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

\[R_{\mu \nu} - {1 \over 2}g_{\mu \nu}\,R + g_{\mu \nu} \Lambda = {8 \pi G \over c^4} T_{\mu \nu}\]

related items

• 틀:수학노트

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

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
• http://en.wikipedia.org/wiki/Four-vector

books

• http://gigapedia.com/items/45025/relativity-demystified---a-self-teaching-guide--2005-12

expositions

• Ashtekar, Abhay, Beverly K. Berger, James Isenberg, and Malcolm A. H. MacCallum. “General Relativity and Gravitation: A Centennial Perspective.” arXiv:1409.5823 [astro-Ph, Physics:gr-Qc, Physics:hep-Th, Physics:math-Ph], September 19, 2014. http://arxiv.org/abs/1409.5823.
• General relativity:a very weird world

articles

• On the electrodynamics of moving bodies
  • A. Einstein, 1905

blogs and webpage

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