Rotating Teo Spacetime

• Rotating Teo spacetime is a stationary, axisymmetric, traversable wormhole geometry featuring a throat, spin parameter, and frame dragging that distinguishes it from Kerr black holes.
• It serves as a laboratory for analyzing gravitational lensing, test-particle dynamics, and high-energy collisions, with applications spanning plasma optics and quantum-field phenomena.
• Analytic studies reveal practical insights into energy extraction via the Penrose process, nonreciprocal scattering, and an emergent conformal structure in AdS extensions.

The rotating Teo spacetime is a stationary, axisymmetric traversable wormhole geometry introduced by Teo and typically written in Boyer–Lindquist–like coordinates $(t,r,\theta,\phi)$. In its asymptotically flat realizations it is characterized by a throat at a minimum areal radius $r=b$ or $r=r_{0}$, a spin parameter $a$, and frame dragging with angular velocity $\omega(r)=2a/r^{3}$. Unlike Kerr, it may possess an ergoregion without an event horizon, and its global structure connects two asymptotically flat regions across a regular throat. Subsequent work has treated the rotating Teo geometry as a laboratory for weak-field lensing, test-particle dynamics, gyroscope precession, high-energy collisions, plasma optics, and quantum-field-theoretic phenomena, including an asymptotically AdS extension with two timelike boundaries (Jusufi et al., 2017, Chakraborty et al., 2016, Tsukamoto et al., 2015, Radhakrishnan et al., 14 Feb 2026).

1. Metric formulations and parameter choices

A common form of the rotating Teo line element is

$$ds^{2} = -\,N^{2}(r,\theta)\,dt^{2} +\frac{dr^{2}}{1-\dfrac{b(r,\theta)}{r}} +r^{2}K^{2}(r,\theta)\,d\theta^{2} +r^{2}K^{2}(r,\theta)\sin^{2}\theta\,(d\phi-\omega(r,\theta)\,dt)^{2}.$$

In the asymptotically flat setting, the large-$r$ conditions are

$$N\to1,\qquad K\to1,\qquad \frac{b}{r}\to0,\qquad \omega\to\frac{2J}{r^{3}}+O(r^{-4}),$$

with $J$ the total angular momentum. On the two half-spaces $r>r_{\rm throat}$, two copies are glued across the throat (Bezdekova et al., 2022).

Several specific realizations are used in the literature. One standard “Teo-choice” sets

$r=b$0

with $r=b$1 the throat radius, $r=b$2 the total angular momentum parameter, and $r=b$3 a constant that is often set to $r=b$4 for simplicity (Chakraborty et al., 2016, Tsukamoto et al., 2015). In the weak-field lensing treatment, restriction to the equatorial plane $r=b$5 gives $r=b$6, so the metric reduces to

$r=b$7

(Jusufi et al., 2017).

A separate asymptotically flat model used for quantum mode mixing adopts

$r=b$8

so that the nonrotating limit $r=b$9 reproduces the Morris–Thorne wormhole with throat radius $r=r_{0}$0 (Radhakrishnan et al., 6 Mar 2026).

An AdS-embedded, slowly rotating version is also studied, with

$r=r_{0}$1

and asymptotic behavior

$r=r_{0}$2

so that global AdS$r=r_{0}$3 is recovered as $r=r_{0}$4 (Radhakrishnan et al., 14 Feb 2026).

2. Topology, regularity, and the ergoregion

The rotating Teo spacetime is constructed to be traversable. In the asymptotically flat Teo-choice, traversability requires $r=r_{0}$5 for all $r=r_{0}$6, so no event horizon forms, and the flare-out condition at the throat is satisfied because $r=r_{0}$7 implies $r=r_{0}$8 (Jusufi, 2018). In the collisional Penrose-process treatment, $r=r_{0}$9 diverges at $a$0, marking the throat, but all scalar invariants remain finite there; the throat is therefore a regular coordinate singularity rather than a curvature singularity (Tsukamoto et al., 2015).

A proper-radial coordinate can be introduced as

$a$1

so that the throat sits at $a$2 and each asymptotically flat region at $a$3 (Tsukamoto et al., 2015). This makes explicit the two-sided topology of the wormhole.

The ergoregion is defined by $a$4. For the Teo-choice metric functions this yields

$a$5

so that, when present, the ergoregion occupies

$a$6

forming a tube around the equatorial plane; no ergoregion exists near the poles $a$7 (Chakraborty et al., 2016). Equivalently, an ergoregion-free cone exists inside

$a$8

(Chakraborty et al., 2016). A closely related presentation states that the ergosurface lies between $a$9 and $\omega(r)=2a/r^{3}$0, provided $\omega(r)=2a/r^{3}$1 (Tsukamoto et al., 2015).

A recurrent point of confusion is the status of $\omega(r)=2a/r^{3}$2. In the rotating Teo geometry, $\omega(r)=2a/r^{3}$3 defines the outer boundary of the ergoregion, not a horizon. This sharply distinguishes the spacetime from rotating black holes, even though both geometries exhibit frame dragging and negative-energy states inside the ergoregion (Tsukamoto et al., 2015).

3. Geodesic structure and effective potentials

On the equatorial plane $\omega(r)=2a/r^{3}$4, stationarity and axial symmetry provide the conserved energy $\omega(r)=2a/r^{3}$5 and angular momentum $\omega(r)=2a/r^{3}$6. In the proper-radial description one defines the corotating energy

$\omega(r)=2a/r^{3}$7

which encodes the forward-in-time condition (Tsukamoto et al., 2014).

For a test particle of rest mass $\omega(r)=2a/r^{3}$8, the radial motion is governed by

$\omega(r)=2a/r^{3}$9

Motion is allowed only where $$ds^{2} = -\,N^{2}(r,\theta)\,dt^{2} +\frac{dr^{2}}{1-\dfrac{b(r,\theta)}{r}} +r^{2}K^{2}(r,\theta)\,d\theta^{2} +r^{2}K^{2}(r,\theta)\sin^{2}\theta\,(d\phi-\omega(r,\theta)\,dt)^{2}.$$0 (Tsukamoto et al., 2014). In the equivalent affine-parameter formulation,

$$ds^{2} = -\,N^{2}(r,\theta)\,dt^{2} +\frac{dr^{2}}{1-\dfrac{b(r,\theta)}{r}} +r^{2}K^{2}(r,\theta)\,d\theta^{2} +r^{2}K^{2}(r,\theta)\sin^{2}\theta\,(d\phi-\omega(r,\theta)\,dt)^{2}.$$1

with $$ds^{2} = -\,N^{2}(r,\theta)\,dt^{2} +\frac{dr^{2}}{1-\dfrac{b(r,\theta)}{r}} +r^{2}K^{2}(r,\theta)\,d\theta^{2} +r^{2}K^{2}(r,\theta)\sin^{2}\theta\,(d\phi-\omega(r,\theta)\,dt)^{2}.$$2 for timelike and null motion (Chakraborty et al., 2016).

Inside the ergoregion, orbits with $$ds^{2} = -\,N^{2}(r,\theta)\,dt^{2} +\frac{dr^{2}}{1-\dfrac{b(r,\theta)}{r}} +r^{2}K^{2}(r,\theta)\,d\theta^{2} +r^{2}K^{2}(r,\theta)\sin^{2}\theta\,(d\phi-\omega(r,\theta)\,dt)^{2}.$$3 exist provided $$ds^{2} = -\,N^{2}(r,\theta)\,dt^{2} +\frac{dr^{2}}{1-\dfrac{b(r,\theta)}{r}} +r^{2}K^{2}(r,\theta)\,d\theta^{2} +r^{2}K^{2}(r,\theta)\sin^{2}\theta\,(d\phi-\omega(r,\theta)\,dt)^{2}.$$4. These negative-energy geodesics are bound and cannot escape to infinity (Tsukamoto et al., 2015). This fact underlies Penrose-type energy extraction in the wormhole setting.

Null circular photon orbits are also present. For equatorial motion, imposing $$ds^{2} = -\,N^{2}(r,\theta)\,dt^{2} +\frac{dr^{2}}{1-\dfrac{b(r,\theta)}{r}} +r^{2}K^{2}(r,\theta)\,d\theta^{2} +r^{2}K^{2}(r,\theta)\sin^{2}\theta\,(d\phi-\omega(r,\theta)\,dt)^{2}.$$5, $$ds^{2} = -\,N^{2}(r,\theta)\,dt^{2} +\frac{dr^{2}}{1-\dfrac{b(r,\theta)}{r}} +r^{2}K^{2}(r,\theta)\,d\theta^{2} +r^{2}K^{2}(r,\theta)\sin^{2}\theta\,(d\phi-\omega(r,\theta)\,dt)^{2}.$$6, and $$ds^{2} = -\,N^{2}(r,\theta)\,dt^{2} +\frac{dr^{2}}{1-\dfrac{b(r,\theta)}{r}} +r^{2}K^{2}(r,\theta)\,d\theta^{2} +r^{2}K^{2}(r,\theta)\sin^{2}\theta\,(d\phi-\omega(r,\theta)\,dt)^{2}.$$7 yields a circular photon radius

$$ds^{2} = -\,N^{2}(r,\theta)\,dt^{2} +\frac{dr^{2}}{1-\dfrac{b(r,\theta)}{r}} +r^{2}K^{2}(r,\theta)\,d\theta^{2} +r^{2}K^{2}(r,\theta)\sin^{2}\theta\,(d\phi-\omega(r,\theta)\,dt)^{2}.$$8

for direct or retrograde equatorial photon orbits (Chakraborty et al., 2016). In the plasma-generalized Hamiltonian treatment, the radial and angular dynamics separate into potentials $$ds^{2} = -\,N^{2}(r,\theta)\,dt^{2} +\frac{dr^{2}}{1-\dfrac{b(r,\theta)}{r}} +r^{2}K^{2}(r,\theta)\,d\theta^{2} +r^{2}K^{2}(r,\theta)\sin^{2}\theta\,(d\phi-\omega(r,\theta)\,dt)^{2}.$$9 and $r$0, with turning points at $r$1 and $r$2, and spherical bound orbits satisfy $r$3 and $r$4 (Bezdekova et al., 2022).

4. Frame dragging and spin precession

The rotating Teo spacetime supports exact Lense–Thirring precession for stationary observers. For the Teo-choice functions, the precession vector can be written explicitly, and its magnitude diverges when

$r$5

that is, on the ergosurface $r$6 (Chakraborty et al., 2016). The divergence is directly tied to the factor $r$7, exactly as in Kerr.

Two limiting directions display qualitatively different strong-field behavior. Along the pole $r$8,

$r$9

so in the strong-field polar regime one has the inverse-$$N\to1,\qquad K\to1,\qquad \frac{b}{r}\to0,\qquad \omega\to\frac{2J}{r^{3}}+O(r^{-4}),$$0 scaling $$N\to1,\qquad K\to1,\qquad \frac{b}{r}\to0,\qquad \omega\to\frac{2J}{r^{3}}+O(r^{-4}),$$1 (Chakraborty et al., 2016). Along the equator $$N\to1,\qquad K\to1,\qquad \frac{b}{r}\to0,\qquad \omega\to\frac{2J}{r^{3}}+O(r^{-4}),$$2,

$$N\to1,\qquad K\to1,\qquad \frac{b}{r}\to0,\qquad \omega\to\frac{2J}{r^{3}}+O(r^{-4}),$$3

which asymptotes to the usual direct-$$N\to1,\qquad K\to1,\qquad \frac{b}{r}\to0,\qquad \omega\to\frac{2J}{r^{3}}+O(r^{-4}),$$4 behavior $$N\to1,\qquad K\to1,\qquad \frac{b}{r}\to0,\qquad \omega\to\frac{2J}{r^{3}}+O(r^{-4}),$$5 (Chakraborty et al., 2016).

A stationary observer with zero angular velocity cannot remain timelike inside the ergoregion. The regularized description uses observers with angular velocity $$N\to1,\qquad K\to1,\qquad \frac{b}{r}\to0,\qquad \omega\to\frac{2J}{r^{3}}+O(r^{-4}),$$6 satisfying

$$N\to1,\qquad K\to1,\qquad \frac{b}{r}\to0,\qquad \omega\to\frac{2J}{r^{3}}+O(r^{-4}),$$7

For this broader observer class, the general spin-precession frequency remains finite throughout the ergoregion, and the parametrization

$$N\to1,\qquad K\to1,\qquad \frac{b}{r}\to0,\qquad \omega\to\frac{2J}{r^{3}}+O(r^{-4}),$$8

gives a closed-form $$N\to1,\qquad K\to1,\qquad \frac{b}{r}\to0,\qquad \omega\to\frac{2J}{r^{3}}+O(r^{-4}),$$9 that is everywhere finite (Chakraborty et al., 2016). The $J$0 case corresponds to ZAMO observers in the discussion of observational signatures.

5. Lensing, optical geometry, plasma propagation, and shadow

Weak-field light bending in the rotating Teo spacetime has been derived by two independent routes: the Gauss–Bonnet theorem on the optical geometry and the standard null-geodesic method. Restricting to the equatorial plane, the null condition can be rewritten in a Finsler–Randers form, and the Gauss–Bonnet theorem yields

$J$1

Approximating the light ray by

$J$2

the leading-order deflection angle is

$J$3

The first term is the static throat contribution, while the second is the spin contribution; the upper and lower signs correspond to retrograde and prograde motion, respectively (Jusufi et al., 2017).

The same structure persists for relativistic massive particles when they are treated as de Broglie wave packets in an isotropic optical metric. Writing the asymptotic particle speed as $J$4, the effective refractive index leads to

$J$5

and the massless limit $J$6 recovers the light-bending result (Jusufi, 2018). Both studies emphasize that the bending angle can be read as a global optical-curvature effect rather than only as a local force-law phenomenon (Jusufi et al., 2017, Jusufi, 2018).

Comparison with Kerr isolates a distinctive signature. In the weak limit,

$J$7

so the wormhole replaces the Kerr mass term $J$8 by the throat term $J$9, and its spin term is independent of any central mass (Jusufi et al., 2017).

In a cold non-magnetized plasma, photon trajectories are governed by the Hamiltonian

$r>r_{\rm throat}$0

Full Hamilton–Jacobi separability requires that $r>r_{\rm throat}$1, $r>r_{\rm throat}$2, $r>r_{\rm throat}$3, and $r>r_{\rm throat}$4 depend on $r>r_{\rm throat}$5 only, together with a plasma frequency of the form

$r>r_{\rm throat}$6

Under these conditions one obtains analytic radial and angular potentials, constructs spherical photon orbits from $r>r_{\rm throat}$7 and $r>r_{\rm throat}$8, and derives the shadow boundary in celestial coordinates (Bezdekova et al., 2022).

6. High-energy collisions and rotational energy extraction

The absence of a horizon does not suppress high-energy processes. For equatorial geodesics, the rotating Teo wormhole admits deep effective potentials, and this enables center-of-mass energies not available in the nonrotating geometry. In the two-particle analysis, the invariant collision energy is

$r>r_{\rm throat}$9

At the throat, in the rotating case with sufficiently small $r=b$00 and appropriately chosen negative angular momenta, the dominant behavior is

$r=b$01

whereas the nonrotating case $r=b$02 remains finite for finite $r=b$03 and $r=b$04 (Tsukamoto et al., 2014).

This kinematics feeds directly into the collisional Penrose process. For two identical particles approaching head-on from opposite asymptotic regions and colliding at the throat, four-momentum conservation can produce one escaping particle with positive energy and one bound particle with negative energy. In the symmetric throat collision,

$r=b$05

and in the flat-potential case $r=b$06 one has $r=b$07 (Tsukamoto et al., 2015). The efficiency can greatly exceed unity for fast rotation $r=b$08, while a deep-potential configuration with $r=b$09 yields $r=b$10 (Tsukamoto et al., 2015).

By contrast, the Kerr collisional Penrose process is described in the same source as having maximal efficiency only a few-tens of percent above unity, with $r=b$11 in the most favorable cases (Tsukamoto et al., 2015). A plausible implication is that the combination of a two-sided throat and negative-energy geodesics creates a qualitatively different extraction channel from the black-hole case.

7. AdS embedding, hidden conformal structure, and quantum mode mixing

In the asymptotically AdS extension, the rotating Teo wormhole has two disconnected timelike AdS conformal boundaries that remain causally connected through the throat. For scalar perturbations,

$r=b$12

separation of variables leads to a radial equation that can be cast into Schrödinger form using the tortoise coordinate

$r=b$13

Near the throat, smoothness implies

$r=b$14

and the radial equation acquires an emergent $r=b$15 structure with quadratic Casimir

$r=b$16

The resulting quasinormal-mode spectrum is

$r=b$17

with $r=b$18 the emergent conformal weight (Radhakrishnan et al., 14 Feb 2026).

The AdS embedding also supports a minimal holographic interpretation. In the large-$r=b$19 geodesic limit, the equal-time cross-boundary two-point function is approximated by

$r=b$20

where $r=b$21 is the regulated length of a spacelike geodesic traversing the wormhole (Radhakrishnan et al., 14 Feb 2026). This construction ties the throat geometry to coupled left/right boundary observables without invoking horizons.

A different quantum extension considers massless scalar perturbations in the asymptotically flat rotating Teo geometry. After separation,

$r=b$22

the radial equation can be written in Schrödinger form with an effective potential that, in the simple model $r=b$23, $r=b$24, $r=b$25, becomes

$r=b$26

Because the term proportional to $r=b$27 changes sign under $r=b$28, the barrier is asymmetric in $r=b$29, producing nonreciprocal scattering (Radhakrishnan et al., 6 Mar 2026).

The in/out bases on the two asymptotic regions are related by an SU(1,1) Bogoliubov transformation,

$r=b$30

with mean particle number

$r=b$31

and two-mode entanglement entropy

$r=b$32

The same study interprets the effect as a stationary, geometric analogue of the Asymmetric Dynamical Casimir Effect. It explicitly distinguishes this phenomenon from Kerr superradiance: in the Teo wormhole there is no horizon, so classical flux amplification is forbidden, while quantum particle creation and entanglement survive through Bogoliubov mode mixing alone (Radhakrishnan et al., 6 Mar 2026).