Constraining Quantum Corrections to Black Hole Structure Through Gravitational-Wave Ringdown
Advisor: Ryan Grove
Internship Location: F-1 Visa Holder / No Placement
Onsite Mentor: F-1 Visa Holder / No Placement
When two black holes merge, the final black hole vibrates and emits gravitational waves in a ringdown phase. In classical general relativity, these vibrations are described by quasi-normal modes whose frequencies and damping times depend only on the black hole's mass and spin, realizing the no-hair picture that no additional structure is visible from outside. Ideas from quantum mechanics and black hole thermodynamics suggest that this classical description may be incomplete and that subtle quantum corrections near the horizon could slightly alter the ringdown signal.This project uses publicly available data from the LIGO and Virgo gravitational wave detectors to test how large such deviations can be while remaining consistent with current observations. The ringdown phase is isolated for several high signal-to-noise merger events. Damped-sinusoid models are fitted to measure the dominant mode's frequency and damping time. These measurements are compared to Kerr predictions inferred from the remnant mass and spin, and any differences are expressed as fractional deviations. By combining results across multiple events, the project obtains upper bounds on these deviations. The derived bounds constrain quantum gravity-motivated models by excluding corrections that would produce shifts larger than the allowed range. Overall, the project shows how gravitational-wave ringdown observations can test efforts to unify general relativity, quantum mechanics, and black hole thermodynamics.
Project Blog
Post 1: Intro Blog: Where Theories Collide
I am drawn to black holes since they sit precisely where our current cosmological theories clash. General relativity paints a clean external picture: once a black hole settles, its spacetime is fully captured by just mass and spin. Meanwhile, quantum mechanics insists that information can never truly be destroyed. At the same time, black hole thermodynamics assigns an enormous entropy to these objects, hinting at countless hidden microstates lurking beneath the surface. Yet when taken together, these three frameworks still don’t mesh into a single coherent story about what actually happens at and beyond the horizon. That fundamental tension is what ultimately drew me to this project.
Gravitational waves, fortunately, offer a way to probe this problem with real observations. When two black holes merge, the resulting remnant doesn’t instantly settle. Instead, it oscillates and gradually decays in what we call the ringdown phase. According to classical general relativity, this pattern follows a precise structure encoded in quasinormal modes, which are essentially the black hole’s characteristic vibrations. Once we know the remnant’s mass and spin, those mode frequencies and damping times are completely determined. However, if quantum corrections or other novel structures exist near the horizon, they might reveal themselves as subtle shifts in these frequencies or in how quickly the oscillations decay. Rather than asking the grand question “which theory is correct,” I’m pursuing something more focused: how much deviation from Einstein's predictions does the data allow, and what does that tell us about which quantum gravity models remain viable?
I want to learn how to turn that inquiry into a rigorous analysis. This involves working with public LIGO and Virgo datasets, isolating the ringdown portion of each signal, fitting straightforward models to the data, and then interpreting upper bounds rather than chasing big breakthroughs.
Week 1: Finding Data and Dealing with Noise
Hi. This week, I have been working on papers about the no-hair theorem and black hole ringdown while learning how to extract ringdown signals from actual LIGO strain data (identify the merger peak, select a post-merger time window, apply filters to remove noise, isolate the ringdown segment).
To address the challenge of measuring parameters from weak and noisy ringdown signals, I've been researching Bayesian inference methods that can calculate probability distributions for each parameter. This is a very effective way to quantify measurement uncertainty, helping determine whether observed deviations from classical predictions are real or just measurement noise. Instead of just a single number, Bayesian methods give a range of possible values, allowing us to check if Einstein’s prediction falls within that range (consistent with the theory) or outside (deviation).
I’ve also been selecting which merger events to analyze. I found some suitable events (GW150914, GW170104, GW190814, GW170814, GW151226) in the Gravitational Wave Open Science Center database (https://www.gw-openscience.org). These events have high signal-to-noise ratios, meaning the gravitational wave amplitude is significantly larger than the background noise level. They also have published measurements of the black holes’ masses and spins, which I need to calculate the ringdown frequencies that Einstein’s theory predicts for comparison with my measurements. In addition, these events span remnant masses from approximately 21 to 62 solar masses, which will help determine whether deviations appear consistently across different mass ranges.
Next week I’ll focus on setting up a Python environment and attempting to load LIGO strain files. I’m also looking forward to learning more and moving to implementing them with real data.
Week 2: Adjusting Parameters
This week I was mainly running analysis code on GW150914, the first event. I spent most of my time downloading packages and debugging. My first attempt at modeling the ringdown with a damped sinusoid gave an R² of about 0.2, meaning the model barely matched the data. The frequency I found was 113 Hz, but the expected Kerr prediction is around 251 Hz. Additionally, the damping time was unrealistically large.
A systematic review of the preprocessing stage identified two sources of error. First, the bandpass filter starts at 30 Hz. That let low-frequency detector noise into the analysis and dominated the FFT. I changed the filter to a range of 100 to 400 Hz to isolate the signal better. Second, the initial ringdown window was defined at 50 ms. Given that the signal typically decays within 10 ms, the model was attempting to fit a damped oscillation to 40 ms of stochastic noise. This necessitated a reduction of the analysis window to prevent the fitting algorithm from converging on non-physical parameters.
After fixing these issues, I moved from simple curve fitting to a full Bayesian inference using the bilby library and the dynesty sampler. This let me create probability distributions and credible intervals for the frequency and damping time. To ensure the robustness of the results, the analysis was executed across three distinct ringdown start times of 3 ms, 5 ms, and 10 ms post-merger, respectively.
Next week I plan to finalize the corrected PSD-weighted Bayesian analysis for GW150914 and verify that the measured frequency and damping time are consistent with the Kerr prediction. Once it's working, I will apply it to the second event, GW170104, which has a lower remnant mass and therefore a different predicted ringdown frequency, to check whether the analysis generalizes across events.
Week 3: Fine-Tuning Analysis Metrics and Literature Review
This week I was debugging the Bayesian inference and reading more recent papers. There are two detector streams: the Hanford detector in Washington (H1) and the Livingston detector in Louisiana (L1). I changed the detector stream to L1 and shortened the ringdown window, and after that the power spectral density (PSD) weighted fast Fourier transform (FFT - which converts time to frequency) peak moved to about 250 Hz, which is much closer to the expected Kerr ringdown frequency for GW150914. Since the rest of the code could not run due to a temporary firewall, I moved to the theory side of the project.
I looked at islands and wormholes. An island is a region near or inside the black hole that must be included when calculating the entropy of Hawking radiation in these papers. Replica wormholes are additional geometries that emerge in the computation of replica entropy. In these calculations, the radiation entropy can follow a page curve, which means it goes up and reaches a peak, and then stops going up. That resulting shape is consistent with the unitary evolution (indicates that information does not disappear).
In “Replica Wormholes and Entanglement Islands in the Karch-Randall Braneworld,” Hao Geng studies a holographic Karch-Randall braneworld with a bath designed to collect radiation. He shows how the island contribution becomes important at late times, resulting in a Page curve.
In “Entanglement Island and Page Curve of Hawking Radiation in Rotating Kerr Black Holes,” Liqiang Wang and Ran Li apply the island framework to rotating Kerr black holes within a small-spin approximation. They still obtain a Page curve and demonstrate how rotation affects the Page time and the scrambling time.
In “Ringing out General Relativity: Quasinormal Mode Frequencies for Black Holes of Any Spin in Modified Gravity,” Adrian Chung and Nicolás Yunes developed METRICS, which is a spectral method for determining the frequencies and damping times of ringdown modes in spinning black holes under modified gravity. This paper shows that slow-spin approximations may fail when the black hole spin is not negligible, so any subsequent comparison between an extracted ringdown frequency and the Kerr-predicted frequency and damping time should use values computed for the correct remnant mass and spin.
Next week I’ll be visiting an aircraft maintenance engineering company. I’m looking forward to that.
Week 4: A Look into Aircraft Maintenance
This week I took a break from my research into black holes to pursue another interest of mine. I visited the Guangzhou Aircraft Maintenance Engineering Company (GAMECO) and observed the work there. I spent most of my time shadowing technicians in the ATE (automatic test equipment) workshop and watching how they tested, disassembled, and repaired aircraft computers reported by the flight crew. ATE is a testing system that simulates the operating environment of the aircraft so that the function and condition of a computer can be checked, and each computer, called UUT (unit under test) can be tested by connecting to an ATE through a specific test adapter. To analyze the error in a test report, we need to trace the fault back to the possible failed area. At that point, technicians may need to replace chips or other electronic components on the circuit board. Sometimes a unit may work abnormally only once in ten to twenty runs, so it’s important to repeat testing in order to confirm whether the fault is consistent or intermittent. During a flight, an aircraft may experience many issues, but some of them are not serious enough to threaten the safety of the whole flight. However, units in poor condition will be sent back for maintenance after the final post-flight report.
I spent the first two days learning the basic operation of the Display Unit (DU) used in the cockpit by reading the repair manual, and then I had the chance to help test faulty units with other people. The test for DU consists of six parts, from sensor checks to automatic tests of internal signal communication and display functions, and the total test usually lasts about one and a half hours.
I spent the rest of the week reading different manuals and shadowing others, specifically the manual for the Slat Flap Control Computer (SFCC) and Brake and Steering Control Unit (BSCU) and trying to understand how its testing and repair process works. Different aircraft computers require different testing steps, and the testing time can vary from a few hours to several days.
Week 5: Calibrating the Code
This week I fixed a lot of errors in the code and found out why the analysis was returning incorrect figures for the first event. I restarted the Bayesian process, however, the first part of the code failed immediately. I fixed this by obtaining the data in a different format from the Gravitational Wave Open Science Center and adjusting the parameter in the first cell. After it worked, another procedure was identified with a fitting error. The code returned a frequency of 323 Hz, which was higher than the expected frequency of ~251 Hz. This happens since the likelihood function did not add all frequency bins correctly. The data were in the range of 100 to 400 Hz, but the likelihood function looked at all the bins up to 2048 Hz. Since the signal has width in terms of frequency, the signal overflowed over the margins of the 100 to 400 Hz band, and the likelihood function identified this spillover as a bad fit and penalized it. This made the final results a bit inaccurate, as the algorithm chose higher frequencies and longer damping durations since those characteristics helped stay in the filter better.
Another issue was how well the code could distinguish the difference between nearby frequencies, as it could only identify frequencies apart in 50 Hz jumps with 20 milliseconds of data (82 data points). The fit lacked sufficient information to figure out the appropriate solution since it only had 7 slots to work with and 4 unknowns to solve for. I fixed this by adding zeros to the data to make it 512 points long, which helped the math zoom in on the frequency spectrum and give more slots to work with. I also changed the code to assess how well a model matches the data by adjusting the comparison range to where the data is actually meaningful rather than limiting it to the 100 to 400 Hz range.
Week 6: Calibrating the Model
This week I focused on finalizing the ringdown pipeline for the first event GW150914 and then adapting the same structure to the rest of the events. At first, the pipeline returned a fitted frequency that was too far from the expected Kerr value and a damping time that was too large, which suggested that the fit was following detector noise instead of the actual ringdown signal. The problem seemed to come from the preprocessing stage since the original bandpass range and ringdown window were both too wide, so the fit still included low-frequency noise and too much late-time decay. After narrowing the bandpass to 100 to 400 Hz and shortening the ringdown window, the FFT (Fast Fourier Transform) peak moved much closer to the expected range of the Kerr ringdown frequency.
The second issue was in the Bayesian step, where the likelihood was still comparing frequencies outside the relevant signal range. As a result, the fit could be pulled away from the true ringdown signal. I fixed this issue by restricting the likelihood to the same frequency range used in preprocessing. The data segment was also so short that the spacing between frequency points was too large to distinguish nearby frequencies well, so I zero-padded the data to make the sampled frequency grid denser. I also added PSD weighting so the fit relied more on cleaner parts of the detector frequencies.
After these changes, the event returned usable values that were close to the Kerr expectation. I applied the same corrected structure to GW170104, GW190814, GW170814, and GW151226, with several fixed parameters adjusted for each event. Next week I will test more events, compare values across events, and expand the results section.
Week 7: Fine-Tuning Analysis of Ringdown Events
This week I focused on comparing the first five ringdown events using the same pipeline to determine which results were usable, which still seemed biased, and which needed more work before they could be analyzed in a consistent way. Although the pipeline ran successfully for all five events, the fitted results were not equally reliable for combined interpretation. GW150914, GW170104, and GW170814 gave the most stable and cleanest results, since they all produced values that remained broadly consistent with the Kerr expectation within uncertainty, as shown by the near-zero central values of the frequency shift and damping-time shift and by the tighter upper bounds of 20.07% for the frequency shift and 43.39% for the damping-time shift. On the other hand, there were still problems with the fitted frequency and damping time for GW190814 and GW151226.
In the earlier version of the code, the resulting frequency for GW190814 was too high, which made the apparent deviation from the current Kerr reference look larger. After narrowing the analysis range and cleaning up the event setup, the fitted result moved into a more stable region. Since the Kerr reference for this event still needs to be recomputed from published remnant mass and spin values using an external Kerr QNM calculation (qnm package), this result is currently provisional.
For GW151226, earlier runs were getting trapped at the edges of the allowed parameter range instead of measuring the signal itself. This has been fixed by increasing the sample rate, moving the ringdown start earlier, shortening the fitting window, and tightening the priors in the high-frequency region, and these changes helped the fitted frequency and damping time move off the boundaries and closer to the expected Kerr scale, making the result more interpretable. However, this still needs to be checked for stability.
Week 8: Applying My Method to a New Set of Events
This week, I tested a second set of events selected from GWOSC. I used the same Bayesian damped-sinusoid fitting method as before to carry out a triage analysis on those events. This allowed me to differentiate between events with interpretable ringdown fits and those whose frequency or damping time estimations were still unusable under the existing standard. After the first screening, I sorted the events by quality and reran the strongest ones with different ringdown start times to see how much the fitted values changed across multiple window choices. I adjusted the structure of the notebook so that it can track how the combined bounds change as more events are added. The larger provisional combination did not change the overall picture of the result as the validated sample still gave an upper bound of 20.07% on the frequency shift and 43.39% on the damping time shift. These bounds became 16.53% and 43.03% when the better provisional events were added. These results remain broadly consistent with the Kerr expectation.
I also adjusted the event-selection procedure of the notebook so that it now can separate events into different categories before core analysis. This helps prevent weak or unstable events from being added directly to the final constraint. In addition, I built a catalog-assisted event sample using metadata from GWOSC. I used qnm to estimate rough Kerr quasinormal-mode reference values based on estimations of remnant mass and an anticipated final spin. This enables a scalable structure for adding more events to the project while keeping the final constraint limited to events with credible ringdown fits.
Week 9: Further Refining Parameters
Building on last week’s work, I refined the automated classification algorithm that assigns events to groups based on their posterior uncertainties and robustness behavior, improving the internal consistency of the analysis. I restructured the combined-results framework to compare multiple event subsets rather than rely on one number, clarifying which events are strong enough to support the final constraint by distinguishing among the historical core sample, the stricter automatically validated sample, and the expanded provisional sample. I also implemented a posterior-sample/qnm Kerr-baseline update that uses public remnant mass and spin estimates to refine the Kerr reference values, thereby strengthening the baseline for comparing measured ringdown parameters to the Kerr prediction and preparing the analysis for a larger catalog-assisted sample.
I also re-examined which types of black-hole structure are still allowed by comparing the observational constraints with the expected deviation scales from various quantum- and modified-gravity models after the results. I have nearly finished completing the qnm baseline update for the entire event catalog and documenting which catalog-only events still require direct ringdown fits. I still need to finish those direct fits and recompute the combined bounds using the updated classification.
Week 10: Digging into Theory
This week I was mainly working on the theory part of the project. Since it still needs more quantitative comparison, I read a few papers, including Cardoso and Pani’s article on dark compact objects, which is a reference for the kinds of horizonless or near-horizon-modified objects that could mimic black holes and for how their ringdown signals can differ. They point out that since the early ringdown signal is determined mainly by the photon sphere rather than directly by the horizon, objects without an event horizon may produce a black-hole-like ringdown at first, with deviations appearing later as echoes. Almheiri et al.’s Reviews of Modern Physics article discusses the island formula and how some recent work has shown that black-hole evaporation can be unitary, which helps explain why near-horizon quantum structure is taken seriously. From these papers, I was building a comparison table, which is useful for updating the theory section and adding a short subsection on what the present bound cannot constrain, showing each candidate non-Kerr model, its predicted fractional frequency shift at stellar-mass scales, and whether the current 17% bound, which comes from combining the validated events and represents the largest fractional shift in the ringdown frequency away from the Kerr prediction that the current data still allow, can disfavor it. Anything much smaller would remain compatible with the present observations, and anything significantly above this level would be disfavored by the current data.
Week 11: The Final Paper
This week I was finishing up the final paper. The headline result was the most significant change from last week’s value of 17% bound on validated events. Repeating the combination using only the 3 events that pass an automated quality rule gives a tighter bound on the fractional frequency and damping-time shift. I kept the historical-core combination as a continuity check against the earlier analysis, but the combination of the 3 events selected by the automated rule is now the one that appears as the main result.
I updated the theory section so it is now based on the comparison table from last week. In particular, higher-curvature modified gravity predicts shifts close to the 11.7% bound, so this is the only case that is starting to be constrained. Other theoretical frameworks like the soft hair, string fuzzballs, and loop-quantum-gravity polymer horizons all predict shifts well below the bound, so my analysis does not constrain them. These models all try to solve the black-hole information paradox by storing the information in tiny features right at the horizon. Unfortunately, my results cannot fully test them. As Cardoso, Franzin, and Pani showed in their 2016 paper, the early ringdown signal is set by the photon sphere, which sits outside the horizon, not by the horizon itself. Therefore, even if horizon-microstructure exists, it would not show up in the part of the signal current measurement looks at.
I also added a few sentences to the method section explaining the rules (uncertainty size, start-time stability, consistency of Kerr scale) used by the classifier so that the validation step is reproducible. In addition, I revised section 5 around the comparison table and added a subsection on what the bound can't constrain. Then I regenerated Figure 2 to incorporate the new 0.117 bound in order to match the result.