficients fixed by Einstein gravity. This does not require an assumed AdS/CFT dual. For de Sitter, $$\ell_\Lambda=\frac{c}{H}, \qquad T_{dS...
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Our cosmic event horizon on a string

A Cosmic Stringy Adventure !   Requiring the reduced Compton wavelength to fit within a cosmic event horizon results in a "minimum mass" (this is not a minimum particle mass) $m_s = \frac{\hbar}{c l_{\Lambda}}$.   In this post  we interpret $m_s$ as a horizon energy gap and model the associated gravitational scale as a  lightlike energy flow along an effective classical string.   McDormand with a cosmic light-like energy flow $m_{s}$ along a string of minimal  radius $2L_p$, giving a centripetal force $F_{max}=c^4/4G$.    Mass-Energy Flux Along the String   Let's think about that string for a bit. In fact, a great number of physicists have spent their entire careers tied up  unravelling  string theory . For a classical string 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_G \prime} \e...
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