Protection without teeth: semiclassical chronology protection on the Ori time machine

Hawking’s chronology protection conjecture is usually stated for horizons that carry a hypersurface of closed null geodesics, or for compactly generated horizons. The Ori time machine is a leading candidate whose horizon is probably, but not proven, non-compactly generated. We compute the image-series energy density and assemble the full tensor on the Ori geometry, using the plane-wave Huygens truncation of the Hadamard form, with connecting geodesics solved as boundary-value problems.

The full tensor changes the sign of the headline quantity. The normalized image-direction eigenvalue is negative, about minus three halves of the positive energy density, and follows the Misner epsilon-to-the-minus-two law on approach to the CTC boundary. A locus correction places the local eikonal horizon below the timelike surface T = f; the stress at that horizon is finite and remains on its rising asymptote. A nine-point scan over rho from 0.10 to 0.50 confirms the same epsilon-to-the-minus-two asymptote and an a-to-the-minus-four scaling. The ratio to the formal past-horizon on-partial-V extrapolation is 6.6 times 10 to the minus five. A true singularity remains on the single closed null geodesic N, and by inference on the Cauchy horizon.

The state-choice section reports the 4D Misner result: the Li-Gott adapted vacuum is exactly stress-free at b = 2 pi, and the 2D statement that the adapted state is worse for every Lambda does not generalize. The Ori f not equal zero core is VSI, so its local trace anomaly vanishes; the Rindler modes are not solutions, and the adapted state on the Ori quotient is not constructed.

Key results

• Full image-series tensor: negative image-direction eigenvalue, about minus three halves of the positive energy density.
• Nine-point Cauchy-horizon scan: finite, on the epsilon-to-the-minus-two asymptote, with an a-to-the-minus-four scaling.
• The positive proxy energy density is about 5.3 times 10 to the minus eighteen joules per cubic metre at a = 0.02 for a metre-scale machine, 55.4 to 55.7 orders below the curvature scale.
• 4D Misner adapted vacuum exactly stress-free at b = 2 pi; the Ori f not equal zero state remains open.
• The conclusion is conditional on non-compact generation, which Ori says must be verified.

Status and limits

This is a 21-page final content draft. The 4D backreaction endpoint, Ori state selection on the f not equal zero quotient, the quotient Cauchy problem and the full gauge-complete nonlinear stability remain open. The paper has not been submitted or peer reviewed.