[Paper Review] Wormholes or Gravastars?

Remo Garattini|arXiv (Cornell University)|Jan 21, 2010

Cosmology and Gravitation Theories14 references4 citations

TL;DR

This paper compares the zero-point energy (ZPE) of wormholes and gravastars using one-loop effective field theory in curved spacetime, employing zeta function regularization and renormalization to compute quantum corrections. It finds that the Casimir energy difference—dependent on the ratio of the wormhole's brick-wall radius to the gravastar's radius—determines which configuration is energetically favored, with lower ZPE indicating greater stability.

ABSTRACT

The one loop effective action in a Schwarzschild background is here used to compute the Zero Point Energy (ZPE) which is compared to the same one generated by a gravastar. We find that only when we set up a difference between ZPE in these different background we can have an indication on which configuration is favored. Such a ZPE difference represents the Casimir energy. It is shown that the expression of the ZPE is equivalent to the one computed by means of a variational approach. To handle with ZPE divergences, we use the zeta function regularization. A renormalization procedure to remove the infinities together with a renormalization group equation is introduced. We find that the final configuration is dependent on the ratio between the radius of the wormhole augmented by the "brick wall" and the radius of the gravastar.

Motivation & Objective

• To determine whether wormholes or gravastars are energetically favored by comparing their zero-point energy (ZPE) contributions.
• To compute the one-loop effective action in Schwarzschild and gravastar backgrounds to extract quantum vacuum energy.
• To apply zeta function regularization and renormalization to handle ZPE divergences and extract finite physical results.
• To investigate how the ratio between the wormhole's brick-wall radius and the gravastar's radius influences the Casimir energy difference.
• To assess the stability of quantum vacuum configurations in alternative compact object models beyond classical black holes.

Proposed method

• Uses the one-loop effective action in a Schwarzschild background to compute the ZPE for both wormhole and gravastar geometries.
• Applies zeta function regularization to systematically remove divergences in the ZPE calculation.
• Implements a renormalization procedure with a renormalization group equation to extract finite physical quantities.
• Compares the ZPE of the two configurations via the Casimir energy difference, defined as $ E_0^W - E_0^{GS} $.
• Analyzes three-dimensional gravitational perturbations using even-parity forms and reduces the system to effective Schrödinger-like equations with position-dependent masses.
• Transforms the radial coordinate using the geodesic distance from the throat to map the perturbation equations into a standard form for spectral analysis.

Experimental results

Research questions

• RQ1 Which configuration—wormhole or gravastar—has a lower zero-point energy and is therefore more quantum-mechanically stable?
• RQ2 How does the Casimir energy difference between the two configurations depend on the geometric parameters, particularly the ratio of the wormhole's brick-wall radius to the gravastar's radius?
• RQ3 Can the one-loop effective action in curved spacetime distinguish between the vacuum energy contributions of these two horizonless compact objects?
• RQ4 To what extent do quantum corrections via zeta regularization and renormalization affect the stability comparison between wormholes and gravastars?
• RQ5 Does the variational approach yield consistent results with the one-loop ZPE computation in these backgrounds?

Key findings

• The ZPE difference between the wormhole and gravastar configurations is equivalent to the Casimir energy, which determines the preferred quantum vacuum state.
• The final configuration is determined by the ratio of the wormhole's augmented radius (including the brick-wall regulator) to the gravastar's radius, with lower ZPE favoring greater stability.
• The one-loop ZPE computation matches results obtained via a variational approach, validating the consistency of the method.
• Zeta function regularization successfully handles divergences in the ZPE, enabling finite physical predictions.
• The renormalization group equation is derived and applied to remove infinities, ensuring a consistent quantum field theory framework.
• The effective potential in the perturbation equations includes position-dependent masses $ m_1^2(r) $ and $ m_2^2(r) $, reflecting the geometry's influence on vacuum fluctuations.