Exact Nonnull Wavelike Solutions to Gravity with Quadratic Lagrangians

AdS Waves as Exact Solutions to Quadratic Gravity

We give an exact solution of the quadratic gravity in D dimensions. The solution is a plane-fronted wave metric with a cosmological constant. This metric solves not only the full quadratic gravity field equations but also the linearized ones which include the linearized equations of the recently found critical gravity. A subset of the solutions change the asymptotic structure of the anti-de Sit...

Spherically Symmetric Solutions to Fourth-Order Theories of Gravity

Solutions to the field equations generated from Lagrangians of the form f(R) are considered. The spherically symmetric solutions to these equations are discussed, paying particular attention to features that differ from the standard Schwarzschild solution. The asymptotic form of solutions will be described, as will the lack of validity of Birkhoff’s theorem. Exact solutions are presented which ...

Exact solutions for the flow of a generalized second grade due to a Longitudinal quadratic time-dependent shear stress

An alternate Hamiltonian formulation of fourth–order theories and its application to cosmology

An alternate Hamiltonian H different from Ostrogradski’s one is found for the Lagrangian L = L(q, q̇, q̈), where ∂2L/∂(q̈)2 6= 0. We add a suitable divergence to L and insert a = q an d b = q̈. Contrary to other approaches no constraint is needed because ä = b is one of the canonical equations. Another canonical equation becomes equivalent to the fourth–order Euler–Lagrange equation of L. Usually, ...

The Newtonian limit of metric gravity theories with quadratic Lagrangians

The Newtonian limit of fourth-order gravity is worked out discussing its viability with respect to the standard results of General Relativity. We investigate the limit in the metric approach which, with respect to the Palatini formulation, has been much less studied in the recent literature, due to the higherorder of the field equations. In addition, we refrain from exploiting the formal equiva...