Spacetime vibration and gravitational wave

[alpha2cen]

We know gravitational wave well.

Mass makes gravity. And, at the view of relativity theory, the gravity is a spacetime deformation phenomena.

And, we have not found the wave yet.

Does spacetime vibration make gavitational wave?

[elfmotat]

Using the linearized field equations in a vacuum, we can get:

 

$\left ( \nabla^2-\frac{\partial^2}{\partial t^2} \right )\bar{h}^{\mu \nu}=0$

 

where $\bar{h}^{\mu \nu}=h^{\mu \nu}-\frac{1}{2} \eta^{\mu \nu } h^\sigma_{~\sigma}$, and $g_{\mu \nu }=\eta_{\mu \nu}+h_{\mu \nu}$. This is just the wave equation for $\bar{h}^{\mu \nu}$. So we see that at first order, gravitational waves are just sinusoidal perturbations of the metric which propagate at c.

 

 

Also note that gravitational waves are generated by quadrupoles. A rotating symmetric sphere will not generate gravitational waves, for example.

Edited January 7, 2013 by elfmotat

[imatfaal]

  On 1/7/2013 at 6:28 PM, elfmotat said:

Using the linearized field equations in a vacuum, we can get:

 

$\left ( \nabla^2-\frac{\partial^2}{\partial t^2} \right )\bar{h}^{\mu \nu}=0$

 

where $\bar{h}^{\mu \nu}=h^{\mu \nu}-\frac{1}{2} \eta^{\mu \nu } h^\sigma_{~\sigma}$, and $g_{\mu \nu }=\eta_{\mu \nu}+h_{\mu \nu}$. This is just the wave equation for $\bar{h}^{\mu \nu}$. So we see that at first order, gravitational waves are just sinusoidal perturbations of the metric which propagate at c.

 

 

Also note that gravitational waves are generated by quadrupoles. A rotating symmetric sphere will not generate gravitational waves, for example.

 

Elfmotat - am I correct in thinking that the earth - as an oblate spheroid - would if spinning perfectly on axis not generate grav waves, but that any variation wobble etc would generate waves. ie it is the change in the moving object, rather than the moving object itself

[elfmotat]

  On 1/8/2013 at 3:07 PM, imatfaal said:

 

Elfmotat - am I correct in thinking that the earth - as an oblate spheroid - would if spinning perfectly on axis not generate grav waves, but that any variation wobble etc would generate waves. ie it is the change in the moving object, rather than the moving object itself

 

That sounds about right to me.

[ACG52]

_{Gravity Probe B has confirmed that frame dragging is real. Would that generate grav waves?}

Edited January 9, 2013 by ACG52

[elfmotat]

  On 1/9/2013 at 3:28 AM, ACG52 said:

_{Gravity Probe B has confirmed that frame dragging is real. Would that generate grav waves?}

 

Frame dragging is separate from gravitational radiation. A spherically symmetric rotating body will produce frame dragging effects, but will not radiate.

[ACG52]

  On 1/9/2013 at 3:39 AM, elfmotat said:

 

Frame dragging is separate from gravitational radiation. A spherically symmetric rotating body will produce frame dragging effects, but will not radiate.

 

So frame dragging doesn't result in the loss of energy from the rotating system?

[elfmotat]

  On 1/9/2013 at 3:48 AM, ACG52 said:

 

So frame dragging doesn't result in the loss of energy from the rotating system?

 

Not by itself, no.

[SamBridge]

  On 1/7/2013 at 6:28 PM, elfmotat said:

Using the linearized field equations in a vacuum, we can get:

 

$\left ( \nabla^2-\frac{\partial^2}{\partial t^2} \right )\bar{h}^{\mu \nu}=0$

 

where $\bar{h}^{\mu \nu}=h^{\mu \nu}-\frac{1}{2} \eta^{\mu \nu } h^\sigma_{~\sigma}$, and $g_{\mu \nu }=\eta_{\mu \nu}+h_{\mu \nu}$. This is just the wave equation for $\bar{h}^{\mu \nu}$. So we see that at first order, gravitational waves are just sinusoidal perturbations of the metric which propagate at c.

 

 

Also note that gravitational waves are generated by quadrupoles. A rotating symmetric sphere will not generate gravitational waves, for example.

So a change in space will propagate as a wave but after that change as a static gravitational field, is it an analogous oscillation?

And isn't there evidence to support that rotation can "drag" space? Wouldn't that create a wave of change in the fabric of space? I think you would say "no" because of what I just explained, that after the change the inner area is just a static field, but the acceleration of a sphere such as Earth is measured to drag the fabric of space in the direction of rotation with it to a degree.