Wormhole geometries in Einstein-aether theory

Hanif Golchin , Hamid R. Bakhtiarizadeh , Mohammad Reza Mehdizadeh

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Pith reviewed 2026-05-05 05:20 UTC · model claude-opus-4-7

classification 🌀 gr-qc hep-th PACS <parameter name="0">04.20.Jb

keywords wormholeenergyconditionsaethergeometriesthreevaluesconstants

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The pith

Einstein-aether gravity admits traversable wormholes whose throat matter does not require energy-condition violation, and in one coupling class the matter stays well-behaved everywhere outside the throat.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

In ordinary general relativity, a static traversable wormhole forces its matter content to violate the null energy condition at the throat — you need exotic matter. The authors ask whether adding a dynamical preferred-frame vector field, the "aether," changes that conclusion. They write the field equations for a zero-tidal-force wormhole metric coupled to an anisotropic fluid, find three sub-classes of the aether coupling constants where the equations close, and for each sub-class they try power-law, logarithmic, and hyperbolic shape functions. In every case there is a parameter window in which the energy density and the radial and tangential pressures jointly satisfy the null and weak energy conditions at the throat. In the third class, with c2 = -c13 ≠ 0 and c14 = 0, the windows extend across the entire exterior, not just the throat. Imposing energy-condition positivity then sharpens the existing observational and theoretical bounds on the couplings: c2 > 0 in Class I, c3 - c4 > 1/2 in Class II (a constraint not present in the prior literature), and -1 < c2 < 0 in Class III.

Core claim

Within Einstein-aether theory — general relativity augmented by a unit timelike vector field that selects a preferred frame — the static, zero-tidal-force, traversable wormhole equations admit closed-form solutions for three specific combinations of the four aether couplings. For each combination, three standard shape functions (power-law, logarithmic, hyperbolic) are tested. Unlike pure Einstein gravity, suitable parameter choices let the matter sector satisfy the null and weak energy conditions at the throat. In the class with c2 = -c13 ≠ 0 and c14 = 0, the energy conditions hold not only at the throat but throughout the wormhole spacetime, provided -1 < c2 < 0. Demanding the energy condit

What carries the argument

A reduction of the Einstein-aether field equations on a Morris-Thorne wormhole metric with diagonal anisotropic stress, combined with three black-hole-style aether profiles a(r) = d/r², a(r) = e/r², and a(r) = -√(c2 r (j c2 - r))/(c2 r) inherited from prior static spherically symmetric solutions. Each profile collapses the system to algebraic energy-condition inequalities in the shape function and the surviving couplings.

If this is right

<parameter name="0">Traversable wormhole geometries in Einstein-aether theory can in principle be sourced by matter satisfying the standard pointwise energy conditions
removing the usual exotic-matter requirement at the throat.

Load-bearing premise

The aether profiles used here were derived for black-hole spacetimes; the paper transplants them unchanged into a wormhole geometry, which has different topology and a hard inner cutoff at the throat, without separately checking that the aether stays regular and asymptotically consistent there.

What would settle it

Re-derive the radial aether function a(r) directly from the aether equation of motion on the wormhole metric (3.1) with the throat boundary condition r > r0 imposed, rather than borrowing the black-hole solutions of Ref. [57]. If the wormhole-native a(r) differs from d/r², e/r², or the Class-III form on the relevant interval, recompute ρ, p_r, p_t and check whether the EC1, EC2, EC3 positivity windows — especially the everywhere-positive Class-III window for -1 < c2 < 0 — survive. If they do not, the central claim that EA wormholes can be supported by non-exotic matter, as stated, fails.

read the original abstract

We present the first analysis of traversable wormhole solutions within the framework of Einstein-aether theory. We show that the corresponding field equations admit three distinct wormhole geometries, obtained by adopting three different classes of combinations for the aether coupling constants. We examine the null and weak energy conditions for three types of wormhole shape functions. Our findings reveal that, in contrast to Einstein gravity, by choosing appropriate parameter values, wormhole geometries can satisfy the energy conditions at the wormhole throat. We also find that in one class, wormholes can satisfy the energy conditions not only at the wormhole throat but also throughout the entire spacetime. Furthermore, the requirement of energy condition satisfaction, imposes some constraints on the values of aether coupling constants. By comparing these constraints with those previously obtained from theoretical and observational analyses, we find that the satisfaction of energy conditions put more stringent limits on the allowed values of the aether couplings.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

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