Rotation slows simulated wormhole collapse, but lasting stability remains unproven

A theoretical throat under stress

Ellis–Bronnikov wormholes are mathematical descriptions of a throat connecting two distant ends of spacetime. In this model, a phantom scalar field holds the throat open. Its kinetic term has the opposite sign from that of a conventional scalar field, allowing the unusual energy conditions required by the throat. The study concerns this particular theoretical matter model, not an observed wormhole.

Without rotation, these wormholes are unstable: a small disturbance can make the throat collapse into a black hole or expand. Earlier calculations that approximate slow rotation suggested that spin weakens the radial instability. The new work investigates what happens when rotating configurations evolve beyond that approximation.

Building and checking the simulations

The researchers first constructed stationary rotating wormholes using an independent spectral solver. This method represents the unknown gravitational fields through mathematical expansions and adjusts their coefficients to satisfy the equations. They built both symmetric configurations, with equivalent ends, and asymmetric “drainholes,” whose ends differ.

Published symmetric solutions provided a benchmark. Additional checks used relationships that the solver did not directly enforce, including consistency conditions from Einstein’s equations. These tests also exposed a misprint in a previously published equation. According to the paper, the earlier authors confirmed that their numerical programs used the correct equation, so their results were unaffected.

The team then transferred the asymmetric configurations onto a three-dimensional numerical grid and evolved them using the GRTeclyn relativity code. Most runs received no deliberately added disturbance: small errors introduced by representing continuous fields on a finite grid supplied the perturbations. Tests at multiple resolutions examined whether the measured behavior persisted as the grid became finer.

Accurate starting configurations mattered. When the researchers instead used backgrounds approximated only through second order in spin, the omitted terms themselves triggered the instability. That result highlights a numerical hazard: an apparent physical response can originate in the approximation used to build the initial wormhole.

Slower collapse and occasional expansion

Along the collapsing sequence, rotation increased the time required for a radial disturbance to grow. The measured e-folding time—the interval over which an exponentially growing disturbance increases by a factor of about 2.7—rose from 5.4 code-time units without rotation to 13.3 in a rotating model. These are simulation units, not a specified number of seconds.

Some intermediate-spin simulations instead expanded. For one configuration, changing resolution and boundary treatment changed whether it shrank or expanded. Separate tests with deliberately added disturbances also demonstrated that the perturbation’s sign can select the direction of departure. Expansion therefore does not establish stability or, by itself, identify a separate unstable mode.

The fastest evolved model had an equatorial rotation parameter of 0.90, defined using the throat’s equatorial radius and angular velocity. Its area-based radius drifted by less than 0.007% through time 150 at all three tested resolutions. That duration corresponds to about 28 e-folding times of the nonrotating reference instability. Two other rapidly rotating models showed no growing radial departure during shorter reliable intervals.

Waves—and unresolved risks

Collapsing rotating throats emitted a quadrupolar gravitational-wave burst symmetric around the rotation axis. Between the two rotating cases compared, the radiated energy relative to the initial mass increased from about 3.3 parts in ten million to eight parts in ten million. These are simulated signals, not detections.

The strongest conclusion remains limited: rotation slowed collapse, and selected high-spin examples showed no detectable growing radial departure over the tested times. A slower instability could emerge later. Initially axisymmetric data also do not establish resistance to disturbances that break rotational symmetry. The paper specifically notes the possibility of a slow nonaxisymmetric instability associated with an ergoregion.

Only the asymmetric drainhole family was evolved; symmetric configurations served as validation cases. Numerical breakdown also prevented reliable throat measurements across part of the intermediate-spin range. Finally, a fitted collapse rate extrapolated to zero is not a measured stability boundary. The preprint offers evidence of prolonged radial quiet, not proof of a permanently stable wormhole.