论文标题
标量调整的重力理论中的流体奖励对应：（in）爱因斯坦和约旦框架的等效性
Fluid-gravity correspondence in the scalar-tensor theory of gravity: (in)equivalence of Einstein and Jordan frames
论文作者
论文摘要
重力张量（ST）的重力理论研究了引力动力学的双重性（预测在无效的超表面上）和流体动力学。在爱因斯坦和约旦框架中，对ST重力的描述是从流体重力观点分析的。在爱因斯坦框架中，公制的动态方程式导致带有外部强迫项的Damour-navier-Stokes（DNS）方程，来自ST重力的标量场。在约旦框架中，情况更加微妙。我们观察到，在此框架中找到DNS方程可能会导致两张图片。在一张图片中，通常的DNS方程是通过类似Coriolis的力项来修改的，该方程完全源自重力侧非最小耦合标量场（$ ϕ $）。此外，确定的流体变量不再与爱因斯坦框架中的液体等效。但是，这张照片与Kovtun-Son-Starinets（KSS）结合的饱和度是一致的。在另一幅图片中，我们发现标准的DNS方程（即没有科里奥利的力），流体变量与爱因斯坦框架中的流体变量同等。但是，第二张图片可能不同意$ ϕ $的某些值的KSS。我们通过根据相关参数重写Raychaudhuri方程和潮汐力方程来结束，以证明时空中的扩展标量和剪切量如何发展。虽然，熵的区域定律在重力中被打破，但我们表明，雷查里（Raychaudhuri）方程的重写形式正确地导致了黑洞热力学的全身第二定律。
The duality of gravitational dynamics (projected on a null hypersurface) and of fluid dynamics is investigated for the scalar tensor (ST) theory of gravity. The description of ST gravity, in both Einstein and Jordan frames, is analyzed from fluid-gravity viewpoint. In the Einstein frame the dynamical equation for the metric leads to the Damour-Navier-Stokes (DNS) equation with an external forcing term, coming from the scalar field in ST gravity. In the Jordan frame the situation is more subtle. We observe that finding the DNS equation in this frame can lead to two pictures. In one picture, the usual DNS equation is modified by a Coriolis-like force term, which originates completely from the presence of a non-minimally coupled scalar field ($ϕ$) on the gravity side. Moreover, the identified fluid variables are no longer conformally equivalent with those in the Einstein frame. However, this picture is consistent with the saturation of Kovtun-Son-Starinets (KSS) bound. In the other picture, we find the standard DNS equation (i.e. without the Coriolis-like force), with the fluid variables conformally equivalent with those in Einstein frame. But, the second picture, may not agree with the KSS bound for some values of $ϕ$. We conclude by rewriting the Raychaudhuri equation and the tidal force equation in terms of the relevant parameters to demonstrate how the expansion scalar and the shear-tensor evolve in the spacetime. Although, the area law of entropy is broken in ST gravity, we show that the rewritten form of Raychaudhuri's equation correctly results in the generalized second law of black hole thermodynamics.
