Study On Gravity/Fluid Duality With Petrov-like Condition

Recently great progress has been made in disclosing the holographic nature ofgravity. One important direction of the holographic gravity is the study ofgravity/fluid duality, which has also been becoming a hot topic in the frontier of thecurrent international research.It has been shown that imposing Petrov-like boundary condition on ahypersurface may reduce the Einstein equation of gravity to the incompressibleNavier-Stokes equation of fluid in one lower dimensional spacetime in thenear-horizon limit. However, the method of imposing Petrov-like boundary conditionpreviously contains an obvious weak point. That is, the gravity/fluid duality can beestablished only in the near-horizon limit.In this thesis, we will employ the new method of the long-wavelength limitinstead of the near-horizon limit under the Petrov-like framework, and construct agravity/fluid duality at an arbitrary finite cutoff surface. In particular, we constructthree explicit models. Firstly, we derived the Navier-Stokes equation from theEinstein equation in Rindler spacetime by imposing the Petrov-like boundarycondition on an arbitrary finite cutoff surface and employing the long-wavelengthlimit. Secondly, we applied the same method to a black brane spacetime which has acosmological constant, and the Navier-Stokes equation of fluid with acutoff-dependent viscosity can be derived. Lastly, a4-dimensional magnetic blackbrane spacetime which has matter fields is considered, and the gravity/fluid dualitycan be established as well.