The classical wormhole solution and wormhole wavefunction with a nonlinear Born-Infeld scalar field

TL;DR

This paper analyzes classical and quantum wormhole solutions involving a nonlinear Born-Infeld scalar field, providing analytical forms at extreme field derivatives and deriving corresponding wavefunctions from the Wheeler-DeWitt equation.

Contribution

It presents new analytical wormhole solutions for both small and large scalar field derivatives and constructs their quantum wavefunctions within the Born-Infeld framework.

Findings

Classical wormhole solutions match known forms at small derivatives.

New wormhole solutions are derived for large derivatives.

Quantum wormhole wavefunctions are obtained for extreme limits.

Abstract

On this paper we consider the classical wormhole solution of the Born-Infeld scalar field. The corresponding classical wormhole solution can be obtained analytically for both very small and large $\dot{\phi}$. At the extreme limits of small $\dot{\phi}$ the wormhole solution has the same format as one obtained by Giddings and Strominger[10]. At the extreme limits of large $\dot{\phi}$ the wormhole solution is a new one. The wormhole wavefunctions can also be obtained for both very small and large $\dot{\phi}$. These wormhole wavefunctions are regarded as solutions of quantum-mechanical Wheeler--Dewitt equation with certain boundary conditions.