本学位论文主要分为三个部分。首先，我们简单地介绍了一类无鬼场的高阶导数引 力的构造以及性质，包括Lovelock 引力、准拓扑引力以及推广的准拓扑引力。它们共同 的特征是，在最大对称背景下的线性运动方程和线性爱因斯坦方程只差一个整体因子， 因此引力传播子的结构和爱因斯坦引力一样，也就避免了一般高阶导数引力存在的鬼场 问题。接下来我们分别从全息剪切粘滞系数、全息蝴蝶效应以及全息热电导率三个方面 研究了五维准拓扑引力的在AdS/CFT 对偶方面的应用。最后，我们采用Pade 近似的方 法，构造了Einsteinian cubic gravity (ECG) 引力的解析近似黑洞解。这些解无论对于理解 ECG 引力的经典性质，还是在全息对偶方面的应用都有着重要的理论意义。

This thesis consists of three parts. First, we briefly introduce the constructions and the properties of ghost-free higher derivative gravities, such as Lovelock gravity, quasi-topological gravity, generalized quasi-topological gravity. The common feature of these gravities is that on maximally symmetric backgrounds the linearized equations of the motion coincide with the linearized Einstein equations up to an overall factor. Since the structure of the graviton propagator is the same as that in Einstein gravity , it avoids the ghost problem for general higher derivative gravities. This paper is organized as follow. First, we studied the holographic application of the five dimensional quasi-topological gravity with respects to shear viscosity, butterfly effect, thermoelectric DC conductivity. Second, using the method of Pade approximation, we construct the analytic approximate black hole solution of Einsteinian cubic gravity (ECG). These solutions are very important for understanding the classical properties of ECG as well as holographic application.