Symbol S

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…signature of chaos, cannot exceed $\lambda_L$ $\le$ 2$\pi$/$\beta$ for a thermal system at inverse temperature $\beta$ , with a black hole horizon saturating the bound [ 3 ] . Combining a Lyapunov-limited spread over $\ln$ S e-foldings of the hole’s Bekenstein-Hawking entropy S gives the estimate $t_* \;\sim\; \frac{\beta}{2\pi}\,\ln S, \qquad \beta \equiv \frac{\hbar}{k_BT_H} = \frac{8\pi GM}{c^3}$. where the second equality for a Schwarzschild hole follows directly from Hawking’s temperature formula [ 7 ] and S = A/4$\ell_P^2$ is the Bekenstein-Hawking entropy [ 6 ] . For a solar-mass hole, $\beta$…

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