Can the Ricci Scalar Depend on Spacetime Coordinates?

[div curl F= 0]

Does it make sense for the Ricci Scalar to be a function of the spacetime coordinates?

In previous calculations I have carried out in the past, everytime the Ricci Scalar has been returned as a constant, rather than being explicitly dependent on the coordinates.

Thanks for any replies

 

[snoopies622]

The value of the Ricci scalar can be computed using only the metric tensor, and the components of the metric tensor may or may not vary with spacetime coordinates. So a Ricci scalar might change as your coordinates change, but it might not. Due to all the contractions, the Ricci scalar might be constant even if the components of the metric change (as with the surface of a sphere), but this varies from case to case.

 

[div curl F= 0]

Thank you for your reply. My metric does indeed vary with the coordinates.

 

[lbrits]

I think in the general Lemaitre-Tolman-Bondi spacetimes you will find that the Ricci tensor is proportional to the density of the dust configuration, and therefore you can tune it to whatever you like. Give 'em a go with GRtensor =]

* C. W. Misner and D. H. Sharp. Relativistic equations for adiabatic, spherically
symmetric gravitational collapse. Phys. Rev., 136:B571, October 1964.

* S. Gon¸calves. Shell crossing in generalized Tolman-Bondi spacetimes. Phys. Rev. D,
63(12):124017, June 2001.