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.

Exact collapse solutions in D = 4, N $$ \mathcal{N} $$ = 4 gauged supergravity and their generalizations

“…and Yörük [9] in an Einstein-Maxwell-dilaton theory (without a scalar potential) that can be embedded in Poincaré supergravity. It is thus of interest to search for more non-static solutions that can arise in gauged supergravities.…”

“…One is from certain generically specified matter energy-momentum tensor, with perhaps the most well-known example of Vaidya's metric and its various generalizations [5][6][7]. The other is from Lagrangians of Einstein gravity coupled with fundamental matter fields such as scalars or vectors (see, e.g., [8,9]). For the past few decades, much effort has been given to inspecting the collapse of a scalar field from both analytical and numerical aspects [3].…”

Robinson-Trautman solution with scalar hair

“…The solutions for "stringy" Robinson-Trautman spacetime corresponding to Einstein-Maxwell-dilaton system were obtained in [18]. Recently, scalar field solutions for Einstein-Maxwell-Lambda system with a conformally coupled scalar field belonging to Plebański-Demiański family (containing type D solutions of RobinsonTrautman class) were derived in [19].…”

Non-Abelian pp-waves in D = 4 supergravity theories

“…The constant spinor η obeys 17) showing that the solutions possess 1/2 of the Poincaré supersymmetry.…”