[Paper Review] Planck stars: new sources in radio and gamma astronomy?

Carlo Rovelli|arXiv (Cornell University)|Aug 5, 2017

Pulsars and Gravitational Waves Research3 citations

TL;DR

The paper proposes that primordial black holes may undergo quantum gravitational collapse and bounce as 'Planck stars,' emitting detectable radio and gamma-ray bursts due to tunnelling at Planck density. These signals feature a flattened wavelength-distance relation distinct from cosmological redshift, offering a potential observational signature of quantum gravity effects.

ABSTRACT

A new phenomenon, recently studied in theoretical physics, may have considerable interest for astronomers: the explosive decay of old primordial black holes via quantum tunnelling. Models predict radio and gamma bursts with a characteristic frequency-distance relation making them identifiable. Their detection would be of major theoretical importance.

Motivation & Objective

• To explore the possibility that quantum gravitational effects in primordial black holes could lead to observable astrophysical phenomena.
• To identify a mechanism—quantum tunnelling at Planck density—that could cause black holes to 'bounce' and explode, bypassing classical stability.
• To propose that such explosions produce two detectable components: a radio burst and a high-energy gamma-ray burst.
• To demonstrate that the wavelength-distance relation of these signals would be flattened compared to standard cosmological redshift, enabling identification.
• To argue that detecting these signals would provide the first direct observational evidence of quantum gravity.

Proposed method

• Model the collapse of matter in the early universe into primordial black holes, reaching Planck density where quantum gravity effects become dominant.
• Apply loop quantum gravity principles to describe the bounce at Planck density, where gravity becomes strongly repulsive, preventing singularity formation.
• Use the time dilation effect of general relativity to explain why the bounce occurs rapidly in proper time (milliseconds) but slowly in external cosmological time (millions of years).
• Derive the decay time of such black holes using a tunnelling model: $ \tau \sim \frac{m^2}{m_{\text{Planck}}^2} t_{\text{Planck}} $, suggesting lifetimes comparable to the Hubble time for planetary-mass black holes.
• Calculate the expected emission spectrum, including a low-energy radio component (~mm wavelength) and a high-energy gamma-ray component (~TeV), based on the size and formation history of the black hole.
• Predict a modified redshift-distance relation (Equation 3) that flattens the standard cosmological redshift, distinguishing the signal from other astrophysical sources.

Experimental results

Research questions

• RQ1 Can quantum gravitational effects in primordial black holes lead to observable explosive phenomena?
• RQ2 What would be the characteristic frequency and distance dependence of signals from such quantum-gravitational explosions?
• RQ3 How does the large gravitational time dilation affect the observed timescale of Planck star explosions?
• RQ4 Can the predicted signals be distinguished from other astrophysical transients like fast radio bursts or gamma-ray bursts?
• RQ5 What observational signatures would confirm the existence of Planck stars as a manifestation of quantum gravity?

Key findings

• Primordial black holes with planetary mass are predicted to have lifetimes comparable to the current Hubble time, making them potentially observable today.
• The explosion of such a black hole would release energy on the order of $ 10^{47} \text{erg} $, equivalent to the mass of a small planet, from a region of millimetre size.
• The radio component of the signal is expected to peak at wavelengths around 0.2 mm, falling within the sensitivity range of instruments like PACS and SPIRE on Herschel.
• The high-energy gamma-ray component is predicted to be in the TeV range, consistent with the energy scale of photons trapped during early universe formation.
• The observed wavelength-distance relation for both components is flattened compared to standard cosmological redshift, described by Equation (3), providing a unique observational signature.
• The integrated diffuse emission from a population of Planck stars would produce a spectrum resembling a slightly distorted blackbody, distinct from any known astrophysical background.