Variable-tension lightlike brane as a gravitational source of traversable Misner–Wheeler-type wormholes

Abstract

Consistent Lagrangian description of variable-tension lightlike p-branes (LL-branes) is presented in two equivalent forms – a Polyakov-type formulation and a dual to it Nambu–Goto-type formulation. An important and non-standard characteristic feature of the LL-branes is that the brane tension appears as a non-trivial additional dynamical degree of freedom. We consider properties of p=2LL-brane dynamics (as a test brane) in D=4 Kerr or Kerr–Newman gravitational backgrounds in some detail. It is shown that the LL-brane automatically positions itself on the horizon and rotates along with the same angular velocity.Finally, we construct explicitly a traversable wormhole of Misner–Wheeler type based on a Reissner–Nordström geometry. This wormhole is constructed as a self-consistent solution of the electrically sourceless Einstein–Maxwell system in the D=4 bulk interacting with a LL-brane. The pertinent wormhole throat is located precisely at the LL-brane sitting on the outer Reissner–Nordström horizon with the Reissner–Nordström mass and charge being functions of the dynamical LL-brane tension.