Special relativity

four-vector 

• can be transformed by Lorentz transformation
• examples
  
  • space-time (ct,x,y,z)
  • four momentum (m,mv_1,mv_2,mv_3)
  • electromagnetic field

 

 

review of Maxwell's equation

• Electromagnetism
  

 

 

Lorentz transformation and Maxwell's equation

• http://en.wikipedia.org/wiki/Lorentz_transformation
  
• one-dimensional example
  \(E_{tt}-E_{zz}=0\)
  

 

 

 

Vacuum field equation and gravitational field equation

• gravitational potentail satisfies the following equation (Poisson's equation)
  \(\nabla^2 \phi = - 4 \pi G \rho\)
  
• \(\rho\) is the matter density
  
• in relativity theory, the metric plays the role of gravitational potential
  

 

 

energy-momentum tensor

• also called as stress-energy tensor
  
• describe the densities and flows of energy and momentum
  
• all forms of mass-energy can be sources of gravitational fields
  
• the stress-energy tensor \(T_{\mu \nu}\) acts as a source of the gravitational field
  

 

 

 

 

 

 

relativistic matter field equation

• Einstein field equation
  \(R_{\mu \nu} - {1 \over 2}g_{\mu \nu}\,R + g_{\mu \nu} \Lambda = {8 \pi G \over c^4} T_{\mu \nu}\)
  

 

 

history

• http://www.google.com/search?hl=en&tbs=tl:1&q=

 

 

 

하위페이지

• special and general relativity
  
  • cosmological constant
    
  • Einstein field equation
    
  • energy-momentum tensor
    
  • Hamiltonian formulation of GR
    
  • light cone coordinates and gauge
    
  • relativistic point particle
    

 

 

 

 

related items

• 미분기하학
  

 

 

encyclopedia

• http://en.wikipedia.org/wiki/Newton's_law_of_universal_gravitation
  
• http://en.wikipedia.org/wiki/Einstein_field_equations
  
• http://en.wikipedia.org/wiki/Solutions_of_the_Einstein_field_equations
  
•  
  http://en.wikipedia.org/wiki/Lorentz_covariant
  
• [1]http://en.wikipedia.org/wiki/Four-vector
  
• http://en.wikipedia.org/wiki/
• http://www.scholarpedia.org/

 

 

books

• http://gigapedia.com/items/45025/relativity-demystified---a-self-teaching-guide--2005-12
  
• 2010년 books and articles
  
• http://gigapedia.info/1/relativity
• http://gigapedia.info/1/
• http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=

 

 

articles

• On the electrodynamics of moving bodies
  
  • A. Einstein, 1905
• http://www.ams.org/mathscinet
• http://www.zentralblatt-math.org/zmath/en/
• http://pythagoras0.springnote.com/
• http://math.berkeley.edu/~reb/papers/index.html[2]
• http://front.math.ucdavis.edu/search?a=&t=&c=&n=40&s=Listings&q=
• http://www.ams.org/mathscinet/search/publications.html?pg4=AUCN&s4=&co4=AND&pg5=TI&s5=&co5=AND&pg6=PC&s6=&co6=AND&pg7=ALLF&co7=AND&Submit=Search&dr=all&yrop=eq&arg3=&yearRangeFirst=&yearRangeSecond=&pg8=ET&s8=All&s7=
• http://dx.doi.org/

 

 

question and answers(Math Overflow)

• http://mathoverflow.net/search?q=
• http://mathoverflow.net/search?q=

 

 

blogs and webpage

• Introduction to Differential Geometry and General Relativity
  
  • Lecture Notes by Stefan Waner
    

• 구글 블로그 검색
  
  • http://blogsearch.google.com/blogsearch?q=
  • http://blogsearch.google.com/blogsearch?q=

 

 

links

• Detexify2 - LaTeX symbol classifier
• 수식표현 안내
• The On-Line Encyclopedia of Integer Sequences
• http://functions.wolfram.com/