Type III and N universal spacetimes
Abstract
Universal spacetimes are spacetimes for which all conserved symmetric rank2 tensors, constructed as contractions of polynomials from the metric, the Riemann tensor and its covariant derivatives of arbitrary order, are multiples of the metric. Consequently, metrics of universal spacetimes solve vacuum equations of all gravitational theories, with the Lagrangian being a polynomial curvature invariant constructed from the metric, the Riemann tensor and its derivatives of arbitrary order. In the literature, universal metrics are also discussed as metrics with vanishing quantum corrections and as classical solutions to string theory. Widely known examples of universal metrics are certain Ricciflat pp waves. In this paper, we start a general study of the geometric properties of universal metrics in arbitrary dimension and arrive at a broader class of such metrics. In contrast with pp waves, these universal metrics also admit a nonvanishing cosmological constant and in general do not have to possess a covariant constant or recurrent null vector field. First, we show that a universal spacetime is necessarily a constant curvature invariant spacetime, i.e. all curvature invariants constructed from the Riemann tensor and its derivatives are constant. Then we focus on type N spacetimes, where we arrive at a simple necessary and sufficient condition: a type N spacetime is universal if and only if it is an Einstein Kundt spacetime. A class of type III Kundt universal metrics is also found. Several explicit examples of universal metrics are presented.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 November 2014
 DOI:
 10.1088/02649381/31/21/215005
 arXiv:
 arXiv:1311.0234
 Bibcode:
 2014CQGra..31u5005H
 Keywords:

 generalized theories of gravity;
 gravity in four and higher dimensions;
 metrics with vanishing quantum corrections;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory
 EPrint:
 17 pages, slightly extended version, to appear in Classical and Quantum Gravity