Well-posedness of Einstein's Equation with Redshift Data
  We study the solvability of a system of ordinary differential equations derived from null geodesics of the LTB metric with data given in terms of a so-called redshift parameter. Data is introduced along these geodesics by the luminosity distance function. We check our results with luminosity distance depending on the cosmological constant and with the well-known FRW model. 
Christopher Winfield
math.CA astro-ph.CO math-ph math.MP