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学术报告:The mathematical validity for the f(R) theory of nonlinear gravity

发布时间:2017年04月10日 浏览次数:发布者:mathky

报告人:马跃副教授,

西安交通大学

报告题目:The mathematical validity for the f(R) theory of nonlinear gravity

报告时间:2017年04月24日15:00

报告地点:海韵实验楼108

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。

联系人:闫卫平副教授

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