I Curved space and gravitational waves

[Nidhi1007]

TL;DR Summary

An object moving in a straight line appears to be attracted to a massive body due to the curvature of space, this gives the appearance of gravity attracting the body. But why does a body at rest tend to move along the curvature of space?

Are gravitational waves purely temporal? An object with no spatial velocity experiences gravity due to temporal velocity?

 

[weirdoguy]

temporal velocity

There is no such thing as temporal velocity.

 

[Dale]

Summary:: An object moving in a straight line appears to be attracted to a massive body due to the curvature of space, this gives the appearance of gravity attracting the body. But why does a body at rest tend to move along the curvature of space?

It is curvature of spacetime, not curvature of space. Even a point particle has temporal extent.

 

[Dale]

There is no such thing as temporal velocity.

No, but the four-velocity is timelike.

 

[Nidhi1007]

It is curvature of spacetime, not curvature of space. Even a point particle has temporal extent.

Thank you

 

[Ibix]

But why does a body at rest tend to move along the curvature of space?

Because it isn't the curvature of space, it's the curvature of spacetime. The curvature of space really isn't important for gravity except for the most precise measurements or in really extreme circumstances. It's actually the curvature in space-time planes that is important for gravity, and objects have an extent in time.

An object with no spatial velocity experiences gravity due to temporal velocity?

Better to say that it is because all objects have an extent in time. There is a kind of meaning to "velocity in a timelike direction" and you do see this written in popsci, but it's a kind of misdirection to associate four velocity with the more familiar velocity from school physics. They are rather different things.

Are gravitational waves purely temporal?

Gravitational waves have nothing to do with this. Gravity as we experience it every day and gravitational waves are related phenomena, but they are not the same thing.

 

[cianfa72]

It's actually the curvature in space-time planes that is important for gravity, and objects have an extent in time.

We can say each object is represented in spacetime by a worldtube.