Stationary Particle Creation and Entanglement in the Rotating Teo Wormhole: A Quantum Mode-Mixing Approach

Abstract: Rotating traversable wormholes allow the effects of frame dragging and rotation to be studied in the absence of event horizons. We develop a quantum field theoretic treatment of massless scalar perturbations in the rotating Teo spacetime. This spacetime is an exact, stationary, horizonless wormhole connecting two asymptotically flat regions. Using the Bogoliubov transformation formalism, we construct in'' andout'' mode solutions defined on the two asymptotic regions and compute the Bogoliubov coefficients that quantify vacuum mode mixing. The effective radial potential induced by rotation and frame dragging forms an asymmetric scattering barrier. This geometric asymmetry allows an exact analytic evaluation of reflection and transmission amplitudes via the barrier-penetration exponent. This results in closed-form expressions for the Bogoliubov coefficients, the mean particle number, and the two-mode entanglement entropy as functions of the rotation parameter. The resulting amplification arises at the level of quantum Bogoliubov mode mixing and vacuum squeezing, rather than classical superradiant flux enhancement. Since this spacetime is stationary, particle creation originates from geometric asymmetry and boundary conditions, and not from explicit time dependence. Co-rotating and counter-rotating modes experience inequivalent scattering. This renders the process intrinsically non-reciprocal. We identify this mechanism as a stationary, geometric analogue of the Asymmetric Dynamical Casimir Effect (ADCE). In the rotating Teo geometry, rotation and frame dragging play the role that moving boundaries play in the dynamical Casimir effect, acting as the source of asymmetric vacuum mode mixing.

• The paper demonstrates the emergence of quantum particle creation, two-mode squeezing, and inter-asymptotic-region entanglement in the rotating Teo wormhole using a mode-mixing approach.
• The analysis relies heavily on the locally measured frequency and effective potential derived from the wormhole's geometry, determining scattering and focal characteristics.
• Using canonical quantization and SU(1,1) Bogoliubov mixing precludes horizon or explicit time dependence for quantum phenomena.

The paper develops a quantum field–theoretic treatment of massless scalar perturbations in the rotating Teo wormhole (2603.06822), an exact, stationary, axisymmetric, horizonless traversable wormhole with two asymptotically flat regions. The central claim is that quantum particle creation, two-mode squeezing, and inter-asymptotic-region entanglement arise from frame dragging alone—without event horizons and without explicit time dependence of the metric. The mechanism is identified as a stationary geometric analogue of the Asymmetric Dynamical Casimir Effect (ADCE), with rotation playing the role that moving boundaries play in conventional dynamical Casimir systems.

Geometry and scalar dynamics

The analysis uses Teo's metric with the simplified profile $N(r)=1$, $K(r,\theta)=1$, $b(r)=b_0^2/r$, and frame-dragging angular velocity $\Omega(r)=2a/r^3$. Separation of the complex Klein–Gordon field into modes $$e^{-i\omega t}e^{im\phi}S_{\omega m}(\theta)R_{\omega m}(r)$$ exploits the two Killing symmetries, yielding conserved $(\omega,m)$ sectors. The key kinematic quantity is the locally measured frequency

$\omega_{\mathrm{loc}}(r)=\omega-m\Omega(r),$

whose sign controls both the Klein–Gordon norm and superradiant kinematics. After introducing a tortoise coordinate and rescaling the radial function, the radial equation reduces to a Schrödinger-like form with a real effective potential,

$$V_{\mathrm{eff}}(r)=\frac{m^2}{r^2}+\frac{b_0^2}{r^4}+\frac{4am\omega}{r^3}-\frac{4a^2m^2}{r^6},$$

which forms a finite barrier peaking near the throat and decaying at both asymptotic ends. The reality of this potential guarantees self-adjointness and global unitarity of the scattering problem—a structural consequence of horizonlessness that shapes all subsequent results.

Classical scattering: unitarity without gain

Using WKB matching through Airy functions at the two turning points bounding the throat-centered forbidden region, the paper obtains closed-form transmission and reflection probabilities,

$$|\mathcal{T}_{\omega m}|^2=\frac{1}{1+e^{2\Theta}}, \qquad |\mathcal{R}_{\omega m}|^2=\frac{1}{1+e^{-2\Theta}},$$

with barrier-penetration exponent $\Theta=\int_{r_{*t1}}^{r_{*t2}}\kappa(r_*)\,dr_*$, supplemented by the Schutz–Will barrier-top refinement $K(r,\theta)=1$0. These satisfy exact flux balance $K(r,\theta)=1$1.

A notable and somewhat counterintuitive result follows: although the ergoregion supplies negative Killing-energy modes satisfying $K(r,\theta)=1$2, classical scalar-wave scattering exhibits no net superradiant amplification ($K(r,\theta)=1$3). Because the geometry is horizonless and symmetric between its two asymptotic regions, negative-energy flux entering the ergoregion on one side is transported through the throat and re-emerges as positive flux on the other. The ergoregion thus provides the kinematic structure for superradiance without the dissipative absorption required for Kerr-type classical gain. This is a sharp contrast with black-hole physics and is stated explicitly by the authors as a distinguishing feature of the Teo background.

Quantization and SU(1,1) Bogoliubov mixing

Canonical quantization proceeds via the conserved but indefinite Klein–Gordon inner product, regulated by restricting the tortoise coordinate to $K(r,\theta)=1$4 before taking $K(r,\theta)=1$5—an infrared regularization analogous to box normalization, not an ultraviolet renormalization. The sign of the regulated inner product tracks $K(r,\theta)=1$6, so modes entering the ergoregion acquire negative norm even at positive asymptotic frequency. This indefiniteness forces an SU(1,1) Bogoliubov transformation between the "in" and "out" mode bases associated with the two asymptotic regions:

$K(r,\theta)=1$7

The authors identify $K(r,\theta)=1$8 and $K(r,\theta)=1$9, establishing a precise algebraic bridge between classical scattering data and quantum mode mixing. The mean out-particle number in the in-vacuum is the standard result $b(r)=b_0^2/r$0, derived in detail from the number-operator expansion.

Entanglement across the asymptotic regions

Pairing modes $b(r)=b_0^2/r$1 with $b(r)=b_0^2/r$2, the squeeze operator $b(r)=b_0^2/r$3 generates a two-mode squeezed vacuum whose Fock expansion is

$b(r)=b_0^2/r$4

obtained via the SU(1,1) disentangling theorem. Tracing over one region yields a diagonal reduced density matrix with geometric eigenvalues $b(r)=b_0^2/r$5, $b(r)=b_0^2/r$6, giving von Neumann entropy

$b(r)=b_0^2/r$7

A single squeezing parameter therefore simultaneously controls particle production, entanglement entropy, and the classical reflection coefficient $b(r)=b_0^2/r$8. The Wightman function decomposes into an incoherent piece proportional to $b(r)=b_0^2/r$9 (particle creation) and off-diagonal pieces proportional to $\Omega(r)=2a/r^3$0 scaling as $\Omega(r)=2a/r^3$1 (coherent pair correlations), with cross-region correlators $\Omega(r)=2a/r^3$2 vanishing identically unless $\Omega(r)=2a/r^3$3. Spectral observables confirm that particle production is diagonal in $\Omega(r)=2a/r^3$4, entirely governed by the analytically determined coefficients.

Nonreciprocity and the ADCE correspondence

Because $\Omega(r)=2a/r^3$5 introduces directional dependence into $\Omega(r)=2a/r^3$6, co-rotating and counter-rotating modes scatter inequivalently despite strict stationarity—the process is intrinsically nonreciprocal. The paper maps this onto the ADCE formalism: the two-mode Bogoliubov matrix of asymmetric Casimir systems, with coefficients $\Omega(r)=2a/r^3$7, is identified element-wise with the wormhole's $\Omega(r)=2a/r^3$8. The distinction is emphasized carefully: the Teo wormhole is not a dynamical Casimir system, since no temporal modulation occurs; rather, frequency mixing is replaced by energy-sign mixing controlled by rotation, making the geometry a static, nonreciprocal SU(1,1) amplifier.

Semiclassical support

Connecting to Teo's original observation that the throat requires null energy condition violation, the paper argues phenomenologically that Casimir energy densities in rotating Teo backgrounds, $\Omega(r)=2a/r^3$9, provide a viable exotic-matter candidate. The squeezed-state expectation value of $$e^{-i\omega t}e^{im\phi}S_{\omega m}(\theta)R_{\omega m}(r)$$0 contains both a positive particle contribution $$e^{-i\omega t}e^{im\phi}S_{\omega m}(\theta)R_{\omega m}(r)$$1 and an oscillatory interference term $$e^{-i\omega t}e^{im\phi}S_{\omega m}(\theta)R_{\omega m}(r)$$2, which can yield locally negative energy densities consistent with quantum energy inequalities. The authors are explicit that this treatment is schematic: no self-consistent solution of the semiclassical Einstein equations or evaluation of backreaction is performed.

Limitations and open questions

Several limitations are conceded directly. The analytic scattering results rest on leading-order WKB approximation, valid away from the barrier top except where the Schutz–Will refinement applies; no numerical validation against exact solutions of the radial equation is provided. The regularization argument addresses infrared issues only, and the stress-energy discussion remains at the level of order-of-magnitude estimates. Ergoregion instabilities—known to afflict horizonless rotating geometries—are cited but not analyzed; whether the stationary squeezed state constructed here survives such instabilities is left open. Specific unresolved questions include: how electromagnetic and gravitational perturbations modify the SU(1,1) mode-mixing structure; whether slowly time-varying rotation $$e^{-i\omega t}e^{im\phi}S_{\omega m}(\theta)R_{\omega m}(r)$$3 produces genuinely dynamical particle creation interpolating toward the true DCE; and what backreaction the computed $$e^{-i\omega t}e^{im\phi}S_{\omega m}(\theta)R_{\omega m}(r)$$4 exerts on the wormhole's long-term stability.

Conclusion

This work demonstrates within a single analytically tractable horizonless geometry that neither horizons nor explicit time dependence are required for quantum particle creation: stationary rotation, global topology, and negative-Killing-energy channels suffice. Classical scattering remains strictly unitary while quantum Bogoliubov mixing produces two-mode squeezing and inter-universe entanglement, unifying superradiant kinematics, Casimir-type emission, and quantum amplification under common SU(1,1) control. The framework provides a clean theoretical laboratory for nonreciprocal quantum amplification driven purely by spacetime structure, pending resolution of the stability and backreaction questions noted above.