Black holes whose cores weaken gravity ring higher and longer in three quantum-gravity calculations

A core hidden behind a horizon can change a sound made outside it because the ringing takes shape at the light ring, the radius at which light can orbit the black hole ^[13]. Roughly speaking, a tone's pitch depends on the speed at which waves circle that ring, and its decay on the rate at which they leak away from it ^[13]. According to the account one of the authors wrote for phys.org, gravity that weakens near the center is also a little weaker out at the light ring ^[14].

Over the past year Davide Batic and a co-author, with Fabio Scardigli on the first two papers, computed these tones for three black holes reshaped by quantum gravity ^[1]. The models differ in what happens to gravity's strength. Several approaches let Newton's constant depend on distance, and in asymptotic safety, an idea due to Steven Weinberg, gravity weakens at the shortest distances ^[15]. The Bonanno-Reuter black hole, built from asymptotic safety in 2000, switches gravity off at its center, has a smooth core where the singularity would be, and gains an inner horizon ^[16]. The Hayward black hole has no singularity. One number sets the size of its core, and at a critical value of 32/27 its two horizons merge ^[17].

The first paper went the other way. Its gravity grows stronger near the center, and the singularity survives, spread over a sphere at the edge of a Planck-density core ^[18]. The results, one of the authors wrote, fall into a simple pattern: "where gravity weakens at short distances, the black hole rings higher and longer; where it grows stronger, it rings lower and dies away sooner" ^[3].

Each comparison is against an Einstein black hole of the same mass ^[4]. A tone that fades 22.1% more slowly has a damping rate 0.779 times Einstein's, so it lasts 1/0.779, or about 1.28 times as long, matching the 28% reported for the Hayward case ^[19]. The same conversion gives the Bonanno-Reuter ring about 29% more time ^[20] and cuts the Planck star's to about 82% of the Einstein figure ^[21].

"Two checks make me trust this contrast," the same author wrote ^[9]. The first uses electromagnetic waves, whose tones depend on the geometry alone, and they shift the same way ^[7]. The second concerns something light does not do. Gravitational waves also shake whatever the core is made of, and the geometry alone does not describe that response ^[8]. The team adopted one model of it. With the other model used in recent studies, the Hayward pitch rises by about 6% instead of 9%, still upward ^[8].

The numerics were built for the extreme cases the main figures come from. The usual WKB approximation pictures the barrier around the black hole as a smooth hump that the waves run into ^[11]. The team instead mapped the whole region outside the black hole onto a finite interval, wrote the wave as a sum of polynomials and solved the resulting matrix eigenvalue problem ^[10]. When the Hayward black hole's two horizons merge, the equations change character at the horizon, so the authors wrote a separate version of the problem to follow it all the way ^[12].

I think the direction of the shift is well supported for these three models, because it survived a change of wave type and a change of core physics ^[7][8]. The Hayward and Bonanno-Reuter figures are each taken at the model's extreme point, and the Planck star's at one Planck mass ^[4][5][6]. The account does not estimate how large the shifts would be for black holes formed in observed mergers, or whether a detector could tell a core apart from a small difference in mass.