# 貝肯斯坦上限

## 表示式

${\displaystyle S\leq {\frac {2\pi kRE}{\hbar c}}}$

${\displaystyle I\leq {\frac {2\pi RE}{\hbar c\ln 2}}}$

${\displaystyle I\leq {\frac {2\pi cRm}{\hbar \ln 2}}\approx 2.577\times 10^{43}mR}$

## 貝肯斯坦-霍金方程

1972年，史蒂芬·霍金证明了黑洞视界的表面积永不会减少，两个黑洞合并后的黑洞面积不会小于原先两个黑洞面积之和。与此同时，雅各布·貝肯斯坦運用此理论提出了黑洞熵的概念。為了符合熱力學第二定律，黑洞必須擁有熵。如果黑洞沒有熵，則可以藉由將物質丟入黑洞中來違反熱力學第二定律。黑洞熵的增加必須超過被吞入物質所減少的熵。贝肯斯坦認為，黑洞的表面积与它的熵含量成正比，从而使其不违反热力学第二定律。贝肯斯坦在他的论文中指出：

${\displaystyle S_{\text{BH}}={\frac {kA}{4\ell _{\mathrm {P} }^{2}}}}$

## 參考資料

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