Wormhole solutions in Einstein-Weyl gravity
Abstract
In this work we are going to study wormhole solutions in Einstein-Weyl gravity. Such solutions emerge when looking for a static spherically symmetric metric in the vacuum, in the more general context of classical quadratic gravity. Classical quadratic gravity is the theory of gravitation that comes out when including quadratic terms in the curvature in the Einstein-Hilbert action of general relativity. The study of such theory is motivated by the presence of quadratic corrections in almost all attempts to nd a consistent description of quantum gravity. Indeed, it is well known that general relativity can be consistent as a quantum eld theory only as a low-energy effective theory. We are not going to discuss the quantum aspects of the quadratic action: instead, we consider what happens to the classical description of the space-time when quadratic corrections are taken into account. In order to do that, we restrict to the simplest non-trivial case, that is a static spherically symmetric space- time in the vacuum. Given these restrictions in general relativity, we have the well known Schwarzschild solution, i.e. black hole solution. In classical quadratic gravity the Schwarzschild solution is still present, but we can also nd many different classes of solutions: the aim of this thesis is to classify the various solutions families, as well as to characterize a specific family that covers a large part of the solution space, i.e. wormhole solutions. We solve the geodesic equation in such solutions which shows the reason why we call them traversable wormholes. We report all the solution families found in previous works while adding a new subfamily of the generic wormhole solutions. When studying different classes of solutions we are assisted by a Lichnerowicz type theorem which removes the contributions of the R2 term from the equations of motion under some assumptions, in particular when an horizon is present. When such contribution is absent, the quadratic theory reduces to Einstein-Weyl gravity. By numerically solving the equations of motion in the Einstein-Weyl theory, we classify the various solution families in a phase diagram of the theory. By using the shooting method for the boundary value problem between spatial infinity and the radius of the wormholes, we nd the geometric properties of the wormhole solutions, and in particular we characterize the behavior of these solutions in function of their position on the phase diagram. Then we use the results to explore …
