What exactly does 'many-fingered time' mean?

[bookworm006]

While studying slicing of black hole geometry, I find this notion of wheeler's 'many-fingered time' which permits non-uniform evolution of spacelike slices that foliate the black hole. Could someone please explain what this notion exactly means? Is such a notion applicable only for black hole geometry or for any curved spacetime?

 

[Matterwave]

I think what Wheeler was getting at, at least from my reading of his work, is that because GR is truly a 4-D theory, trying to split it into a 3+1 D form makes time into this kind of "weird" object that moves at different rates at different places (on your 3-D Cauchy surface), rather than moving forward all nice and uniform like in Newtonian time.

This is how I read this anyways.

 

[Demystifier]

While studying slicing of black hole geometry, I find this notion of wheeler's 'many-fingered time' which permits non-uniform evolution of spacelike slices that foliate the black hole. Could someone please explain what this notion exactly means? Is such a notion applicable only for black hole geometry or for any curved spacetime?

The 'many-fingered time' is the formalism in which a different time variable is associated with each point in space, or with each physical degree of freedom. It is applicable to any flat or curved spacetime. It is particularly useful when one wants the time-evolution of a quantum state make compatible with relativistic covariance.

 

[bookworm006]

Thanks.