报告题目：The mathematical validity for the f(R) theory of nonlinear gravity
报告摘要：We study a nonlinear gravity theory, specifically the so-called f(R)-theory, which is a "higher-order" version of Einstein’s gravity theory and is based on a nonlinear function f =f(R) of the scalar curvature of the space-time. First of all, we formulate the initial value problem and, in particular, introduce a notion of ‘initial data set for nonlinear gravity’. For definiteness, the matter is described by a scalar field. Our main contribution is the derivation of an ‘augmented conformal formulation’ (as we call it) which, in wave coordinates, leads us to a coupled system of wave equations and Klein-Gordon equations. The main unknowns of this system are, both, the conformally-transformed metric and scalar curvature of the space-time. Based on this novel formulation of nonlinear gravity, we establish here the existence of a maximal hyperbolic Cauchy development associated with any given initial data set, and we provide a rigorous justification that space-times of nonlinear gravity are ‘close’ to Einstein space-times when the defining function f = f(R) is ‘close’ to the scalar curvature function R.
报告人简介：马跃，2014年博士毕业于法国巴黎六大。毕业后在西安交通大学任职，主要研究数学中的相对论的研究，在Comm. Math. Phys等著名期刊发表学术论文。