Hyperbolic equations in a double null gauge

The hyperbolic nature of the Einstein equations is well-known and has been used in many different contexts. More recently, the double null gauge has proven to be a powerful tool for quantitative analysis of the Einstein equations. It has the advantage of reducing the equations for many dynamical quantities to ODEs along null curves, and the Bianchi equations to a first-order hyperbolic system. The double null gauge has been used extensively and to great effect in analyzing the structure of spacetime for many purposes, including (for instance) stability problems and trapped surface formation. However, the local existence problem for the Einstein equations in a double null gauge has never been treated in full in its own right. In this talk, we discuss how to formulate a general procedure for solving the linearized problem, namely, the local existence theory for systems of first-order hyperbolic equations in a double null gauge.

https://harvard.zoom.us/j/97045416188?pwd=39VefbNb9885h4mbtcray0pwmYl8jk.1

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