All Questions
Tagged with adm-formalism curvature
6
questions
0
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Extrinsic Curvature in a conformally-flat spacetime that is also asymptotically-flat spacetime
I would appreciate if someone can confirm or correct my understanding of extrinsic-curvature (as in the ADM 3+1 decomposition of spacetime) when dealing with a conformally-flat spacetime.
(I updated ...
- 21
2
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answers
35
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Partial integration of the Gibbons-Hawking-York boundary term
In https://arxiv.org/abs/1402.6334 on page 16 in their Eq. (5.21), they go from the equation
$$S_G+S_\chi\approx\int d^2x\sqrt{-g}XR+\int dt\sqrt{-\gamma}XK$$
to the equation
$$=\int d^2x \sqrt{-g}\...
- 109
3
votes
2
answers
504
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Is the mass of curved space, additional mass?
According to Einstein, mass, say in the form of matter, curves space. It is the curvature of space that gives rise to gravity. Now I have heard there is an energy associated with the curvature of ...
- 131
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Extrinsic curvature, Gauss equation and Christoffel symbol contribution
This question is in the context of geometry of hypersurfaces and ADM formalism. In a $4$-dimensional manifold, we define a $3$-hypersurface with space-like tangent basis $e_a$, $a=1,2,3$, and a normal ...
- 175
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1
answer
391
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Extrinsic Curvature expression (ADM Formalism)
I'm reading The ADM Formalism chapter of Baez's book Gauge Fields, Knots and Gravity and on page 429 we have the expression
$$ K_{ij}=\frac{1}{2}N^{-1}(\dot{q}_{ij}- {}^3\nabla_i N_j - {}^3\nabla_j ...
- 403
1
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0
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How to compute the scalar $^{(4)}R_{\mu\nu} \; ^{(4)}R^{\mu\nu}$ in the ADM formalism in General Relativity?
In the Arnowitt-Deser-Misner (ADM) formalism in General Relativity, the line element takes the form
$$
ds^2 = - N^2 dt^2 + \gamma_{ij} ( N^i dt + dx^i) (N^j dt + dx^j) \ ,
$$
where $\gamma^{ij}$ is ...
- 3,719