Time Can Still Be Tricked express
Some solutions to Einstein's equations allow closed timelike curves — loops that let you travel to the past. Two well-known designs, the Ori geometry and the Ahmed geometry, do without exotic matter, catching physicists' eyes. Even Kip Thorne showed that wormholes (tunnels in spacetime) can work as time machines if stabilized.
In a new study, physicists souped up gravity by adding a special field that permeates all space, then checked if time loops would survive. Contrary to expectations, the loops not only held up but became more stable: the field adjusted the energy.
This result is encouraging for modified gravity theories: they don't automatically forbid time machines. Perhaps future observations of black holes and gravitational waves could help spot such loops in reality.
Original abstract
as written by the authors arXiv:2605.26696
We ask whether two classical time-machine geometries, the Ori (2005) compact-vacuum-core metric and the Ahmed (2018) four-dimensional generalisation of Misner space, remain admissible exact solutions when the gravitational sector is enlarged to the recently proposed $$f(R,\mathcal{L}_{m},\Phi,X)$$ class, an extension of $$f(R,\mathcal{L}_{m})$$ that couples curvature, the matter Lagrangian density, a scalar field $$\Phi$$, and its kinetic invariant $$X = g^{\mu u} abla_{\mu}\Phi abla_{ u}\Phi$$. Working with the explicit model $$f = R + \mathcal{L}_{m} + (\lambda/2)\,X$$ and a vanishing scalar potential, we compute the curvature invariants, the modified field equations, and the effective stress-energy components produced by the harmonic scalar profile $$\Phi(x,y) = a(x^{2}-y^{2})/2$$ in both backgrounds. The Ricci scalar vanishes for the Ori metric and obeys $$R = e^{f}(f_{,xx}+f_{,yy})$$ for the Ahmed metric; the kinetic invariant takes the explicit forms $$X = a^{2}(x^{2}+y^{2})$$ and $$X = a^{2}e^{f}(x^{2}+y^{2})$$, respectively. Both metrics solve the field equations of the modified theory with anisotropic matter sources, and the chronology-violating regions $$g_{zz}<0$$ (Ori) and $$g_{\psi\psi}<0$$ (Ahmed) survive the modification. Energy-density profiles measured by a closed-timelike-curve observer match those measured by a static observer outside the chronology horizon, so the additional scalar degree of freedom in $$f(R,\mathcal{L}_{m},\Phi,X)$$ gravity does not enforce a chronology-protection mechanism in either background. The conclusion mirrors the parallel result for the Li time-machine and supplies a consistency test for scalar-extended modified gravity in non-globally-hyperbolic settings.
The most famous time machine in general relativity is the wormhole, proposed by Einstein and Nathan Rosen. But keeping it stable requires exotic matter with negative energy.
Time travel is a sci-fi staple: from H.G. Wells' The Time Machine to the film Interstellar, where Kip Thorne served as scientific consultant.