STEADILY ROTATING PERFECT-FLUID GRAVITATING PROLATE SPHEROIDS IN WEYLGRAVITY

It is shown that the equations of hydrodynamics do not admit solutions describing gravitating, incompressible, perfect fluid, prolate sphero ids within the context of Weyl gravity, i.e. a theory whose static, sp herically symmetric solution admits, besides the usual 1/r potential, an additional linear one, which has been invoked to solve the galactic rotation curve problem without the introduction of 'dark matter'. Thi s extends the similar, recent result obtained by Florides and Spyrou w ithin Newtonian gravity to this alternative gravitational theory.