LQG inspired spacetimes as solutions of the Einstein equations

TL;DR

This work demonstrates that Loop Quantum Gravity–inspired spacetimes, including Simpson–Visser black-bounce, holonomy-corrected Schwarzschild, and polymerized BHs, can be realized as solutions of General Relativity by reconstructing a minimal classical matter content consisting of a phantom scalar field ($\epsilon=-1$) and nonlinear electrodynamics (NED). The authors derive the field equations for both magnetic and electric cases, obtain explicit expressions for the source functions $L(r)$, $L_F(r)$, $F(r)$, $V(\phi)$ and $\phi(r)$ (or use the auxiliary-field formulation when needed), and analyze energy conditions for each field separately. They show that the electromagnetic sector can satisfy NEC/SEC/DEC in some models, while the phantom scalar sector inevitably violates NEC, consistent with the non-vacuum, regular geometries involved. The work provides a GR-compatible, perturbation-friendly framework to study quantum-inspired corrections via effective stress-energy, enabling future analyses of stability, quasinormal modes, echoes, shadows, and lensing in these spacetimes, and suggests avenues for extensions to modified gravity theories. $ε=-1$ and $F$-dependent Lagrangians play crucial roles in matching the LQG-inspired metrics to classical GR solutions.

Abstract

Black bounces are compact objects with a wormhole structure hidden behind an event horizon. This type of metric can be obtained through general relativity by considering the presence of exotic matter. Such spacetimes can also arise within the framework of effective theories inspired by loop quantum gravity. In this work, we verify the possibility of obtaining black bounce models inspired by loop quantum gravity as solutions of general relativity. For this, we examine which sources can generate these solutions and the consequences of using these types of sources. We find that the sources can be expressed as a combination of a phantom scalar field and nonlinear electrodynamics. Once we obtain the sources in terms of fields, we analyze the energy conditions for each field separately to verify which of the fields is responsible for the violation of the energy conditions.

Figures (3)

• Figure 1: Behavior o the scalar field potential to the Simpson-Visser solution as a function of $\phi$ considering different values of $a$.
• Figure 2: Behavior o the scalar field potential as a function of $\phi$ considering different values of $r_0$.
• Figure 3: Plot of the functions $F(r)$, $F(P)$, and $L(F)$ to the polymerized solution \ref{['poly']}, with $q_e=k=0.5m$. The extreme points $P_1$ and $P_2$ inform us about the points where the electromagnetic Lagrangian changes its behavior.