The twopoint function and the entanglement entropy can be seen as quantities to describe properties of the quarkgluon plasma. For this an anisotropicc 5dimensional system is considered. A homogeneous anisotropic but O (2) symmetric solution to the 5dimensional vacuum Einstein equations is equivalent to a homogeneous and isotropic solution to the Einstein equations including a scalar field. The corresponding 5dimensional EinsteinHilbert action without scalar field can be dimensionally reduced to a 2dimensional dilaton gravity action with two scalar fields. The same 2dimensional dilaton gravity action arises from reducing isotropic Ein stein gravity with a minimally coupled massless scalar field. Therefore, the 2dimensional dilaton gravity is equivalent to the 5dimensional anisotropic system with matter and the 5dimensional isotropic system with a scalar field. In this thesis the twopoint function of operators of large conformal weight and the holographic entanglement entropy for a spherical region in a 2dimensional dilaton gravity theory are calculated numerically using the Antide Sitter/conformal field theory correspondence. The twopoint function, which is computed in the geodesic approximation, amounts to a geodesics length in the gravity theory. Similarly the calculation of the entanglement entropy reduces to finding geodesics in an auxiliary spacetime. To obtain the geometry the Einstein equations need to be solved numerically. The Einstein equations of the 2dimensional dilaton gravity theory are mapped to the vacuum Einstein equations for an anisotropic geometry. The numerical calculation of geodesics is performed using a Mathematica package, which calculates the geodesics with a relaxation method. The results for the entanglement entropy and twopoint function vary strongly, depending on the chosen boundary region.
