$\tt BlackHawk$ $\tt v3.0$: Hawking Radiation from Regular Black Holes

BlackHawk v3.0: Expanding Hawking Radiation Spectra for Regular Black Holes

How do we reconcile the predictable mathematics of General Relativity with the chaotic, infinite densities predicted at the heart of a black hole? Scientists have long struggled with the "singularity"—a point where gravity becomes so intense that our current laws of physics simply break down. To address this, researchers have proposed "regular" black holes, which replace that central point of infinite density with a smooth, manageable core.

A new update to a specialized computational tool, BlackHawk v3.0, aims to bridge this gap. The software calculates the energy emitted by these exotic objects through Hawking radiation. This is a quantum process where black holes slowly leak particles and eventually evaporate. By simulating how different types of non-singular black holes radiate, scientists hope to find clues about dark matter and the nature of quantum gravity.

Can non-singular geometries change the signature of evaporation?

The central question driving this work is whether the mathematical "fixes" we use to remove spacetime singularities actually change the observable physics of a black hole. In standard General Relativity, a black hole is described by the Schwarzschild metric, which inevitably leads to a singularity. However, many theories of quantum gravity suggest that at extremely high energies, spacetime is "smoothed out," preventing infinite density.

The authors of this study investigate how these smoothed-out geometries—referred to as Regular Black Holes (RBHs) or Black Bounces (BBs)—alter the Hawking radiation spectrum. This is critical for research into primordial black holes (hypothetical small black holes formed in the early universe). If these objects are a candidate for dark matter, their survival depends on their internal structure. If a regular black hole evaporates differently than a standard one, our current constraints on dark matter might be fundamentally incorrect.

The limitations of the Schwarzschild baseline

For decades, the benchmark for black hole physics has been the Schwarzschild metric. It is the simplest model, describing a static, non-rotating black hole, but it possesses a fatal flaw: the singularity. Relying solely on this model is like trying to map a coastline using a ruler that breaks whenever it hits a jagged rock.

While the Schwarzschild model provides a clear baseline, it fails to capture the nuances of more complex, "regularized" spacetimes. Previous versions of BlackHawk lacked the breadth to cover the diverse array of models proposed by modern theorists. Furthermore, when dealing with rotating (Kerr) black holes, older numerical methods faced significant stability issues. Specifically, in the "superradiant regime"—a state where waves can extract energy from a rotating black hole—previous approaches often produced inaccurate, overestimated radiation spectra. This created a gap in the reliability of simulations for the very objects most likely to be observed by next-generation telescopes.

Solving the scattering problem across new metrics

To move beyond these limitations, the researchers implemented a suite of new spherically symmetric metrics into BlackHawk v3.0. These include the Bardeen and Hayward models, which utilize a de Sitter core (a region of constant energy density that prevents a singularity). They also added "black bounce" geometries like the Simpson-Visser and Peltola-Kunstatter models. These bounces allow spacetime to contract to a minimum radius before re-expanding, avoiding a singular endpoint.

The heavy lifting in this investigation is done through the integration of GrayHawk, a companion code that calculates Greybody Factors (GBFs). You can think of GBFs as a filter. While a black hole might emit radiation like a perfect blackbody, the curved spacetime surrounding it acts as a gravitational barrier. This barrier scatters some particles back and lets others pass. The resulting spectrum seen by a distant observer is "greyed" by these factors.

The authors also introduced a "direct method" to fix the errors in rotating black hole simulations. Instead of using traditional coordinates that became mathematically "non-invertible" (meaning you could not uniquely trace a position back to a single point) during high-speed rotation, they employed a new rescaling technique. This allowed them to solve the Teukolsky equation—the master equation for field perturbations in curved spacetime—with much higher numerical stability.

Mapping the thermal fingerprints of regularity

This improved numerical stability allows for a precise look at how different geometries leave distinct "fingerprints" on radiation. As shown in, different regularizing parameters ($\ell$) lead to vastly different Hawking temperatures compared to the standard Schwarzschild case.

Some models cause the temperature to drop as the regularization increases. This suggests that regular black holes might live much longer than their singular counterparts.

The authors validated their new routines by comparing their outputs for Bardeen and Hayward black holes against existing literature. The results, visualized in, were "visually indistinguishable" from established benchmarks.

This confirms that the new implementation is accurate.

When looking at the complexities of rotation, the code reveals how specific modes of emission dominate. For highly spinning black holes ($a^* = 0.99$), the authors report that the $l=m$ mode becomes the overwhelming contributor to the emission spectrum, as illustrated in .

This provides a much clearer picture of what an observer might actually see when looking at a rapidly rotating, potentially regular black hole.

Implications for the dark matter hunt

The deployment of BlackHawk v3.0 has immediate consequences for how we interpret cosmological data. If regular black holes evaporate more slowly or with different energy signatures than previously thought, the "asteroid-mass window" for primordial black hole dark matter may need to be recalculated. This means current limits on how much dark matter could consist of black holes might be inaccurate.

Furthermore, the improved precision for rotating black holes allows researchers to more reliably predict signals for upcoming missions like LISA or the Einstein Telescope. If we can accurately model the "greyed" spectra of these objects, we can better distinguish between a standard black hole and one that carries the fingerprints of quantum gravity.

The authors note a significant limitation: the code currently treats the regularization parameter as a constant. In a real, evaporating black hole, this parameter would likely change over time as the mass decreases. A logical next step for the community would be to develop a consistent dynamical framework that links the evolution of the black hole's mass to its internal regularizing core.