Testing the Generalized Second Law in 1+1 dimensional Conformal Vacua: An Argument for the Causal Horizon
Testing the Generalized Second Law in 1+1 dimensional Conformal Vacua: An Argument for the Causal Horizon
复制标题
在 1 维共形真空中测试广义第二定律：因果视界的论证
DOI：
10.1103/physrevd.85.024015
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发表时间：
2011
影响因子：
5
通讯作者：
Aron C. Wall
中科院分区：
文献类型：
--
作者：
Aron C. Wall
对于中心电荷为c=tide{c}的1+1共形物质扇形的膨胀粒子引力，找到了广义熵的反常共形变换规律。(当$c\ne\tide{c}$时，广义熵在局部Lorentz提升下不是不变的。)证明了在一般的保角变换下，熵的一个二阶零导数$S_\文本{gen}“+(6/c)(S_\文本{out}‘)^2$是原数的，因此在一般的保角变换下保持其符号不变。因此，所有共形真空在因果视界上都具有递增的熵。视界或动力学视界的不同定义在任何维的视界中都可以具有递减的熵。这表明广义第二定律应该用因果视界来定义。
The anomalous conformal transformation law of the generalized entropy is found for dilaton gravity coupled to a 1+1 conformal matter sector with central charges $c = \tilde{c}$. (When $c \ne \tilde{c}$ the generalized entropy is not invariant under local Lorentz boosts.) It is shown that a certain second null derivative of the entropy, $S_\text{gen}" + (6/c)(S_\text{out}')^2$, is primary, and therefore retains its sign under a general conformal transformation. Consequently all conformal vacua have increasing entropy on causal horizons. Alternative definitions of the horizon, including apparent or dynamical horizons, can have decreasing entropy in any dimension $D \ge 2$. This indicates that the generalized second law should be defined using the causal horizon.