Wormhole Dynamics: Nonlinear Collapse and Gravitational-Wave Emission

Abstract

We present 3D numerical-relativity evolutions of the unstable Ellis-Bronnikov wormhole using GRTeclyn, starting from exact isotropic initial data for the coupled Einstein-phantom-scalar system. With a flat initial lapse (alpha=1) and full phantom support, truncation-level noise eventually drives the rarefactive instability and rapid throat expansion. To force a clean collapse while breaking spherical symmetry, we reduce the phantom stress-energy support to S_support=0.5 and add a quadrupolar scalar-field perturbation (A_phi=+0.02, sigma_phi=0.5). The resulting compressive evolution forms a trapped surface and emits a gravitational-wave signal whose peak propagates between extraction radii at v approx c, distinct from superluminal CCZ4 constraint modes. After horizon formation the swallowed phantom matter triggers a violent rebound ("phantom bounce") that launches an outward curvature shock. For the moderate perturbation amplitude simulated here, an intermediate-mass (10^3 solar mass) wormhole at D=1 Mpc falls slightly below the Advanced LIGO design sensitivity; detection requires either closer sources, larger initial asymmetries, or next-generation detectors.

Figures (7)

• Figure 1: Embedding diagram illustrating the two instability pathways: compressive collapse (top) and rarefactive expansion (bottom). Note that classical GR evolution mathematically preserves the underlying spatial topology ($\mathbb{R} \times S^2$). The "pinch-off" depicts a metric degeneration where the throat's areal radius shrinks and an apparent horizon forms, severing causal contact between the two asymptotic regions without tearing the manifold itself.
• Figure 2: Diagnostics of the unperturbed, noise-driven evolution ($A_\phi{=}0$, $b_0{=}0.5$, $\alpha(t{=}0){=}1$). (a)$\min(\alpha)$ remains perfectly flat near $1.0$ during the static phase, but undergoes "anti-collapse" (rising above $1.0$) during late-time inflation, as the moving-puncture gauge fails to handle the expanding geometry. (b)$\min(\chi)$ sits at the $10^{-8}$ floor until high-frequency numerical noise from the compactified origin disrupts the grid. (g)$R_{\rm areal,min}$ sits in perfect saddle-point equilibrium at exactly $0.50$ for the first $t \approx 1.5M$, before grid noise knocks it into the expansion branch, causing exponential growth. (h)$dR_{\rm areal}/dt$ starts at exactly zero, then accelerates continuously to $v > 0.6c$ as the throat inflates. (j, k) The scalar field momentum $\Pi$ remains exactly zero while the wormhole is static, confirming perfect analytical initial balance, but grows rapidly once the inflating geometry begins to shear the scalar field. (l) Instability growth rate ($\lambda\approx 9.012\, M^{-1}$): The departure from equilibrium $\Delta R_{\rm areal}$ reveals a violent, exponential inflationary runaway.
• Figure 3: Fine-level diagnostics of the perturbed collapse ($S_{\rm support}=0.5$, $A_\phi=+0.02$). (g) The throat areal radius rapidly plunges to $\sim 0.14$, but physically rebounds at $t \approx 4M$ due to the extreme phantom pressure, expanding to a plateau of $\sim 0.28$. (k) The scalar momentum $\Pi$ starts exactly at zero and is dynamically generated to $\sim 0.4$ by the initial crush. (d, a) The apparent horizon proxy $r_{\rm AH}$ forms rapidly, dips, and then significantly inflates during the phantom bounce. At $t \approx 18.5M$, the interior shockwave completely destroys the trapped surface ($r_{\rm AH} \to 0$) and drives the minimum lapse $\alpha$ into the $10^{-10}$ numerical floor. (c) The maximum extrinsic curvature $|K|$ grows steadily at late times, reflecting the intensifying interior shockwave.
• Figure 4: Gravitational-wave extraction analysis ($\Psi_4$) for the perturbed collapse. (a, b) Raw and retarded-time waveforms for the dominant $\ell=2, m=0$ mode. The perfect alignment in retarded time ($t - R_{\rm ext}$) confirms a coherent outgoing wavefront, with the late-time tail fit to a QNM template ($f \approx 0.403, \tau \approx 5.03 \times 10^6$). The effectively infinite damping time is an artifact of the grid being contaminated by the expanding phantom bounce, which prevents the remnant from settling into a quiescent state. (c) The Power Spectral Density (PSD) peaks strongly at low frequencies ($f \sim 0.5 M^{-1}$). (d) Tracking the waveform peaks yields a propagation speed of $v \approx 0.995c$ between $R=12$ and $R=16$, confirming physical radiation rather than superluminal gauge modes. (e) A Continuous Wavelet Transform (CWT) spectrogram of the $R=12$ extraction, visualizing the broadband initial crush at $t-R_{\rm ext} \approx 0$ transitioning into a constant-frequency QNM ringdown. (f) The characteristic strain projection. An intermediate-mass wormhole ($1000\, M_\odot$) at $1$ Mpc produces a signal peaking in the most sensitive frequency band ($100-300$ Hz) of the Advanced LIGO design sensitivity, though closer proximity or a larger perturbation amplitude is required for detection.
• Figure 5: Evolution snapshots of the trace of the extrinsic curvature ($K$) in the $z{=}0$ plane for the perturbed collapse ($S_{\rm support}=0.5$, $A_\phi=+0.02$). At $t=0.10$, the initial scalar perturbation has already generated a prompt $K<0$ (red) response at the origin. By $t=5.01$, the global reduction in phantom support drives the initial collapse, generating a compressive, positive-$K$ core. Between $t=10.01$ and $t=15.01$, the interior "phantom bounce" initiates, launching a massive interior expansion ($K<0$, dark red) that drives an outward-propagating compressive shockwave ($K>0$, blue ring) driven by the extreme repulsive pressure of the crushed phantom matter. By $t=22.50$, this shockwave dominates the grid, eventually disrupting the local coordinate foliation.