# NEB-19 Recent Developments in Gravity, Athens (Online)

20-23 September 2021
Europe/Athens timezone

## Robinson-Trautman Einstein-Maxwell fields of Petrov type D

Not scheduled
20m
Oral presentation

### Speaker

Prof. Norbert Van den Bergh (Ghent University)

### Description

In the quest for exact solutions of the Einstein-Maxwell (EM) equations a considerable amount of research has been devoted to the study of aligned EM fields, in which at least one of the principal null directions (PND) of the electromagnetic field $\mathbf{F}$ is parallel to a PND of the Weyl tensor, a so called Debever-Penrose (DP) direction. One of the main triumphs of this effort - spread out between 1960 and 1980-- has been the complete integration of the field equations (with a possible non-0 cosmological constant $\Lambda$), for the Petrov type D doubly aligned non-null EM fields, in which \emph{both} real PNDs of $\mathbf{F}$ are parallel to a corresponding double DP vector, the so called ''class $\mathcal{D}$ metrics''. In a recent systematic treatment of the non aligned algebraically special EM fields it was noted that, at least for non-0 $\Lambda$, the double alignment condition of the class $\mathcal{D}$ metrics is actually a consequence of their multiple DP vectors being geodesic and shear-free. A natural question therefore arises as to whether EM solutions exist which are of Petrov type D, have $\Lambda=0$ and in which the two real DP vectors $\mathbf{k},\mathbf{\ell}$ are geodesic and shearfree, but are \emph{both non aligned} with the PND's of $\mathbf{F}$. Recently [Class. Quantum Grav. 37, 21, 2020] we have been able to answer this question affirmatively, by completing the full integration of the EM field equations for the double Robinson-Trautman family, under the additional assumption that also the complex eigenvectors of the canonical Weyl-tetrad are hypersurface-orthogonal.

### Primary authors

Prof. Norbert Van den Bergh (Ghent University) Prof. John Carminati (Deakin University)

### Presentation Materials

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