Well-posedness of Einstein's Equation with Redshift Data

TL;DR

This paper investigates the mathematical solvability of Einstein's equations using redshift data, focusing on the LTB metric and comparing results with standard cosmological models like FRW.

Contribution

It establishes conditions for the well-posedness of Einstein's equations with redshift data and analyzes the impact of the cosmological constant within this framework.

Findings

Demonstrates solvability of the differential system derived from null geodesics.

Validates results using luminosity distance in cosmological models.

Shows consistency with the FRW model.

Abstract

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.