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This seminar talk from the Harvard CMSA General Relativity Seminar features Christopher Stith from the University of Michigan discussing hyperbolic equations in a double null gauge. Explore how the double null gauge serves as a powerful tool for quantitative analysis of Einstein equations, offering the advantage of reducing equations for many dynamical quantities to ODEs along null curves and the Bianchi equations to a first-order hyperbolic system. Learn about the applications of double null gauge in analyzing spacetime structure for stability problems and trapped surface formation. Despite its extensive use, the local existence problem for Einstein equations in a double null gauge has not been fully treated in its own right. The presentation focuses on formulating a general procedure for solving the linearized problem, specifically addressing the local existence theory for systems of first-order hyperbolic equations in a double null gauge.
