时空各向异性与Finsler几何李昕 中国科学院高能物理研究所E-mail:lixinihep.ac.cn一.Finsler几何Shiing-Shen Chern: Finsler Shiing-Shen Chern: Finsler geometry is just Riemannian geometry is just Riemannian geometry without the geometry without the quadratic restrictionquadratic restriction 计算太复杂了计算太复杂了计算太复杂了计算太复杂了! ! ( (线元的形式为四次根式线元的形式为四次根式线元的形式为四次根式线元的形式为四次根式) )Finsler geometry is base on the so called Finsler Finsler geometry is base on the so called Finsler structure structure F F with the following property with the following property F(x,F(x, y)=y)= F(x,y),F(x,y), where where x x MM represents the position and represents the position and y y T_xMT_xM represent velocity, represent velocity, MM is an n-dimensional manifold. The is an n-dimensional manifold. The Finslerian metric is given asFinslerian metric is given asThe length in Finsler geometry is given asThe length in Finsler geometry is given asGeodesic equationGeodesic equationThe inner product of two The inner product of two parallel transported vectors is preservedparallel transported vectors is preservedif if F F is Riemannian metric, thenis Riemannian metric, thenFlag curvature (generation of section curvature )Flag curvature (generation of section curvature )Examples of Finsler spacetime“ “平坦平坦” ”FinslerFinsler时空时空 F=F(y)F=F(y)RandersRanders时空时空BimetricBimetricKilling equation “平坦”Finsler时空中最大独立Killing矢量个数N(N-1)/2+1Finsler引力测地线偏离方程：Newton引力泊松方程广义相对论真空场方程Finsler 时空真空场方程 ？真空场方程的弱场近似解We suppose the metric is close to the “flat” metricThe solution of the gravitational vacuum field equation is of the formFinslerFinsler引力波引力波如果eta_munu是Randers度规，则引力波的超光速传播牛顿近似静态场、低速R = 0处有一引力源MDynamical equation取MONDFinsler物理的过去Dark matterNeutrino mass and Glashows VSRPioneer anomalyGZK cutoffNow: 观测与实验1.Keck与VLT望远镜通过类星体吸收谱发现精细结构常数的偶极结构2.OPERA实验组发现muon中微子超光速?3.子弹星系团的引力中心与物质中心分离1.精细结构常数的偶极结构在Randers 时空下引力红移 A10-7, B10-8 A10-7, B10-82.OPERAT. Adam et al. OPERA Collaboration, arXiv: 1109.4897.T. Adam et al. OPERA Collaboration, arXiv: 1109.4897.Muon中微子的速度OPERA(red), MINOS(blue), FERMILAB(black)OPERA(red), MINOS(blue), FERMILAB(black)A. Cohen and S. Glashow, arXiv: 1109.6562A. Cohen and S. Glashow, arXiv: 1109.6562BremsstrahlungSolution: Finsler spacetime?Finsler线元色散关系粒子运动速度A10-183.子弹星系团的引力中心与物质中心分离观测手段X-ray imaging of the hot intracluster medium (ICM)Strong and weak gravitational lensing surveys子弹星系团暗物质（Dark Matter） ？修改引力 （Modified Gravity）？或空间曲率分布（蓝色）ICM气体表面密度分布（红色）子弹星系团的-Map子弹星系团的-MapPrefer direction?Finsler物理的未来 Finslerian effects in QEDFinslerian black hole: solutions and thermodynamics Anisotropy in large scale spacetime Some applicationsThank You !