| Summary: | <p>The transseries is an ansatz for generating solutions to classical problems which are both perturbative and non-perturbative in some limit of parameter space. In this thesis we apply this technique to three systems described by classical gravity with relevance to holographic plasmas of strongly coupled gauge theories. </p>
<p>To begin we compute the gradient expansion to arbitrarily high orders for an N=4 Super Yang-Mills (SYM) plasma at infinite 't Hooft coupling undergoing Bjorken evolution, later finding the full transseries by including non-perturbative (in gradient) terms. Mathematical relations exist between these transseries sectors, which we verify by calculating the leading terms of the first non-hydrodynamic series solution entirely through the coefficients of the gradient expansion. Relaxing the limit of infinite 't Hooft coupling we compute the leading transseries solution for a family of finitely coupled gauge theories, and estimate the typical path of Bjorken evolution a far-from-equilibrium system might take while evolving to the hydrodynamic regime.</p>
<p>Next we consider a holographic Bjorken expanding system in arbitrary spacetime dimensions D, now instead using the number of dimensions as our large parameter. Due to a greater degree of analytic control we can compute combinations of transport coefficients relevant for Bjorken flow up to 6-th order in gradients to 3rd order in 1/D, finding that our perturbative solution recovers the same dynamics controlled by the hydrodynamic gradient expansion. Computing the non-perturbative (in 1/D) contributions of this set up we demonstrate an identification between these terms and the non-hydrodynamic solutions of the small gradient transseries.</p>
<p>Lastly we apply the transseries to study the near equilibrium dynamics of blackbranes. Due to the simplicity of this system we can analytically find the time-evolving divergence of the entropy current to second order in the transseries, determined entirely the blackbrane's quasinormal modes frequencies and equilibrium temperature. This pedogogical example demonstrates the power of the expansion which can be easily applied to wider contexts.</p>
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