Equation 65 · Part 4 · The Bit Comes Back Before the Bearing

=

S = A/4\ell_P^2

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

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The passage around this formula

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, $\beta$ $\approx$ 1.24 $\times$ 10^{-4}\, $\mathrm s$ and $\ln$ S $\approx$ 177 , giving $t_*$ $\approx$ 3.5\, $\mathrm{ms}$ — an exact evaluation of the stated formulas, illustrative of the scrambling scale and not a claim about any particular measured hole.

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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

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Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.