Stringy Robinson-Trautman Solutions

Abstract

A class of solutions of the low energy string theory in four dimensions is studied. This class admits a geodesic, shear-free null congruence which is non-twisting but in general diverging and the corresponding solutions in Einstein's theory form the Robinson-Trautman family together with a subset of the Kundt's class. The Robinson-Trautman conditions are found to be frame invariant in string theory. The Lorentz Chern-Simons three form of the stringy Robinson-Trautman solutions is shown to be always closed. The stringy generalizations of the vacuum Robinson-Trautman equation are obtained and three subclasses of solutions are identified. One of these subclasses exists, among all the dilatonic theories, only in Einstein's theory and in string theory. Several known solutions including the dilatonic black holes, the pp- waves, the stringy C-metric and certain solutions which correspond to exact conformal field theories are shown to be particular members of the stringy Robinson-Trautman family. Some new solutions which are static or asymptotically flat and radiating are also presented. The radiating solutions have a positive Bondi mass. One of these radiating solutions has the property that it settles down smoothly to a black hole state at late retarded times.

Latex, 30 Pages, 1 Figure; to appear in Phys. Rev. D

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• Critical Behavior in a Massless Scalar Field Collapse with Self-interaction Potential
• Robinson-Trautman solution with scalar hair
• New family of C-metrics in $\mathcal{N}=2$ gauged supergravity
• Non-Abelian pp-waves in D=4 supergravity theories
• Well-posed non-vacuum solutions in Robinson--Trautman geometry
• Chaos in Kundt type III Spacetimes
• Gravitational wave solutions of quadratic curvature gravity using a null coframe formulation
• Self-similar solutions and critical behavior in Einstein-Maxwell-dilaton theory sourced by charged null fluids
• Non-Riemannian Description of Robinson-Trautman Spacetimes in Brans-Dicke Theory Of Gravity
• Robinson-Trautman solutions with scalar hair and Ricci flow
• On the integrability of spherical gravitational waves in vacuum