Vojtěch Pravda

Kerr–Schild spacetimes with an (A)dS background

General properties of Kerr–Schild spacetimes with an (A)dS background in arbitrary dimension n > 3 are studied. It is shown that the geodetic Kerr–Schild vector k is a multiple WAND of the spacetime. Einstein Kerr–Schild spacetimes with non-expanding k are shown to be of Weyl type N, while the expanding spacetimes are of type II or D. It is shown that this class of spacetimes obeys the optical constraint. This allows us to solve Sachs equation, determine r-dependence of boost weight zero components of the Weyl tensor and discuss curvature singularities.

Type II universal spacetimes

We study type II universal metrics of the Lorentzian signature. These metrics simultaneously solve vacuum field equations of all theories of gravitation with the Lagrangian being a polynomial curvature invariant constructed from the metric, the Riemann tensor and its covariant derivatives of an arbitrary order. We provide examples of type II universal metrics for all composite number dimensions. On the other hand, we have no examples for prime number dimensions and we prove the non-existence of type II universal spacetimes in five dimensions. We also present type II vacuum solutions of selected classes of gravitational theories, such as Lovelock, quadratic and L(Riemann) gravities.

Universal spacetimes in four dimensions

A bstractUniversal spacetimes are exact solutions to all higher-order theories of gravity. We study these spacetimes in four dimensions and provide necessary and sufficient conditions for universality for all Petrov types except of type II. We show that all universal spacetimes in four dimensions are algebraically special and Kundt. Petrov type D universal spacetimes are necessarily direct products of two 2-spaces of constant and equal curvature. Furthermore, type II universal spacetimes necessarily possess a null recurrent direction and they admit the above type D direct product metrics as a limit. Such spacetimes represent gravitational waves propagating on these backgrounds. Type III universal spacetimes are also investigated. We determine necessary and sufficient conditions for universality and present an explicit example of a type III universal Kundt non-recurrent metric.

Type N universal spacetime

Universal spacetimes are vacuum solutions to all theories of gravity with the Lagrangian L = L(gab, Rabcd, ∇a1 Rbcde,..., ∇a1...ap Rbcde). Well known examples of universal spacetimes are plane waves which are of the Weyl type N. Here, we discuss recent results on necessary and sufficient conditions for all Weyl type N spacetimes in arbitrary dimension and we conclude that a type N spacetime is universal if and only if it is an Einstein Kundt spacetime. We also summarize the main points of the proof of this result.

Electromagnetic fields with vanishing quantum corrections

Abstract We show that a large class of null electromagnetic fields are immune to any modifications of Maxwells equations in the form of arbitrary powers and derivatives of the field strength. These are thus exact solutions to virtually any generalized classical electrodynamics containing both non-linear terms and higher derivatives, including, e.g., non-linear electrodynamics as well as QED- and string-motivated effective theories. This result holds not only in a flat or (anti-)de Sitter background, but also in a larger subset of Kundt spacetimes, which allow for the presence of aligned gravitational waves and pure radiation.

Universal electromagnetic fields

We study universal electromagnetic (test) fields, i.e., p-forms fields F that solve simultaneously (virtually) any generalized electrodynamics (containing arbitrary powers and derivatives of F in the field equations) in n spacetime dimensions. One of the main results is a sufficient condition: any null F that solves Maxwells equations in a Kundt spacetime of aligned Weyl and traceless-Ricci type III is universal (in particular thus providing examples of p-form Galileons on curved Kundt backgrounds). In addition, a few examples in Kundt spacetimes of Weyl type II are presented. Some necessary conditions are also obtained, which are particularly strong in the case n=4=2p: all the scalar invariants of a universal 2-form in four dimensions must be constant, and vanish in the special case of a null F .

On higher dimensional Einstein spacetimes with a non-degenerate double Weyl aligned null direction

We prove that higher dimensional Einstein spacetimes which possess a geodesic, non-degenerate double Weyl aligned null direction (WAND)

HIGHER DIMENSIONAL TYPE N AND III SOLUTIONS OF EINSTEIN GRAVITY AND QUADRATIC GRAVITY

\ell

On a Five-Dimensional Version of the Goldberg-Sachs Theorem

must additionally possess a second double WAND (thus being of type D) if either: (a) the Weyl tensor obeys

Higher Dimensional Kerr-Schild Spacetimes with (A)dS Background

C_{abc[d}\ell_{e]}\ell^c=0