- #1

- 26

- 0

[itex]ds^2 = -dt^2 + dx^2 + dy^2 + dt^2[/itex]? Thanks.

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter Mazulu
- Start date

- #1

- 26

- 0

[itex]ds^2 = -dt^2 + dx^2 + dy^2 + dt^2[/itex]? Thanks.

- #2

Matterwave

Science Advisor

Gold Member

- 3,966

- 327

...

- #3

HallsofIvy

Science Advisor

Homework Helper

- 41,847

- 969

- #4

- 26

- 0

It's a differential equation. Shouldn't there be an equation of the form [itex]s(t,x,y,z)[/itex] that when differentiated, will satisfy the equation. I actually wanted to solve some more difficult metrics, but I started with something easy (flat space-time). I was hoping that a solution of the form [itex]e^{i(kx+ky+kz-\omega t)}[/itex]} might pop out of it; or something that looks like light or a Poynting vector.

By the way, thank you for the heads up that a metric is used to find the curvature tensor of a geodesic. I just thought that Maxwell's equations should pop out of it as well.

- #5

Matterwave

Science Advisor

Gold Member

- 3,966

- 327

[tex]S=\sqrt{(t-t_0)^2-(x-x_0)^2-(y-y_0)^2-(z-z_0)^2}[/tex]

That's just the non-differential form of the equation. In general, doing something like this is not possible for general metric, but because of the niceness of the Minkowski metric, you can do this.

- #6

- 26

- 0

[tex]S=\sqrt{(t-t_0)^2-(x-x_0)^2-(y-y_0)^2-(z-z_0)^2}[/tex]

That's just the non-differential form of the equation. In general, doing something like this is not possible for general metric, but because of the niceness of the Minkowski metric, you can do this.

I don't think the Minkowski metric is what I'm looking for. The AdS/CFT correspondence model contains both gravity and quantum mechanics. I think I need to look there. It would be amazing if I actually found what I'm looking for. There should be a solution that looks like a Fourier series with arguments [itex](\vec{k}\vec{r}-\omega_i t)[/itex], where [itex]\vec{r}[/itex] is along the radii of a black hole and ω

Share: