时空各向异性与 finsler 几何
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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:[email protected]. 一 .Finsler 几何. Shiing-Shen Chern: Finsler geometry is just Riemannian geometry without the quadratic restriction 计算太复杂了 ! ( 线元的形式为四次根式 ). - PowerPoint PPT PresentationTRANSCRIPT
时空各向异性与时空各向异性与 FinslerFinsler 几何几何
李昕 李昕 中国科学院高能物理研究所中国科学院高能物理研究所E-mail:[email protected]:[email protected]
一一 .Finsler.Finsler 几何几何
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 !!
(( 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 FF with the following property with the following property F(x,F(x,λλy)=y)=λλF(x,y),F(x,y), where where xxMM represents the represents the position and position and yyT_xMT_xM represent velocity, represent velocity, MM is an n- is an n-dimensional manifold. The Finslerian metric is dimensional manifold. The Finslerian metric is given asgiven as
• The length in Finsler geometry is given asThe length in Finsler geometry is given as
• Geodesic equationGeodesic equation
• The inner product of two The inner product of two parallel transported vectors is preservedparallel transported vectors is preserved
• if if F F is Riemannian metric, thenis Riemannian metric, then
• Flag curvature (generation of section curvature )Flag curvature (generation of section curvature )
2)]^,([),(),(:),(
VygVVgyyg
VRVVyK
Examples of Finsler spacetimeExamples of Finsler spacetime
• ““平坦平坦”” FinslerFinsler 时空 时空 F=F(y)F=F(y)
• RandersRanders 时空时空
• BimetricBimetric4
yyhyygF
• Killing equation Killing equation
• ““平坦平坦”” FinslerFinsler 时空中最大独立时空中最大独立 KillingKilling矢量个数矢量个数
N(N-1)/2+1N(N-1)/2+1
FinslerFinsler 引力引力
• 测地线偏离方程:测地线偏离方程:• NewtonNewton 引力引力泊松方程泊松方程
• 广义相对论广义相对论真空场方程真空场方程
• Finsler Finsler 时空时空
• 真空场方程真空场方程 ??
真空场方程的弱场近似解真空场方程的弱场近似解
• We suppose the metric is close to the “flat” metric
• The solution of the gravitational vacuum field equation is of the form
• FinslerFinsler 引力波引力波
• 如果如果 \eta_{\mu\nu}\eta_{\mu\nu} 是是 RandersRanders 度规,度规,则则
引力波的超光速传播引力波的超光速传播
牛顿近似牛顿近似
• 静态场、低速静态场、低速
•R = 0 处有一引力源 M
• Dynamical equationDynamical equation
• 取取
• MONDMOND
FinslerFinsler 物理的过去物理的过去
• Dark matterDark matter
• Neutrino mass and GlashowNeutrino mass and Glashow’’s VSRs VSR
• Pioneer anomalyPioneer anomaly
• GZK cutoffGZK cutoff
Now: Now: 观测与实验观测与实验
1.1. KeckKeck 与与 VLTVLT 望远镜通过类星体吸收谱发现望远镜通过类星体吸收谱发现精细结构常数的偶极结构精细结构常数的偶极结构
2.2. OPERAOPERA 实验组发现实验组发现 muonmuon 中微子超光速中微子超光速 ??
3.3. 子弹星系团的引力中心与物质中心分离子弹星系团的引力中心与物质中心分离
1.1. 精细结构常数的偶极结构精细结构常数的偶极结构
•在在 Randers Randers 时空下时空下
引力红移引力红移
A~10^-7, B~10^-8A~10^-7, B~10^-8
2.OPERA2.OPERA
T. Adam et al. [OPERA Collaboration], arXiv: 1109.4897.T. Adam et al. [OPERA Collaboration], arXiv: 1109.4897.
• MuonMuon 中微子的速度中微子的速度
• 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: 1109.6562
• BremsstrahlungBremsstrahlung
• Solution: Finsler spacetime?Solution: Finsler spacetime?
• FinslerFinsler 线元线元
• 色散关系色散关系
• 粒子运动速度粒子运动速度
A~10^-18A~10^-18
3.3. 子弹星系团的引力中心与物质中心分子弹星系团的引力中心与物质中心分离离
观测手段观测手段• X-ray imaging of the hot intracluster X-ray imaging of the hot intracluster
medium (ICM)medium (ICM)
• Strong and weak gravitational Strong and weak gravitational lensing surveyslensing surveys
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 Σ-Map
子弹星系团的 κ-Map
Prefer direction?
FinslerFinsler 物理的未来 物理的未来
• Finslerian effects in QEDFinslerian effects in QED
• Finslerian black hole: solutions and Finslerian black hole: solutions and thermodynamics thermodynamics
• Anisotropy in large scale spacetime Anisotropy in large scale spacetime
• Some applicationsSome applications
Thank You !Thank You !