Přesná a perturbativní řešení kvadratické gravitace

Tajčovský, Jan Vendelín

This thesis investigates exact and perturbative aspects of four-dimensional quadratic gravity, with particular emphasis on purely radial, linear gravita- tional perturbations of the Schwarzschild black hole. The analysis is formulated within the Newman-Penrose formalism and employs a Teukolsky-like approach based on tetrad projections of the perturbed Ricci tensor. For the Schwarzschild background, it is shown that the resulting system of linearized field equations admits a substantial reduction to a single second-order, gauge-invariant master ordinary differential equation. Local analytic solutions of this equation are con- structed by means of explicit Frobenius expansions about the central singularity and the event horizon of the black hole. The remaining Ricci projections are then reconstructed from the master variable, and the corresponding perturbed metric functions are obtained in the Robinson-Trautman chart. By comparing these perturbative solutions with the exact Schwarzschild-Bach family, the free perturbative parameter is identified with the Bach parameter of the associated exact solution, allowing the metric contribution linear in this parameter to be isolated explicitly. This provides a direct analytic description of the leading non-Einstein correction, which is not immediately transparent from...

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