Emergence of ER=EPR from non-local gravitational energy

TL;DR

This work presents a regular, non-singular realization of ER=EPR by coupling entangled subsystems to a spacetime regularized via non-local gravitational self-energy with a T-duality–inspired minimal length. The authors derive a family of Einstein–Rosen–type wormholes sourced by quantum-gravity–induced energy conditions, classify their horizons and throat structures, and compute the exotic matter needed at the throat. A central result is that among the regular geometries, only the zero-throat wormhole with $r_{\text{throat}}=0$ and a horizon at $u=l_0$ satisfies all ER=EPR criteria (non-traversable, causal, and regular), providing a concrete entanglement-induced bridge. The work further discusses implications for microscopic ER networks in vacuum fluctuations, replica wormholes in Hawking radiation, and speculative links to entanglement-driven dark energy, suggesting a deep geometrical link between quantum entanglement and spacetime structure.

Abstract

We construct a class of wormhole geometries supported by the non-local gravitational self-energy that regularizes the particle and black-hole sectors of spacetime. Using this framework, inspired by T-duality, we show that two entangled particles (or particle-black-hole pairs) naturally source an Einstein-Rosen-type geometry in which the required violation of the strong energy condition arises from intrinsic quantum-gravity effects rather than from ad hoc exotic matter, which is matter that violates the null energy condition. We classify the resulting wormholes, analyze their horizons, throat structure and embedding properties, and we identify the exotic energy needed at the minimal surface. Imposing the ER=EPR requirement of non-traversability and the absence of a macroscopic throat, we find that only the zero-throat geometry is compatible with an entanglement-induced Einstein-Rosen bridge, providing a concrete realization of ER=EPR within a fully regular spacetime. Finally, we briefly discuss possible implications for microscopic ER networks from vacuum fluctuations, replica-wormhole interpretations of Hawking radiation, and possible links to entanglement-driven dark-energy scenarios.

Figures (3)

• Figure 1: Embedding diagram of the one-way traversable wormhole with horizon (extremal configuration). This represents an entanglement-induced wormhole geometry between two entangled particle–black holes of Planck-mass order. We have used $u_{\min}=1.8297$ and $M_{\text{ext}}=1.16537$, and we have set the Planck quantities to unity, namely $M_{\text{Pl}}=l_{0}=1$.
• Figure 2: Embedding diagram of the two-way traversable wormhole without a horizon for the case $\zeta=2$ which implies that $u_{\min} = \sqrt{5}$. This represents an entanglement-induced wormhole geometry between two entangled particles of particle mass sector. We have set $M = 0.1$ along with $M_{\text{Pl}}=l_{0}=1$.
• Figure 3: Embedding diagram of the non-traversable wormhole with horizon having zero throat radius $r_{\rm throat}=0$ and $u_{\min} =1$, respectively. This also represents an entanglement-induced wormhole geometry between two entangled particles of particle mass sector. We have further set the mass parameter to $M = 0.1$, along with $M_{\text{Pl}}=l_{0}=1$.