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Hairy black hole solutions in nonlocal quadratic gravity

Roldao da Rocha

TL;DR

The paper addresses whether quantum-inspired nonlocal quadratic gravity can host hairy black hole solutions that depart from Reissner–Nordström geometry. It develops a perturbative EFT approach in the small nonlocal coupling $\alpha$, solving the field equations to leading and next-to-leading order to obtain Yukawa-like hair encoded in $f(r)$. It analyzes thermodynamics, showing horizon shifts, modified Hawking temperature $T_H$ and entropy $S$, reduced negative specific heat, and that the first-law $dM= T_H dS + \Upphi dQ$ and Gibbs/Helmholtz energies signal no first-order phase transitions. It also demonstrates the classical stability of the nonlocal theory via a healthy spin-2 propagator with a positive-residue massive pole, ensuring ghost-free behavior within the EFT.

Abstract

Hairy black hole solutions are constructed within quantum-inspired nonlocal quadratic gravity. Nonlocal effects induce Yukawa screening, which shifts the event horizon inward and modifies both the Bekenstein--Hawking entropy and the Hawking temperature, while also renormalizing the chemical potential. Nonlocal corrections also reduce the magnitude of the negative specific heat, making small hairy black holes more stable, with Helmholtz and Gibbs free energies consistent with the absence of first-order phase transitions. The nonlocal spin-2 propagator contains, in addition to the massless graviton, a massive pole with positive residue and positive norm. Consequently, hairy black holes in nonlocal quadratic gravity are free of ghost instabilities at the quadratic and classical levels, in the effective field theory.

Hairy black hole solutions in nonlocal quadratic gravity

TL;DR

The paper addresses whether quantum-inspired nonlocal quadratic gravity can host hairy black hole solutions that depart from Reissner–Nordström geometry. It develops a perturbative EFT approach in the small nonlocal coupling , solving the field equations to leading and next-to-leading order to obtain Yukawa-like hair encoded in . It analyzes thermodynamics, showing horizon shifts, modified Hawking temperature and entropy , reduced negative specific heat, and that the first-law and Gibbs/Helmholtz energies signal no first-order phase transitions. It also demonstrates the classical stability of the nonlocal theory via a healthy spin-2 propagator with a positive-residue massive pole, ensuring ghost-free behavior within the EFT.

Abstract

Hairy black hole solutions are constructed within quantum-inspired nonlocal quadratic gravity. Nonlocal effects induce Yukawa screening, which shifts the event horizon inward and modifies both the Bekenstein--Hawking entropy and the Hawking temperature, while also renormalizing the chemical potential. Nonlocal corrections also reduce the magnitude of the negative specific heat, making small hairy black holes more stable, with Helmholtz and Gibbs free energies consistent with the absence of first-order phase transitions. The nonlocal spin-2 propagator contains, in addition to the massless graviton, a massive pole with positive residue and positive norm. Consequently, hairy black holes in nonlocal quadratic gravity are free of ghost instabilities at the quadratic and classical levels, in the effective field theory.
Paper Structure (10 sections, 57 equations, 3 figures)

This paper contains 10 sections, 57 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Black hole solutions in nonlocal quadratic gravity
  3. Leading-order nonlocal metric corrections
  4. Next-to-leading order nonlocal corrections to the Reissner--Nordström metric
  5. Thermodynamics of hairy black holes in nonlocal quadratic gravity
  6. Nonlocal Ricci-Tensor and scalar curvature Effects and Classical Black Holes
  7. Nonlocal propagator structure and classical stability
  8. Phenomenological analysis of classical black holes with nonlocal corrections
  9. Conclusions
  10. Details of the spin-2 propagator, poles, and residue analysis

Figures (3)

  • Figure 1: Metric function (\ref{['fm1']}) as a function of the radial coordinate, for $M=3 M_\odot$, $Q= M/3$, and $\upmu=0.4$. The black line regards the Reissner--Nordström case ($\alpha = 0$), the gray line refers to $\alpha = 0.01$; the light-gray line is plotted for $\alpha = 0.1$, and the dashed line shows the $\alpha = 0.2$ case.
  • Figure 2: Metric function (\ref{['fm1']}) as a function of the radial coordinate, for $M=10^2 M_\odot$, $Q= M/3$, and $\upmu=0.4$. The black line regards the Reissner--Nordström case ($\alpha = 0$), the gray line refers to $\alpha = 0.01$; the light-gray line is plotted for $\alpha = 0.1$, and the dashed line shows the $\alpha = 0.2$ case.
  • Figure 3: Hawking temperature ($\times\, 10^{-7}$ K), as a function of $M/M_\odot$, for $Q= M/3$, and $\upmu=0.001$. The black line regards the Reissner--Nordström case ($\alpha = 0$), the gray line refers to $\alpha = 0.2$; the light-gray line is plotted for $\alpha = 0.5$.