Robinson-Trautman Family Research Articles

Nonsymmetric dynamical thin-shell wormhole in Robinson\u2013Trautman class

The thin-shell wormhole created using the Darmois–Israel formalism applied to Robinson–Trautman family of spacetimes is presented. The stress energy tensor created on the throat is interpreted in terms of two dust streams and it is shown that asymptotically this wormhole settles to the Schwarzschild wormhole with a throat located at the position of the horizon. This behavior shows a nonlinear stability (within the Robinson–Trautman class) of this spherically symmetric wormhole. The gravitational radiation emitted by the Robinson–Trautman wormhole during the transition to spherical symmetry is indistinguishable from that of the corresponding black hole Robinson–Trautman spacetime. Subsequently, we show that the higher-dimensional generalization of Robinson–Trautman geometry offers a possibility of constructing wormholes without the need to violate the energy conditions for matter induced on the throat.

Algebraic structure of Robinson–Trautman and Kundt geometries in arbitrary dimension

We investigate the Weyl tensor algebraic structure of a fully general family of D-dimensional geometries that admit a non-twisting and shear-free null vector field . From the coordinate components of the curvature tensor we explicitly derive all Weyl scalars of various boost weights. This enables us to give a complete algebraic classification of the metrics in the case when the optically privileged null direction is a (multiple) Weyl aligned null direction (WAND). No field equations are applied, so the results are valid not only in Einsteinʼs gravity, including its extension to higher dimensions, but also in any metric gravitation theory that admits non-twisting and shear-free spacetimes. We prove that all such geometries are of type I(b), or more special, and we derive surprisingly simple necessary and sufficient conditions under which is a double, triple or quadruple WAND. All possible algebraically special types, including the refinement to subtypes, are thus identified, namely II(a), II(b), II(c), II(d), III(a), III(b), N, O, IIi, IIIi, D, D(a), D(b), D(c), D(d), and their combinations. Some conditions are identically satisfied in four dimensions. We discuss both important subclasses, namely the Kundt family of geometries with the vanishing expansion () and the Robinson–Trautman family (, and in particular ). Finally, we apply Einsteinʼs field equations and obtain a classification of all Robinson–Trautman vacuum spacetimes. This reveals fundamental algebraic differences in the and cases, namely that in higher dimensions there only exist such spacetimes of types D(a) ≡ D(abd), D(c) ≡ D(bcd) and O.

Lanczos Potential for Arbitrary Petrov Type II Spacetimes

The Lanczos potential for an arbitrary Petrov type II spacetime has been obtained and Robinson–Trautman family of metrics has been considered as an example.

Photon rockets in the (anti-)de Sitter universe

A class of exact solutions to Einstein's equations is presented, which describes accelerating photon rockets in the de Sitter and anti-de Sitter universes. These are particular members of the Robinson-Trautman family of axially symmetric spacetimes with pure radiation. In particular, generalizations of (type D) Kinnersley's rockets and (type II) Bonnor's rockets to the case of a nonvanishing cosmological constant are given. Some of the main physical properties of these solutions are investigated, and their relation to the C-metric solution which describes uniformly accelerated black holes is also given.

Radiative spacetimes approaching the Vaidya metric

We analyze a class of exact type II solutions of the Robinson-Trautman family which contain pure radiation and (possibly) a cosmological constant. It is shown that these spacetimes exist for any sufficiently smooth initial data, and that they approach the spherically symmetric Vaidya-(anti-)de Sitter metric. We also investigate extensions of the metric, and we demonstrate that their order of smoothness is in general only finite. Some applications of the results are outlined.

Stringy Robinson-Trautman solutions.

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 nontwisting but in general diverging and the corresponding solutions in Einstein's theory form the Robinson-Trautman family together with a subset of 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 always be 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 $\mathrm{pp}$ 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.

On the absence of the Painlevé property in Petrov type III Robinson–Trautman solutions

It is shown that solutions of the exact reduced generalized Liouville-like equation, determining Petrov-type III gravitational fields within the Robinson–Trautman family of metrics, possess movable critical points, that is, they do not exhibit the Painlevé property.

Einstein-Maxwell null fields of Petrov type D

A proof is given that the Robinson-Trautman family exhausts the full set of Petrov type-D Einstein-Maxwell null solutions.

Diverging Einstein-Maxwell null fields of Petrov type D

Diverging Einstein-Maxwell null fields of Petrov type D, with zero or non-zero cosmological constant, are considered. A proof is given that the principal null direction of the Maxwell field is non-twisting. Therefore all diverging solutions belong to the Robinson-Trautman family.

Algebraically special, nonaligned, non-null Einstein-Maxwell fields

A class of algebraically special non-null electrovac solutions is presented, in which the repeated principal null congruence is shear free, twist free, and geodesic, and is not aligned with a principal null direction of the electromagnetic field. This class includes all previously known solutions of this type as special cases. It can also be considered as a generalization of the Robinson-Trautman family of solutions.