General Relativity
Tags: #physics #relativityEquation
$$\frac{\mathrm{d}^{2} x^{\alpha}}{\mathrm{d} s^{2}}+\Gamma^{\alpha}_{\beta\gamma}\frac{\mathrm{d} x^{\beta}}{\mathrm{d} s}\frac{\mathrm{d} x^{\gamma}}{\mathrm{d} s}=0$$Latex Code
\frac{\mathrm{d}^{2} x^{\alpha}}{\mathrm{d} s^{2}}+\Gamma^{\alpha}_{\beta\gamma}\frac{\mathrm{d} x^{\beta}}{\mathrm{d} s}\frac{\mathrm{d} x^{\gamma}}{\mathrm{d} s}=0
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Introduction
Latex code for the principles of general relativity. I will briefly introduce the notations in this formulation.
- The geodesic postulate: free falling particles move along geodesics of space-time with the proper time
or arc length
as parameter. For particles with zero rest mass (photons), the use of a free parameter is required because for them holds
. From
the equations of motion can be derived as :
- The principle of equivalence: inertial mass ? gravitational mass->gravitation is equivalent with a curved space-time were particles move along geodesics.
- By a proper choice of the coordinate system it is possible to make the metric locally flat in each point
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