Perturbations and phenomenology of compact objects in quantum gravity theories
This thesis investigates the perturbative dynamics and observational signatures of compact objects within quadratic gravity and asymptotic safety, revealing unique instabilities and horizonless mimics in Einstein-Weyl gravity while demonstrating how quantum corrections in asymptotically safe gravity lead to regular black holes with modified evaporation rates that could impact dark matter models.
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Gravity is the force that holds the universe together, governing the motion of planets and the collapse of stars. For over a century, Albert Einstein's theory of General Relativity has provided the most accurate description of how gravity works, predicting that massive objects warp the fabric of space and time. This theory has passed every test thrown at it, from the bending of starlight to the detection of ripples in spacetime known as gravitational waves. However, the theory has a fatal flaw: it predicts that under extreme conditions, such as at the center of a black hole, the laws of physics break down completely. In these regions, known as singularities, the curvature of space becomes infinite, and the theory can no longer tell us what happens next. To fix this, physicists are searching for a theory of quantum gravity, a framework that would unite Einstein's smooth spacetime with the jittery, uncertain world of subatomic particles.
Two leading candidates for this missing theory are quadratic gravity and asymptotic safety. Quadratic gravity attempts to improve Einstein's equations by adding terms that account for the curvature of space squared, which helps the math work at very high energies but introduces a strange, heavy particle that behaves differently than normal matter. Asymptotic safety, on the other hand, suggests that gravity does not break down at high energies but instead settles into a stable, predictable pattern, effectively smoothing out the infinite spikes that plague classical black holes. The central question for researchers is whether these theoretical fixes actually change what we would see if we could observe a black hole up close, or if they simply remain mathematical curiosities that vanish in the real world.
In a recent doctoral thesis, physicist Andrea Spina set out to answer this question by treating black holes not as static, frozen objects, but as dynamic systems that can be shaken and studied. The core idea is simple: if you tap a bell, it rings with a specific tone that reveals its shape and material. Similarly, if a black hole is disturbed—perhaps by a passing star or a collision with another black hole—it vibrates, emitting gravitational waves that fade away over time. These vibrations, known as quasinormal modes, act as a fingerprint for the black hole. By calculating exactly how these vibrations behave in the new theories of quantum gravity, Spina could determine if the theories produce stable black holes and if they leave any detectable traces that current telescopes might one day see.
The research focused on two distinct areas. First, Spina examined the predictions of quadratic gravity, specifically looking at a version of the theory that includes a massive spin-2 particle. In standard Einstein gravity, the simplest vibrations of a black hole are well understood, but this new theory adds a heavy component that changes the rules. The study found that while some black hole solutions in this theory are stable, others are not. Specifically, certain configurations of black holes with small sizes become unstable, suggesting that nature would likely avoid forming them. More surprisingly, the research uncovered a class of objects called "veiled singularities." These are not black holes with an event horizon, but rather naked points of infinite density that are hidden from view by an extreme redshift. Light trying to escape from near these points loses so much energy that it becomes invisible to distant observers. Despite lacking a traditional horizon, these objects cast a shadow that looks remarkably similar to a standard black hole, making them difficult to distinguish with current technology.
The second part of the work explored the asymptotic safety framework, which aims to remove the singularity entirely. Instead of a point of infinite density, this theory predicts a "regular" black hole with a smooth, finite core. Spina constructed a new model of such a black hole formed by the gravitational collapse of matter, tracking how the object evolves from a collapsing star into a stable, quantum-corrected remnant. The simulations showed that as the star collapses, quantum effects kick in to prevent the formation of a singularity, causing the collapse to slow down and the object to settle into a stable state. When the team analyzed the vibrations of these quantum-corrected black holes, they found that the fundamental tones were very close to those of a standard black hole, but the higher-frequency overtones showed distinct deviations. These subtle differences could serve as a signature for quantum gravity if future detectors become sensitive enough to hear them.
The study also looked at how these quantum corrections affect the radiation black holes emit. According to classical theory, black holes slowly evaporate by emitting particles, a process that speeds up as the black hole gets smaller. However, the quantum-corrected models showed a dramatic slowdown. As the black hole approaches its smallest possible size, its temperature drops, and the emission of particles nearly stops. This suggests that instead of vanishing completely, these black holes could leave behind long-lived, cold remnants. This has profound implications for the search for dark matter. If primordial black holes formed in the early universe are actually these quantum-corrected objects, they would emit far less radiation than previously thought. This means that a much larger population of them could exist without being detected by current gamma-ray telescopes, potentially allowing them to account for all the dark matter in the universe.
Finally, the research tested a long-standing idea that the way a black hole vibrates is directly linked to the paths that light takes around it. In standard Einstein gravity, this connection holds true, but the study found that in quadratic gravity, this link breaks down. The complex structure of the new theory means that the vibrations cannot be predicted simply by looking at the orbits of light. This failure of the standard correspondence is a clear sign that the underlying physics has changed in a fundamental way.
Overall, the work demonstrates that while quantum gravity theories can produce stable, realistic-looking black holes, they also introduce new, exotic possibilities like veiled singularities and cold, long-lived remnants. The findings suggest that the universe might be hiding these quantum effects in plain sight, masked by the fact that they look so much like the black holes we already know. However, the subtle differences in their vibrations and the way they evaporate offer a path forward. As our ability to listen to the universe improves, these tiny deviations could become the key to unlocking the true nature of gravity and resolving the mystery of what lies at the heart of a black hole.
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