Black bounce as a quantum correction from string T-duality: Thermodynamics, energy conditions, and observational imprints from EHT

Abstract

Motivated by quantum gravity effects suggested by string theory, we investigate gravitational configurations sourced by an effective energy density inspired by T-duality. This density naturally introduces a minimal length scale $l_0$ that acts as an ultraviolet regulator, allowing the description of nonsingular geometries within a classical framework. By employing it as the matter source in the Einstein equations, we construct static and spherically symmetric spacetimes that interpolate smoothly between regular black holes and traversable wormholes, providing a geometric realization of the black bounce scenario. We examine the curvature invariants and confirm the absence of curvature singularities throughout the spacetime. The conditions for the existence of event horizons are analyzed in detail, which allows us to determine the causal structure of the solution. A comprehensive study of the geodesic motion is performed for both massive and massless particles, revealing the presence of photon circular orbits and an innermost stable circular orbit for massive particles. Using observational data from the Event Horizon Telescope, we constrain the minimal length parameter through the black hole shadow radius, finding that for $l_0 \lesssim 1.15\, M_{\text{ADM}}$ our solution remains consistent with observations within the $2σ$ confidence level. The optical appearance of spacetime is further investigated by considering a thin accretion disk surrounding the black bounce. From the heat capacity, we analyze the thermodynamic stability of the solution and identify the presence of a phase transition. Finally, we examine the energy conditions and discuss which of them are violated by the effective fluid supporting this geometry.

Figures (22)

• Figure 1: Event horizon radius as a function of $l_0$.
• Figure 2: Carter-Penrose diagram for the case $l_0 >6M$, where we have a traversable wormhole.
• Figure 3: Carter-Penrose diagram for the case $l_{0}=6M$, where the null throat coincides with the extremal horizon. The geometry is one way traversable, and the maximal analytic extension produces an infinite chain of asymptotic regions.
• Figure 4: Carter-Penrose diagram for the case $l_{0}<6M$, where the throat is hidden behind the horizon and the singularity is replaced by a spacelike bounce.
• Figure 5: Effective potential for massive particles as a function of the radial coordinate for different values of $l_0$, for the case with horizon fixing $\ell = 12M$ (top panel) and the case without a horizon fixing $\ell = 15M$ (bottom panel).