[Paper Review] Planck Scale Remnants in Resummed Quantum Gravity

B. F. L. Ward|ArXiv.org|May 4, 2006

Quantum Electrodynamics and Casimir Effect3 references3 citations

TL;DR

This paper proposes that in a resummed quantum gravity framework, which tames ultraviolet divergences by resumming large infrared effects, the final state of Hawking radiation from a very massive black hole is a stable, Planck-scale remnant fully accessible to our universe. The remnant arises due to a modified Newtonian potential with exponential screening, leading to complete evaporation down to a remnant mass of 2.38 M_Pl, which could decay into Planck-scale cosmic rays.

ABSTRACT

We show that, in a new approach to quantum gravity in which its UV behavior is tamed by resummation of large IR effects, the final state of the Hawking radiation for an originally very massive black hole is a Planck scale remnant which is completely accessible to our universe. This remnant would be expected to decay into n-body final states, leading to Planck scale cosmic rays.

Motivation & Objective

• To resolve the black hole information paradox by identifying a stable final state for Hawking radiation in quantum gravity.
• To address the ultraviolet (UV) divergence problem in quantum general relativity through a novel resummation technique.
• To show that the final remnant state of a massive black hole is not hidden behind an event horizon but is fully accessible to our universe.
• To connect the modified gravitational potential from resummed quantum gravity to the effective running of Newton's constant in black hole evaporation.
• To propose a testable signature: decay of the remnant into n-body final states producing Planck-scale cosmic rays.

Proposed method

• Adopts a resummation approach to quantum gravity that extends non-Abelian infrared methods to tame UV divergences in Einstein's theory.
• Uses a modified graviton propagator with a resummed self-energy correction, leading to a propagator that falls faster than any power of momentum in the UV regime.
• Applies the resummed theory to compute one-loop corrections to the graviton propagator, incorporating contributions from all Standard Model particles and a small cosmological constant.
• Derives an improved Newtonian potential with an exponential cutoff, $\Phi_N(r) = -\frac{G_N M}{r}(1 - e^{-ar})$, where $a \approx 0.210 M_{Pl}$, arising from effective degrees of freedom and an infrared cutoff.
• Matches this potential to the effective running Newton constant $G(r)$ from the asymptotic safety approach, enabling a smooth transition at the outermost horizon.
• Solves the modified Schwarzschild metric with $G_{\text{eff}}(r) = G_N(1 - e^{-ar})$ for $r < r_>$, showing that the inner horizon becomes unphysical and the outer horizon collapses to $r=0$, leaving a remnant.

Experimental results

Research questions

• RQ1 What is the final state of Hawking radiation for a very massive black hole in a UV-finite quantum gravity framework?
• RQ2 How does resummation of infrared effects alter the behavior of the graviton propagator and the effective gravitational coupling?
• RQ3 Can the modified Newton potential from resummed quantum gravity reproduce the running of Newton's constant observed in asymptotic safety approaches?
• RQ4 Does the modified gravitational potential lead to a stable, accessible Planck-scale remnant after complete black hole evaporation?
• RQ5 What are the observable signatures of such a remnant, particularly in the form of high-energy cosmic rays?

Key findings

• The resummed quantum gravity approach renders all quantum gravity loop corrections UV finite by modifying the graviton propagator with a resummed self-energy term.
• The effective Newton potential acquires an exponential screening: $\Phi_N(r) = -\frac{G_N M}{r}(1 - e^{-ar})$, with $a \approx 0.210 M_{Pl}$, due to contributions from all Standard Model particles and a gravitational infrared cutoff of $m_g \approx 3.1 \times 10^{-33}$ eV.
• The matching between the resummed potential and the asymptotic safety result $G(r)$ occurs at $r_>$, where $G(r) = G_N(1 - e^{-ar})$, ensuring consistency with phenomenological models.
• For $\gamma = 0$ and $\Omega = 0.2$, the outer horizon collapses to $r = 0$, and the inner horizon becomes unphysical, leading to complete evaporation down to a remnant.
• The final remnant has a mass of $M'_{\text{cr}} = 2.38\, M_{\text{Pl}}$, which is stable and fully accessible to our universe.
• This remnant is expected to decay into $n$-body final states with $n \geq 2$, producing Planck-scale cosmic rays, a signature consistent with current data and recent work by Hawking.