论文标题
熵在标态脱发lovelock重力下以线性顺序增加
Entropy increases at linear order in scalar-hairy Lovelock gravity
论文作者
论文摘要
在本文中，我们研究了lovelock重力中黑洞的第二定律，当时在扰动物质场满足无效能量条件时，在第一阶近似下通过共耦合标量场来提出的第二定律。首先，我们表明，该理论的WALD熵不遵守标态脱发的Lovelock重力的线性第二定律，即使我们用Jacobson-Myers（JM）熵代替Wald Entrody的重力部分，它也包含较高的曲率项。这意味着我们不能天真地将WALD熵的标量场项添加到纯Lovelock Gravity的JM熵中，以获得有效的线性化第二定律。通过重新定位度量，标量场的作用可以写成纯粹的Lovelock动作。使用此属性，通过与纯Lovelock重力的JM熵进行类比，我们在标量脱发Lovelock Gravity中引入了熵的新公式。然后，我们表明，这种新的JM熵在事件范围内增加了类似Vaidya的黑洞溶液，因此遵守线性的第二定律。此外，我们表明，与$ f（$ riemann $）$ GRAVITY中的熵不同，JM熵和Wald Entropy之间的差异还包含来自标量字段的一些其他更正。
In this paper, we investigate the second law of the black holes in Lovelock gravity sourced by a conformally coupled scalar field under the first-order approximation when the perturbation matter fields satisfy the null energy condition. First of all, we show that the Wald entropy of this theory does not obey the linearized second law for the scalar-hairy Lovelock gravity which contains the higher curvature terms even if we replace the gravitational part of Wald entropy with Jacobson-Myers (JM) entropy. This implies that we cannot naively add the scalar field term of the Wald entropy to the JM entropy of the purely Lovelock gravity to get a valid linearized second law. By rescaling the metric, the action of the scalar field can be written as a purely Lovelock action with another metric. Using this property, by analogy with the JM entropy of the purely Lovelock gravity, we introduce a new formula of the entropy in the scalar-hairy Lovelock gravity. Then, we show that this new JM entropy increases along the event horizon for Vaidya-like black hole solutions and therefore it obeys a linearized second law. Moreover, we show that different from the entropy in $F($Riemann$)$ gravity, the difference between the JM entropy and Wald entropy also contains some additional corrections from the scalar field.
