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2012년 10월 28일 (일) 15:01 판
==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
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 Vacuum field equation
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
하위페이지
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/
- Princeton companion to mathematics(Companion_to_Mathematics.pdf)
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)
blogs and webpage
- Introduction to Differential Geometry and General Relativity
- Lecture Notes by Stefan Waner
- Lecture Notes by Stefan Waner