Proof of classical versions of the Bousso entropy bound and of the generalized second law
Proof of classical versions of the Bousso entropy bound and of the generalized second law
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DOI：
10.1103/physrevd.62.084035
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发表时间：
1999-08
影响因子：
5
通讯作者：
E. Flanagan;D. Marolf;R. Wald
中科院分区：
文献类型：
--
作者：
E. Flanagan;D. Marolf;R. Wald
Bousso已经证明，在任何满足爱因斯坦方程和主能量条件的时空中，通过任何零超曲面L的“熵通量”S必须满足S<=A/4，该零超曲面L是从面积为A的某个类空2表面开始的非正膨胀测地线生成的。这一猜想重新表述了贝肯斯坦以及费施勒和苏斯金德早先提出的熵界，并且可以被解释为所谓的全息原理的陈述。我们表明，Bousso的熵界可以来自两组假设。第一组假设是（i）与时空中的每个零表面L相关联，存在熵通量4-向量s^a_L，其在L上的积分是通过L的熵通量，以及（ii）沿着L的每个零测地线生成元，我们有|s^a_L k_a|\le \pi（\lambda_\infty - \lambda）T_{ab} k^a k^B$，其中$T_{ab}$是应力-能量张量，$\lambda$是仿射参数，$k^a =（d / d\lambda）^a$，$\lambda_\infty$是仿射参数在测地线端点处的值。第二组（纯局部）假设是（i）存在绝对熵流4-向量s^a，使得通过任何零曲面L的熵流是s^a在L上的积分，以及（ii）该熵流4-向量服从逐点不等式$（s_a k^a）^2 \le T_{ab} k^a k^B b ^/（16 \pi）$和$|k^a k^B \nabla_a s_B|\le \pi T_{ab} k^a k^B /4$对于任何零向量k^a。在第一组假设下，我们还证明了可以导出更强的熵界，这直接意味着广义热力学第二定律。
Bousso has conjectured that in any spacetime satisfying Einstein's equation and satisfying the dominant energy condition, the "entropy flux" S through any null hypersurface L generated by geodesics with non-positive expansion starting from some spacelike 2 surface of area A must satisfy S<=A/4. This conjecture reformulates earlier conjectured entropy bounds of Bekenstein and also of Fischler and Susskind, and can be interpreted as a statement of the so-called holographic principle. We show that Bousso's entropy bound can be derived from either of two sets of hypotheses. The first set of hypotheses is (i) associated with each null surface L in spacetime there is an entropy flux 4-vector s^a_L whose integral over L is the entropy flux through L, and (ii) along each null geodesic generator of L, we have $|s^a_L k_a| \le \pi (\lambda_\infty - \lambda) T_{ab} k^a k^b$, where $T_{ab}$ is the stress-energy tensor, $\lambda$ is an affine parameter, $k^a = (d / d\lambda)^a$, and $\lambda_\infty$ is the value of affine parameter at the endpoint of the geodesic. The second (purely local) set of hypotheses is (i) there exists an absolute entropy flux 4-vector s^a such that the entropy flux through any null surface L is the integral of s^a over L, and (ii) this entropy flux 4-vector obeys the pointwise inequalities $(s_a k^a)^2 \le T_{ab} k^a k^b / (16 \pi)$ and $|k^a k^b \nabla_a s_b| \le \pi T_{ab} k^a k^b /4$ for any null vector k^a. Under the first set of hypotheses, we also show that a stronger entropy bound can be derived, which directly implies the generalized second law of thermodynamics.