The regular state in higher-order gravity

TL;DR

This paper analyzes higher-order gravity with quadratic Lagrangian, demonstrating that analytic solutions can be characterized by free functions and formal power series expansions, confirming their generality.

Contribution

It provides a first-order ADM formulation of quadratic gravity and shows that analytic solutions are fully characterized by free functions and asymptotic expansions.

Findings

Solutions contain the correct number of free functions.

Regular solutions can be expressed as formal power series.

Analytic solutions satisfy constraints and evolution equations.

Abstract

We consider the higher-order gravity theory derived from the quadratic lagrangian $R+\epsilon R^2$ in vacuum as a first-order (ADM-type) system with constraints, and build time developments of solutions of an initial value formulation of the theory. We show that all such solutions, if analytic, contain the right number of free functions to qualify as general solutions of the theory. We further show that any regular analytic solution which satisfies the constraints and the evolution equations can be given in the form of an asymptotic formal power series expansion.