[Paper Review] Traversable wormholes in Chern-Simons modified gravity

J. R. Nascimento, A. Yu. Petrov+1 more|arXiv (Cornell University)|Dec 22, 2017

Cosmology and Gravitation Theories1 references3 citations

TL;DR

This paper demonstrates the existence of traversable wormhole solutions in dynamical Chern-Simons modified gravity without requiring matter sources that violate energy conditions—unlike in general relativity. The authors derive a non-trivial solution using a dynamical Chern-Simons coefficient, showing that the geometry's consistency arises from the field's dynamics rather than exotic matter, marking a significant departure from standard GR expectations.

ABSTRACT

In this paper, we examine the existence of traversable wormhole solutions within the Chern-Simons modified gravity. We find a non-trivial solution in the theory with dynamical Chern-Simons coefficient in the absence of matter sources. This result displays a situation opposite to GR where the matter sources violating the energy conditions are required.

Motivation & Objective

• To investigate whether traversable wormhole solutions can exist in Chern-Simons modified gravity, a CPT- and Lorentz-breaking gravity extension of general relativity.
• To determine whether such solutions require matter sources violating energy conditions, as in standard general relativity.
• To explore the consistency of wormhole geometries in the dynamical Chern-Simons framework where the CS coefficient is not fixed but evolves via its own dynamics.
• To analyze the energy conditions and the role of the scalar field's energy-momentum tensor in supporting the wormhole geometry.

Proposed method

• The study employs a spherically symmetric, traversable wormhole metric with shape function b(r) and redshift function Φ(r), consistent with Morris-Thorne traversability conditions.
• The action of dynamical Chern-Simons modified gravity is used, incorporating a pseudoscalar field ϑ coupled to the Pontryagin density, with a non-minimal coupling to curvature.
• The field equations are derived from the action, and the Cotton tensor components are computed explicitly to determine the effective energy-momentum tensor of the ϑ field.
• The energy-momentum tensor T^(ϑ)μν is computed in terms of radial and angular functions r(x), U(x), Y(θ), and A(x), with non-vanishing components derived from the field equations.
• The analysis checks the null energy condition (NEC) by evaluating T^(m)μνk^μk^ν for null vectors k^μ, showing that the NEC is not violated in the solution.
• The solution is constructed by solving the field equations under the assumption of a non-trivial, dynamical ϑ field, leading to a self-consistent wormhole geometry without external matter sources.

Experimental results

Research questions

• RQ1 Can traversable wormhole solutions exist in dynamical Chern-Simons modified gravity without requiring matter that violates energy conditions?
• RQ2 How does the dynamics of the Chern-Simons coefficient ϑ influence the existence and stability of wormhole geometries?
• RQ3 What is the role of the effective energy-momentum tensor of the ϑ field in supporting the wormhole structure?
• RQ4 Does the modified gravity framework allow for traversable wormholes that are consistent with causality and local Lorentz invariance?
• RQ5 How does the energy condition behavior in this theory differ from that in general relativity?

Key findings

• A non-trivial traversable wormhole solution exists in dynamical Chern-Simons modified gravity even in the absence of matter sources, which is a direct contrast to general relativity.
• The solution is supported by the dynamics of the Chern-Simons scalar field ϑ, whose energy-momentum tensor provides the necessary geometric support without violating energy conditions.
• The null energy condition (NEC) is not violated in this solution, as T^(ϑ)μνk^μk^ν ≥ 0 for all null vectors k^μ, indicating that exotic matter is not required.
• The effective energy-momentum tensor T^(ϑ)μν is derived explicitly, with non-vanishing components depending on r(x), U(x), Y(θ), and A(x), showing the field's contribution to the geometry.
• The Cotton tensor components are computed and used to derive the field equations, confirming consistency of the solution within the theory’s framework.
• The result demonstrates that the dynamical nature of the Chern-Simons coefficient enables traversable wormhole solutions independently of matter energy conditions, offering a new mechanism for such geometries.