Linearized stability of T-duality quantum-inspired thin-shell wormholes

Abstract: Wormholes that are traversable in principle offer fascinating insights into general relativity, yet they typically require exotic matter and suffer from stability issues. We construct a thin-shell wormhole by gluing two copies of a quantum-corrected, regular spacetime obtained from string T-duality. This regularisation replaces the classical curvature singularity with a smooth core and introduces a fundamental length scale $l_0$. For the static configuration, we derive the surface stresses and show that, unlike the Schwarzschild case, the null and strong energy conditions can be satisfied for sufficiently large throat radii. A linearised stability analysis reveals a rich landscape: close to the minimum allowed throat radius the configuration is unstable; at intermediate radii ($a \sim l_0$) the geometric stability threshold becomes negative, yielding a window of \emph{unconditional stability} where any convex surface mass function suffices; at large radii the wormhole recovers Schwarzschild-like behaviour and stability requires a stiff equation of state. The T-duality scale $l_0$ is thus not merely a regulariser but a key physical parameter that opens a novel region of unconditional stability absent in classical thin-shell wormholes. Our results suggest that quantum-gravity-motivated modifications can simultaneously cure singularities and make traversable wormholes dynamically viable, providing new targets for gravitational-wave astronomy and theoretical studies of exotic compact objects.

• The paper constructs a traversable thin-shell wormhole from two T-duality-regularized black-hole geometries and applies Israel junction conditions and GLMV linearized stability analysis to its radial dynamics.
• The regularized geometry allows the null and strong energy conditions to hold for sufficiently large throats, although negative energy density persists and the weak and dominant energy conditions remain violated.
• The stability landscape includes inevitable near-horizon instability, an intermediate unconditional stability window near the T-duality scale—for example, roughly 1.5–3 l₀ when M/l₀ = 1—and large-radius stability requiring a suitably stiff shell equation of state.

Overview and construction

This paper constructs a traversable thin-shell wormhole by gluing two identical copies of a quantum-corrected, regular black-hole spacetime derived from string T-duality, and analyzes its energy conditions and linearized radial stability. The background metric function is

$f(r) = 1 - \frac{2M r^2}{(r^2 + l_0^2)^{3/2}},$

which arises from a smeared Gaussian-like matter source characterized by the T-duality zero-point length $l_0$ (Nicolini et al., 2019). The key structural feature is that $b(r)/a \to 0$ as $r \to 0$, so the classical Schwarzschild singularity is replaced by a regular core with $f \to 1$, while the geometry is asymptotically Schwarzschild at large radii. The cut-and-paste construction follows Israel's junction formalism: two copies of the spacetime are excised at $r = a(\tau)$ outside any horizon and identified across a timelike hypersurface $\Sigma$ carrying a perfect-fluid surface stress tensor $\mathrm{diag}(-\sigma, \mathcal{P}, \mathcal{P})$.

The static configuration exists only where $f(a) > 0$, i.e. $M < (a^2 + l_0^2)^{3/2}/(2a^2)$; below a minimum throat radius $l_0$0 (the outer horizon of the underlying regular black hole) the shell would sit inside a horizon. The analysis is restricted to this horizonless regime.

Surface stresses and energy conditions

In the static limit, the Lanczos equations give

$l_0$1

with an analogous expression for $l_0$2. The surface energy density is negative for all allowed throat radii, so the weak energy condition (WEC) is always violated — exotic matter remains unavoidable, as in all thin-shell wormholes in general relativity.

The central departure from the Schwarzschild case concerns the null and strong energy conditions. The NEC quantity $l_0$3 is controlled by the numerator $l_0$4, so the NEC holds iff

$l_0$5

Combining this with the static condition yields the mass-independent necessary bound $l_0$6. Moreover, $l_0$7 precisely when $l_0$8, since its sign is set by $l_0$9. Consequently, for suitable $b(r)/a \to 0$0, both the NEC and SEC are satisfied for sufficiently large throats — in sharp contrast to the Schwarzschild thin-shell wormhole, where both are always violated [gr-qc/9506083]. The WEC and dominant energy condition remain violated throughout. Physically, the regularization softens the gravitational potential at small radii, reducing the magnitude of the negative surface pressure needed to support the throat.

Linearized stability via the GLMV geometric threshold

The throat dynamics reduce to a unit-mass particle of zero total energy in an effective potential $b(r)/a \to 0$1, where $b(r)/a \to 0$2 is the normalized surface mass. Static equilibrium requires $b(r)/a \to 0$3, and linearized stability requires $b(r)/a \to 0$4. Using the GLMV unified formalism (Garcia et al., 2011, Martin-Moruno et al., 2011), the master condition takes the form

$b(r)/a \to 0$5

where the geometric threshold

$b(r)/a \to 0$6

depends exclusively on the background metric through $b(r)/a \to 0$7 and its first two derivatives. Via the surface conservation equation, $b(r)/a \to 0$8, where $b(r)/a \to 0$9 is the squared sound speed of the shell material, so the inequality constrains the equation of state only through this single parameter.

Introducing the dimensionless variables $r \to 0$0 and $r \to 0$1, with domain $r \to 0$2, the threshold becomes a dimensionless function $r \to 0$3 whose sign structure organizes the entire stability landscape.

Three stability regimes

The analysis identifies three qualitatively distinct regimes:

• Near-horizon instability: as $r \to 0$4, the redshift factor $r \to 0$5 and $r \to 0$6 diverges to $r \to 0$7 through terms scaling as $r \to 0$8 and $r \to 0$9. No finite $f \to 1$0 can satisfy the inequality, so configurations with throats close to the would-be horizon are always unstable.
• Intermediate unconditional stability: for intermediate radii of order $f \to 1$1, the second term of $f \to 1$2 — governed by the polynomial $f \to 1$3 — can drive the threshold negative. For the representative case $f \to 1$4, numerical evaluation shows $f \to 1$5 over roughly $f \to 1$6. In this window the stability inequality is automatically satisfied for any convex surface mass function ($f \to 1$7), i.e., for any physically reasonable causal shell material, without fine-tuning of the equation of state. This window has no analogue in the Schwarzschild construction, where $f \to 1$8 is strictly positive for all $f \to 1$9.
• Large-radius conditional stability: for $r = a(\tau)$0 the metric asymptotes to Schwarzschild and $r = a(\tau)$1, so stability again demands a sufficiently stiff equation of state, matching the classical behavior at leading order.

The implication is that the T-duality scale $r = a(\tau)$2 plays a dual role: it regularizes the curvature singularity and simultaneously opens a finite interval of parameter space in which the geometry itself is stabilizing, removing the need for finely tuned shell matter that plagues classical thin-shell wormholes.

Limitations and open questions

Several caveats qualify these results. First, the existence and extent of the unconditional stability window depends on the ratio $r = a(\tau)$3; the paper demonstrates it explicitly only for $r = a(\tau)$4 and states that it occurs "for certain values" of this ratio, so a systematic map of the $r = a(\tau)$5 plane identifying precisely which mass ratios admit $r = a(\tau)$6 is not provided. Second, the stability analysis is restricted to radial perturbations; whether the unconditional stability window survives non-spherical, higher-multipole deformations is left open. Third, no explicit, physically motivated equation of state for the exotic shell fluid is constructed or tested against the master inequality — the claim of "unconditional" stability is conditional on convexity of $r = a(\tau)$7, which is assumed rather than derived from microphysics. Fourth, the DEC may become marginally satisfied only at very large $r = a(\tau)$8, and the WEC is violated everywhere, so the model does not eliminate exotic matter. Finally, the analysis assumes symmetric junctions ($r = a(\tau)$9, $\Sigma$0); asymmetric configurations, which would introduce a net gravitational force on the shell, are deferred to future work, as are observational signatures such as lensing, shadows, and gravitational-wave echoes.

Conclusion

By joining two copies of the T-duality-regularized spacetime, the authors obtain a singularity-free thin-shell wormhole whose shell can satisfy the NEC and SEC for sufficiently large throat radii — impossible in the Schwarzschild case — and whose linearized stability landscape splits into three regimes: near-horizon instability, an intermediate window of unconditional stability at $\Sigma$1 arising from a negative geometric threshold, and large-radius conditional stability requiring stiff shell matter. The result establishes the regularization scale $\Sigma$2 as a dynamical parameter controlling wormhole viability rather than merely a UV regulator, and leaves open the questions of non-radial stability, explicit equations of state, asymmetric junctions, and observable signatures that would determine whether such regularized wormholes constitute viable astrophysical compact objects.