Equivalence: A Covariantly Constant Problem in General Relativity

In studying the space-time structures described by Einstein’s theory of general relativity, it is often useful to identify particular properties referred to as geometrical invariants. These are attributes of the space-times which do not change regardless of the underlying coordinate systems used to study them. This project is part of a larger effort to catalogue space-times studied in general relativity. Specifically, computational software was used to identify structures known as covariantly constant vector fields

Forward Model for Temperature Derivation from Atmospheric Lidar

Atmospheric Lidar takes advantage of Rayleigh backscattering to create a relative density profile of the atmosphere. The method for temperature derivation is based on the work of Chanin and Hauchecorne (CH). Beginning with an initial temperature, and utilizing the ideal gas law, a downward integration procedure is applied to create a temperature profile from the density profile down to forty- five kilometers. Since this initial temperature is only a best guess, the temperatures towards the top of the profile may not be accurate. However, so long as the guess is reasonable, within perhaps a fifty Kelvin margin (though hopefully not so much), multiple guesses seem to converge after working down fifteen or so kilometers