153
edits
Einstein's General Relativity equation: Difference between revisions
no edit summary
(Created page with ": $$R_{\mu v}-\frac{1}{2}Rg_{\mu v} = 8 \pi T_{\mu v}$$ == Resources: == *[https://en.wikipedia.org/wiki/General_relativity#Einstein's_equations Einstein's equations] == Di...") Â |
No edit summary |
||
| Line 1: | Line 1: | ||
'''Albert Einstein''' (b. 1879) | |||
'''''General relativity''''' 1915 | |||
Using the equivalence principle, this tensor is readily generalized to curved spacetime. Drawing further upon the analogy with geometric Newtonian gravity, it is natural to assume that the field equation for gravity relates this tensor and the Ricci tensor, which describes a particular class of tidal effects: the change in volume for a small cloud of test particles that are initially at rest, and then fall freely. In special relativity, conservation of energyâmomentum corresponds to the statement that the energyâmomentum tensor is divergence-free. This formula, too, is readily generalized to curved spacetime by replacing partial derivatives with their curved-manifold counterparts, covariant derivatives studied in differential geometry. With this additional conditionâthe covariant divergence of the energyâmomentum tensor, and hence of whatever is on the other side of the equation, is zeroâ the simplest set of equations are what are called Einstein's (field) equations: | |||
: $$R_{\mu v}-\frac{1}{2}Rg_{\mu v} = 8 \pi T_{\mu v}$$ | : $$R_{\mu v}-\frac{1}{2}Rg_{\mu v} = 8 \pi T_{\mu v}$$ | ||