Question

Prove that $\Gamma_{abc}=\frac{1}{2}\left(\partial_bg_{ac} + \partial_cg_{ab}-\partial_ag_{bc}\right)$

score 294 · Answer 1 · 2026-03-28 06:40:46

294

Views

Prove that $\Gamma_{abc}=\frac{1}{2}\left(\partial_bg_{ac} + \partial_cg_{ab}-\partial_ag_{bc}\right)$

Published on 28 Mar 2026 - 6:40

score 45 · Answer 2 · 2022-06-20 09:23:35

45

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Variation of Pontryagin density $*R^{abcd}R_{abcd}$ with respect to inverse metric $g^{ab}$

Published on 20 Jun 2022 - 9:23

score 276 · Answer 3 · 2022-06-22 19:06:42

276

Views

Two ways of defining connection coefficients

Published on 22 Jun 2022 - 19:06

score 36 · Answer 4 · 2026-02-23 13:01:54

36

Views

World line and light cones in two dimensions

Published on 23 Feb 2026 - 13:01

score 96 · Answer 5 · 2022-06-29 01:06:15

96

Views

Why are the red parts of this expression present $\int_a^b \sqrt{g_{cd}\frac{dx^c}{\color{red}{d\lambda}}\frac{dx^d}{\color{red}{d\lambda}}}d\lambda$?

Published on 29 Jun 2022 - 1:06

score 326 · Answer 6 · 2022-06-30 07:49:01

326

Views

Using $g^{ab}\nabla_a\nabla_b\phi$ show that $\nabla^2 \phi=\left(\partial_r^2+\frac1r\partial_r+\frac{1}{r^2}\partial_\theta^2\right)\phi$

Published on 30 Jun 2022 - 7:49

score 74 · Answer 7 · 2022-07-01 16:28:47

74

Views

Does every globally hyperbolic spacetime admit a maximal slicing?

Published on 01 Jul 2022 - 16:28

score 191 · Answer 8 · 2022-07-04 21:13:54

191

Views

Why is $R_{\rho \mu} = \eta^{\sigma \nu} R_{\rho \sigma \mu \nu}$?

Published on 04 Jul 2022 - 21:13

score 67 · Answer 9 · 2026-03-26 17:51:52

67

Views

Einstein field equation from covariant derivative

Published on 26 Mar 2026 - 17:51

score 45 · Answer 10 · 2026-03-26 09:40:27

45

Views

Is there a general linear group version of general relativity (not diffeomorphism)?

Published on 26 Mar 2026 - 9:40

score 460 · Answer 11 · 2022-07-10 18:21:05

460

Views

The Rindler metric - show that a quantity is constant along geodesics using coordinate independence.

Published on 10 Jul 2022 - 18:21

score 582 · Answer 12 · 2022-07-17 17:32:36

582

Views

The killing vectors of flat space in polar coordinates

Published on 17 Jul 2022 - 17:32

score 841 · Answer 13 · 2022-08-02 16:54:13

841

Views

Showing metric is coordinate independent implies Killing vector field.

Published on 02 Aug 2022 - 16:54

score 85 · Answer 14 · 2022-08-04 17:53:39

85

Views

Can the equivalence of the covariant and contravariant "connection coefficients" be proved simply by using the flatness of the tangent plane?

Published on 04 Aug 2022 - 17:53

score 71 · Answer 15 · 2026-03-27 07:35:34

71

Views

If $\mathcal{M}$ is a manifold, what is meant by "the standard pairing on $\mathcal{M}^2$"?

Published on 27 Mar 2026 - 7:35

List Question

Prove that $\Gamma_{abc}=\frac{1}{2}\left(\partial_bg_{ac} + \partial_cg_{ab}-\partial_ag_{bc}\right)$

Variation of Pontryagin density $*R^{abcd}R_{abcd}$ with respect to inverse metric $g^{ab}$

Two ways of defining connection coefficients

World line and light cones in two dimensions

Why are the red parts of this expression present $\int_a^b \sqrt{g_{cd}\frac{dx^c}{\color{red}{d\lambda}}\frac{dx^d}{\color{red}{d\lambda}}}d\lambda$?

Using $g^{ab}\nabla_a\nabla_b\phi$ show that $\nabla^2 \phi=\left(\partial_r^2+\frac1r\partial_r+\frac{1}{r^2}\partial_\theta^2\right)\phi$

Does every globally hyperbolic spacetime admit a maximal slicing?

Why is $R_{\rho \mu} = \eta^{\sigma \nu} R_{\rho \sigma \mu \nu}$?

Einstein field equation from covariant derivative

Is there a general linear group version of general relativity (not diffeomorphism)?

The Rindler metric - show that a quantity is constant along geodesics using coordinate independence.

The killing vectors of flat space in polar coordinates

Showing metric is coordinate independent implies Killing vector field.

Can the equivalence of the covariant and contravariant "connection coefficients" be proved simply by using the flatness of the tangent plane?

If $\mathcal{M}$ is a manifold, what is meant by "the standard pairing on $\mathcal{M}^2$"?

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