Nonsymmetric Dynamical Thin-Shell Wormhole in Robinson--Trautman Class

TL;DR

This paper constructs a nonsymmetric dynamical thin-shell wormhole within Robinson-Trautman spacetimes, demonstrating its stability, gravitational wave emission during transition, and potential for higher-dimensional models without violating energy conditions.

Contribution

It introduces a new class of dynamical wormholes in Robinson-Trautman spacetimes, analyzes their stability and gravitational radiation, and explores higher-dimensional generalizations avoiding energy condition violations.

Findings

The wormhole asymptotically approaches a Schwarzschild wormhole.

The emitted gravitational radiation matches that of Robinson-Trautman black holes.

Higher-dimensional models can form wormholes without violating energy conditions.

Abstract

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 horizon position. 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.