Derivative expansion and large-D expansion are two perturbation techniques, which are used to generate dynamical black-brane solutions to Einstein’s equations in presence of negative cosmological constant. In this paper we have compared these two techniques and established the equivalence of the gravity solutions generated by these two different techniques in appropriate regime of parameter space up to first non-trivial order in both the perturbation parameters for Einstein–Maxwell systems, generalizing the earlier works of [1, 2] for non-charged systems. An one-to-one map between dynamical black-brane geometry and AdS space, which also exists at finite number of dimensions, has also been established.

导数展开和大D展开是两种微扰技术，用于在存在负宇宙常数的情况下生成爱因斯坦方程的动力学黑膜解。在本文中，我们比较了这两种技术，并在爱因斯坦-麦克斯韦系统的两个扰动参数中建立了这两种不同技术在适当的参数空间范围内产生的重力解的等价性，概括了早期的[1, 2] 对非带电系统的工作。还建立了动态​​黑膜几何和 AdS 空间之间的一对一映射，该映射也存在于有限维数中。