Why Can't There Be Gravity in 2 Spatial Dimensions?

[lolgarithms]

Why do they say there can there be no gravity in 2 spatial dimensions (and 1 temporal dimension)?

wouldn't the gravitational law be an inverse-law instead of an inverse-square law?

 

[Gear300]

Why can there be no gravity in 2 spatial dimensions (and 1 temporal dimension)?

I don't think anyone clearly proved that there couldn't be (as far as I know). Not to mention, gravity is still relatively mysterious to us, so we don't know enough to assert whether there is or is not any gravity in 2 spatial dimensions.

 

[Combustible]

According to GR there can not be a non zero gravitational field in empty space in two or three dimensions. For a gravitational field in a region it is necessary that space is curved. But in 2 or 3 dimensions it is not possible for the Einstein field equations to be satisfied in a vacuum and for space to be curved. In 4 dimensions there are a lot more independent components of the curvature tensor which means that space can be curved whilst still satisfying the field equations in empty space.