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Results tagged with general-relativity
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user 136463
A theory that describes how matter interacts dynamically with the geometry of space and time. It was first published by Einstein in 1915 and is currently used to study the structure and evolution of the universe, as well as having practical applications like GPS.
2
votes
Falling toward a black hole
This is a simplified answer that makes one approximation (distant initial point) to get nicer formulas and clarify the big picture of the calculation. To see the precise final formulas (without approx …
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1
vote
Divergence of the stress-energy tensor
Notice that Leibniz's rule $\mathcal{L}_X(L\eta)=(\mathcal{L}_XL)\eta +L(\mathcal{L}_X\eta)$ holds for the Lie derivative. The Lie derivative of the lagrangian is
\begin{equation}
\mathcal{L}_XL=\fr …
- 4,733
0
votes
In spacetime, how do we interpret the "4th dimension"?
The trajectory-dependent time, the one that an observer followong a given trajecrory measures, is called the proper time. The time coordinate of $\mathbb{R}^4$ is not an absolute time, but just the pr …
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3
votes
Why doesn't renormalization with a Planck-scale cutoff work for quantum gravity?
Gravity is in fact an effective quantum field theory with the energy cut-off being the Planck scale $M_{Pl}$. The Einstein-Hilbert action is just the lowest order in an expansion in inverse powers of …
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4
votes
Rigorous definition of the variation
A definition can be given by direct generalization of the one on the question. Take the space of fields to be the space $C^\infty(X, M)$ of smooth functions between two manifolds. For any smooth funct …
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