Thin-shell wormholes in cosmic voids

Technical Summary: Thin-shell wormholes in cosmic voids

Problem and Motivation
This work addresses the interaction between local strong-gravity configurations and the large-scale environment in which they are embedded. While compact objects are typically modeled as isolated systems, the universe is structured on scales much larger than galaxies, specifically within cosmic voids—extended underdense regions with de Sitter-like gravitational behavior. Recent studies have constructed black-hole solutions embedded in universal void density profiles, resulting in spacetimes with two characteristic horizons: an inner black-hole horizon and an outer cosmological-like horizon.

The central question investigated is whether this "black-hole-in-void" geometry can serve as a seed spacetime for constructing a symmetric thin-shell wormhole. Unlike continuous Morris–Thorne wormholes supported by bulk fluids, this approach confines the exotic matter to a junction surface (the throat) located within the positive-lapse region between the two horizons. The study aims to determine how the void's underdense environment modifies the standard thin-shell wormhole picture, specifically regarding surface stresses, energy conditions, thermodynamic properties, and linear stability.

Methodology
The authors employ the cut-and-paste procedure (Darmois–Israel formalism) to construct the wormhole:

1. Seed Geometry: Two copies of the static region ($r_h < r < r_{++}$) of a black-hole-in-void metric are joined at a timelike hypersurface $\Sigma$ (the throat). The seed metric is generated by a central mass $M$ embedded in a Hamaus–Sutter–Wandelt universal void density profile.
2. Junction Conditions: The induced metric, unit normal vector, and extrinsic curvature are calculated. The surface stress-energy tensor is derived from the jump in extrinsic curvature using the Lanczos equation.
3. Energy Conditions: The null (NEC), weak (WEC), dominant (DEC), and strong (SEC) energy conditions are evaluated explicitly in terms of the void mass function and density profile.
4. Thermodynamics: A thermodynamic framework is developed for the static shell, defining a local Unruh temperature and deriving a first law relating shell entropy to the mass variation and horizon entropies.
5. Radial Dynamics and Stability: The radial motion of the throat is reduced to a one-dimensional effective potential problem. The local stability of static configurations is analyzed by examining the second derivative of this potential. Two specific equations of state (EoS) for the exotic matter on the shell are tested:
   • Generalized Cosmic Chaplygin Gas (GCCG).
   • Modified Cosmic Chaplygin Gas (MCCG).

Key Contributions and Results

• Geometric Construction and Energy Conditions:
  The construction yields a symmetric thin-shell wormhole where the surface energy density $\sigma$ is necessarily negative, a direct consequence of the flare-out condition and the symmetric junction. Consequently, the WEC and DEC are always violated. However, the NEC ($\sigma + p \ge 0$) and SEC ($\sigma + 2p \ge 0$) combinations are not universally violated; they depend on the throat's position. These conditions are satisfied only in the inner portion of the static patch (near the black-hole horizon) and are violated as the throat approaches the outer cosmological-like horizon, where the shell enters a tension-dominated regime.

• Thermodynamic Framework:
  The authors derive a first law for the shell fluid. For a sequence of static configurations with fixed ADM mass $M$, the shell entropy is conserved ($dS_{shell} = 0$). When $M$ is treated as a thermodynamic variable, a differential relation emerges: $dS_{shell} = (8\pi/|G'_v|) dM$. This links the shell entropy directly to the black-hole and cosmological-like horizon entropies. In the limit where the throat approaches the black-hole horizon, the relation simplifies to $dS_{shell} \to 2 dS_h$.

• Stability Analysis:
  The stability of the throat is governed by the sign of the second derivative of the effective potential, $\Upsilon''_{eff}(\chi_0)$.

  • GCCG Model: Numerical results indicate that configurations supported by the Generalized Cosmic Chaplygin Gas are generically linearly unstable across the explored parameter range.
  • MCCG Model: Configurations supported by the Modified Cosmic Chaplygin Gas can achieve linear stability, but only if the linear term $A$ in the equation of state is sufficiently large. This suggests that a specific modification to the EoS can compensate for the exotic nature of the shell and stabilize the throat.

• Parameter Dependence:
  The stability and energy condition profiles are sensitive to the central mass $M$ and the void depth $\delta_c$. Increasing $M$ narrows the available static interval between the horizons and shifts the region where energy conditions are satisfied. The void depth primarily affects the location of the outer horizon, slightly extending the admissible interval for deeper voids.

Significance and Claims
The paper claims to establish a direct link between the large-scale underdense structure of cosmic voids and the local physics of thin-shell wormholes. By embedding the wormhole in a void profile rather than an asymptotically flat or pure de Sitter space, the authors demonstrate that the void geometry introduces an external scale that enriches the thermodynamic phase space and constrains the admissible static interval.

The primary significance lies in providing a starting point for identifying stable or unstable wormhole configurations located between the black-hole and cosmological-like horizons of a void spacetime. The work highlights that while the exotic matter requirement (negative energy density) is intrinsic to the thin-shell formalism, the stability of such structures is highly dependent on the equation of state and the specific large-scale environment. The authors note that their results connect the de Sitter-like structure of voids with standard thin-shell formalism, offering a controlled framework to study how environmental boundaries influence local gravitational stability. They explicitly state that future work is needed to systematically scan the full void parameter space, investigate non-linear dynamical evolution, and address the near-Nariai limit where horizons merge.