Quantum-gravity-inspired Alcubierre warp-drive geometries

RESUMO

String T-duality, through its correspondence with path-integral duality, endows the low-energy propagator with a zero-point length $l_0=2\pi\sqrt{\alpha'}$ that softens the short-distance behavior of gravitational fields. Motivated by the regular black-hole construction obtained from the corresponding smeared source, we formulate a T-duality-inspired Alcubierre geometry by identifying the warp profile with the complementary cumulative mass fraction of that source. For the effective one-scale choice $f(r_s)=1-r_s^3/(r_s^2+l^2)^{3/2}$, with $l^2=R^2+l_0^2$, the metric is $C^2$ at the bubble center and smooth elsewhere, while the energy density, its volume integral, and the York expansion are available in closed form. In particular, $E=-(15\pi/1024)v_s^2 l$ in geometric units and $|\rho_E|$ is bounded by a constant times $v_s^2/l^2$. Within this one-scale family, the model therefore removes the divergence associated with the profile-contraction limit $R\to 0$ at fixed velocity, because $l$ cannot fall below $l_0$. This should not be confused with a regularization of the conventional Alcubierre thin-wall limit at fixed macroscopic bubble radius, in which an independent wall thickness is taken to zero. We emphasize, however, that the construction is an effective ansatz rather than a derivation from string-corrected field equations: $R$ is a macroscopic profile scale, the choice $l^2=R^2+l_0^2$ is an interpolation, and the classical $l_0\to 0$ limit remains a smooth thick-walled profile rather than the distributional Alcubierre top hat. Exotic matter remains necessary, and neither semiclassical stability nor a modified quantum energy inequality is claimed without an explicit renormalized stress-tensor calculation.