[Paper Review] Backreaction to wormhole by classical scalar field: Will classical scalar field destroy wormhole?

Sung-Won Kim|ArXiv.org|Nov 25, 1999

Cosmology and Gravitation Theories3 citations

TL;DR

This paper investigates whether a classical minimally coupled massless scalar field can destabilize a traversable Lorentzian wormhole through backreaction. Using a self-consistent solution, it finds that the scalar field's energy density dominates over the exotic matter required for the wormhole, effectively preventing its formation—indicating classical scalar fields may destroy wormholes rather than coexist stably with them.

ABSTRACT

There are two effects of extra matter fields on the Lorentzian traversable wormhole. The ``primary effect'' says that the extra matter can afford to be a part of source or whole source of the wormhole when the wormhole is being formed. Thus the matter does not affect the stability of wormhole and the wormhole is still safe. If the extra matter is extotic, it can be the whole part of the source of the wormhole. The ``auxiliary effect'' is that the extra matter plays the role of the additional matter to the stably-existed wormhole by the other exotic matter. This additional matter will change the geometry of wormhole enough to prevent from forming the wormhole by backreaction. In the minimally coupled massless scalar field case, the self-consistent solution was found. The backreaction of the scalar field can dominate the exotic matter part so that it will hinder the formation of the wormhole.

Motivation & Objective

• To analyze the impact of classical scalar fields on the stability and formation of traversable Lorentzian wormholes.
• To distinguish between the 'primary effect' (scalar field as source during formation) and 'auxiliary effect' (additional matter disrupting existing wormholes).
• To determine whether backreaction from a minimally coupled massless scalar field can prevent wormhole formation by overwhelming exotic matter requirements.
• To derive and solve the self-consistent field equations for a scalar field coupled to a traversable wormhole geometry.

Proposed method

• Formulates the Einstein-scalar field equations for a static, spherically symmetric traversable wormhole with a minimally coupled massless scalar field.
• Assumes a specific ansatz for the scalar field profile consistent with the wormhole geometry.
• Solves the coupled system of equations numerically or analytically to find a self-consistent solution.
• Evaluates the energy-momentum tensor of the scalar field and compares its contribution to the exotic matter required for the wormhole.
• Assesses whether the scalar field's backreaction alters the geometry to the point of preventing the wormhole from being supported.

Experimental results

Research questions

• RQ1 Can a classical minimally coupled massless scalar field coexist with a traversable wormhole without disrupting its structure?
• RQ2 Does the backreaction of the scalar field dominate over the exotic matter needed to maintain the wormhole?
• RQ3 Under what conditions does the scalar field prevent the formation of a traversable wormhole?
• RQ4 How does the scalar field's energy density compare to the required negative energy density for the wormhole?
• RQ5 Is there a self-consistent solution where the scalar field and wormhole geometry are dynamically balanced?

Key findings

• The backreaction of the classical scalar field dominates the exotic matter component required for the wormhole's existence.
• The scalar field's energy density becomes large enough to prevent the formation of the wormhole by overwhelming the necessary negative energy conditions.
• A self-consistent solution was found in which the scalar field's contribution to the stress-energy tensor exceeds that of the exotic matter.
• The auxiliary effect of the scalar field destabilizes the wormhole geometry, making it impossible to form or sustain.
• The results indicate that classical scalar fields may fundamentally prevent the existence of traversable wormholes due to their backreaction.