Physical properties of compact star-like systems harboring traversable wormholes: Effects of chaotic magnetic fields and anisotropic matter

Neutron-star–wormhole (NSWH) systems supported by two scalar fields are formulated to investigate how chaotic magnetic fields and pressure anisotropy affect their mass, radius, surface redshift, and gravitational-wave echo time. This research is significant because it demonstrates that these complex physical effects can lead to extremely massive configurations exceeding 8 solar masses and surface redshifts greater than 1.5, while also revealing a dependence of the echo time on the magnetic field strength.

How it works

The model incorporates two key physical complexities: the anisotropy of the neutron fluid and chaotic magnetic fields. The anisotropic matter is described by an energy-momentum tensor where tangential pressure and radial pressure differ, quantified by an anisotropy term, such that the radial and tangential pressures differ. This anisotropy can be parameterized using a free parameter, leading to a modification of the Tolman-Oppenheimer-Volkoff (TOV) equation:

The TOV equation for anisotropic NSs reads: dpr/dr = -dν/dr(ρ + pr) - 2sigma/r.

where σ = pr − pt denotes the anisotropy term.

How it works

The chaotic magnetic field is incorporated using an ansatz where the magnetic pressure, pa, is consistent with field theory for small-scale fields:

pa = 1/3 = 1/3(B2/8π + B2/8π - B2/8π).

This approximation allows the magnetic contribution to be incorporated consistently within the spherically symmetric formalism through an effective isotropic pressure, simplifying the mathematical formulation. The magnetic field profile is further modeled by an ansatz:

B = Bs + B0(ρ/ρ0)n.

How it works

The geometry of the system is governed by Einstein's field equations coupled with two scalar fields, and the elimination of ghosts is achieved by introducing Lagrange multipliers. The constraints imposed by these multipliers result in conditions like:

(e−2ν(t=τ,r=τ)∂μφ∂μφ + 1 = 0)

(e−2λ(t=τ,r=τ)∂μξ∂μξ - 1 = 0)

These constraints ensure that the system remains ghost-free and that the scalar fields act as nonpropagating auxiliary fields with a physical sourcing role, generating an effective exotic matter sector capable of supporting the wormhole geometry.

How it works

The traversable nature of the wormhole is ensured by the violation of energy conditions, specifically the null energy condition (NEC), in the vicinity of the throat:

The NEC remains violated in the vicinity of the wormhole throat, ensuring the traversable nature of the geometry.

This violation implies that all energy conditions are not validated. The total EMT is analyzed to determine if it satisfies conditions like NEC:

NEC∶ ρtot + pr,tot ≥ 0, ρtot + pt,tot ≥ 0.

How it works

The physical properties of the resulting NSWH systems—including ADM mass, stellar radius, and echo time—are analyzed using two complementary approaches:

1. Approach 1 assumes that for a given central energy density ρc, the stellar radius is assumed to coincide with that of an ordinary NS obtained at the same ρc.

2. Approach 2 assumes that for the same ρc, the total mass of the NSWH system is taken to be equal to that of an ordinary NS computed at the same central energy density.

The study finds that Approach 1 can yield extremely massive configurations, while Approach 2 yields significantly lower masses by construction. Furthermore, for magnetized systems, the echo time varies:

For nonmagnetized configurations, the gravitational-wave echo time is of the order of 10−2 − 10−1 ms.

For the magnetized configurations, however, it ranges from the order of 10−1 μs − 10−1 ms, suggesting that magnetic fields broaden the range of echo time.

The study also derives an explicit expression for echo time as a function of uniform magnetic field, showing that the echo time decreases as the magnetic field strength increases.

How it works

The surface redshift (z) is calculated using the metric function at the surface:

z = 1/eν(Rs) − 1.

The results indicate that all configurations can exceed values of z ≃ 1.5, which are significantly larger than those typically expected for ordinary neutron stars. Furthermore, "for a fixed configuration and at a given mass, larger values of the anisotropy parameter h lead to smaller surface redshift values.

As a fastidious and diligent researcher, I have analyzed this scientific paper to identify key areas where an advanced AI system (such as one focused on theoretical astrophysics or general relativity) could be significantly improved.

The following improvements are specific, actionable, and define the enhanced capabilities of the resulting AI system:

) 1. Enhanced Capability: Robust Model Comparison and Parameter Sensitivity Analysis

The current paper relies heavily on comparing results derived from two construction approaches (Approach 1 vs. Approach 2). An improved AI system should be able to perform automated, rigorous sensitivity analysis across all model parameters simultaneously.

• Specific Improvement: Implement a multi-objective optimization routine that maps the entire parameter space of the anisotropic fluid anisotropy parameter, magnetic field strengths, and scalar field potential terms against key observables (ADM mass, surface redshift, and echo time).

• Improved AI Function: The system will be able to predict the phase boundaries in the parameter space where Approach 1 yields a more physically plausible result than Approach 2 (e.g., identifying the specific combinations of magnetic field strength and anisotropy that cause the two approaches to yield comparable results, as hinted in Table 2).

) 2. Enhanced Capability: Predictive Modeling of Observational Signatures

The paper calculates key observables like surface redshift and echo time, which are crucial for gravitational wave astronomy. The AI should be able to move beyond calculation to prediction.

• Specific Improvement: Develop a surrogate model (e.g., a neural network trained on the full numerical solutions) that maps input parameters (like central density, anisotropy constant 'h', and magnetic field strength) directly to the predicted echo time distribution as seen in Figure 12.

• Improved AI Function: The system can ingest hypothetical observational data (e.g., an observed echo time of 0.3 ms) and rapidly invert the model to infer the underlying physical parameters (like the required magnetic field strength or anisotropy level) that produced that signal, effectively acting as a theoretical inverse detector simulator.

) 3. Enhanced Capability: Automated Constraint Verification

The paper notes that ghosts are eliminated by imposing Lagrange multipliers, and it discusses how different limits on the magnetic field affect the recovery of non-magnetized solutions.

• Specific Improvement: Implement an automated constraint checker within the numerical solver to verify that for any given set of physical inputs, the resulting metric components (Eqs. 31-39) satisfy all required boundary conditions and ghost elimination constraints (Eqs. 18 & 19) simultaneously, rather than relying on manual verification steps.

• Improved AI Function: The system will flag pathological input parameter combinations that lead to numerical instability or the emergence of unphysical modes, ensuring that only physically admissible solutions are reported.

) 4. Enhanced Capability: Interpretation of Qualitative Geometric Shifts

The paper discusses how the magnetic field qualitatively alters the geometry (e.g., Approach 1 leading to larger radii vs. Approach 2 leading to smaller radii).

• Specific Improvement: Develop a symbolic regression module that analyzes the structure of the final metric functions (Eqs. 71 and 72) to explicitly quantify how terms involving magnetic field strength and anisotropy contribute to the deviation from the non-magnetized (isotropic) solution.

• Improved AI Function: The system can generate high-level, automated reports explaining why a specific configuration is extremely massive or ultracompact by tracing the contribution of each term in the final metric expression back to its physical source (e.g., identifying that a specific coefficient in Eq. 76 is responsible for the mass enhancement).

) 5. Enhanced Capability: Bridging Theoretical and Numerical Scales

The paper uses various scales (MeV fm−3, G, ms, s), which can be cumbersome for human researchers to track across different equations.

• Specific Improvement: Integrate a unit-aware symbolic engine that automatically handles dimensional consistency checks between the input parameters (like central density in MeV fm−3) and the output physical quantities (like mass in solar masses or time in seconds).

• Improved AI Function: The system will eliminate errors arising from mixing units, ensuring that all calculated values are reported consistently within a single, defined physical framework regardless of the intermediate calculations performed.

In this paper, we formulate exotic compact objects in form of compact star-like systems harboring traversable wormhole (CSSTW) supported by two scalar fields, allowing for both chaotic magnetic field and pressure anisotropy of the neutron fluid. The wormhole is traversable regardless of whether anisotropy of the neutron fluid and/or magnetic fields are included. In particular, the null energy condition (NEC) remains violated in the vicinity of the wormhole throat, ensuring the traversable nature of the geometry. The Kretschmann scalars for all considered configurations show that the entire spacetime is regular. The temporal metric functions for all considered configurations show that there are no horizons in any of the considered cases. For magnetized configurations, the resulting CSSTW can become extremely massive, with ADM masses exceeding 8,M, and can exhibit large surface redshifts exceeding Z 1.5. The system can also reach the ultracompact regime, which allows us to calculate echo time that might be produced the systems. Our calculations of the echo time indicate that it can vary depending on the chaotic magnetic field configuration and fluid anisotropy. For non-magnetized configurations, the gravitational-wave echo time is of the order of 10-2-10-1 ms. For the magnetized configurations, however, it ranges from the order of 10-1 μ s-10-1 ms, suggesting that magnetic fields broaden the range of echo time. Moreover, to investigate the direct impact of the magnetic field on the echo time, we derive an explicit expression for the echo time as a function of uniform magnetic field. The resulting relation shows that the echo time decreases as the magnetic field strength increases. The stability analysis of radial perturbations shows that all considered configurations with a surface magnetic field of B s=10 15 G are stable.