THE STRESS-ENERGY TENSOR AND THE DEFLECTION OF LIGHT IN 6-DIMENSIONALGENERAL-RELATIVITY

We find the stress-energy tensor of a perfect fluid in the 6-dimension al spacetime proposed by Cole. Using the weak-field Newtonian approxim ation of general relativity gives a constant of proportionality in Ein stein's held equations that differs by a factor of 4/6 from the usual one and shows that Cole's extension of the Schwarzschild metric to 6 d imensions is not valid for a gravitating mass of ''ordinary'' matter. A subsequent evaluation of the deflection of starlight for the 6-d spa cetime gives a result that is 4/6 of the 4-d result. We conclude that if spacetime is 6-dimensional, one must find a different way to deal w ith gravity.