Periodic Reporting for period 1 - ThorGW (Testing the horizon of black holes with gravitational waves)
Berichtszeitraum: 2024-05-01 bis 2026-04-30
Black holes are, in many ways, the simplest objects in the Universe. According to general relativity, black holes are described by only two parameters: their mass and their spin. Yet this apparent simplicity hides a profound mystery. A black hole is thought to be surrounded by an event horizon — a boundary beyond which nothing, not even light, can escape. At this surface, space and time effectively swap roles, and any information crossing it is forever hidden from the outside world.
The black hole paradigm leads to deep puzzles. One of the most famous ones is the information-loss paradox, which questions whether information that falls into a black hole is truly lost forever. If so, this would clash with the fundamental laws of quantum physics, which state that information must be preserved. This raises a fascinating possibility: is the event horizon a physical surface, or is it a mathematical prediction of Einstein’s theory that might need revision?
Gravitational waves offer a unique way to investigate this question. When two compact objects — such as black holes — orbit around each other, they gradually spiral inward and eventually merge. The newly formed object "rings" as it settles down, emitting gravitational waves like a bell produces sound. By measuring the frequency and how quickly these vibrations fade, we can infer the nature of the final object. If it has an event horizon, its ringing follows the predictions of general relativity. In the absence of a horizon, subtle differences may appear in the gravitational signal.
The ThorGW project set out to explore exactly this possibility. First, it developed a general description of how compact objects without an event horizon would vibrate, and connected these predictions to observable gravitational-wave signals. Second, it used current data to place the first constraints on whether astrophysical black holes truly possess an event horizon. Finally, it looked ahead, forecasting how next-generation gravitational-wave detectors will sharpen these tests and bring us closer to answering one of the most fundamental questions about the nature of space and time.
The black hole paradigm leads to deep puzzles. One of the most famous ones is the information-loss paradox, which questions whether information that falls into a black hole is truly lost forever. If so, this would clash with the fundamental laws of quantum physics, which state that information must be preserved. This raises a fascinating possibility: is the event horizon a physical surface, or is it a mathematical prediction of Einstein’s theory that might need revision?
Gravitational waves offer a unique way to investigate this question. When two compact objects — such as black holes — orbit around each other, they gradually spiral inward and eventually merge. The newly formed object "rings" as it settles down, emitting gravitational waves like a bell produces sound. By measuring the frequency and how quickly these vibrations fade, we can infer the nature of the final object. If it has an event horizon, its ringing follows the predictions of general relativity. In the absence of a horizon, subtle differences may appear in the gravitational signal.
The ThorGW project set out to explore exactly this possibility. First, it developed a general description of how compact objects without an event horizon would vibrate, and connected these predictions to observable gravitational-wave signals. Second, it used current data to place the first constraints on whether astrophysical black holes truly possess an event horizon. Finally, it looked ahead, forecasting how next-generation gravitational-wave detectors will sharpen these tests and bring us closer to answering one of the most fundamental questions about the nature of space and time.
The work performed was divided according to the identified Work Packages (WPs). Below, I provide a brief description of the work for each WP and its main achievements.
WP1 - Derivation of the quasinormal modes of horizonless objects in the spinning configuration: I derived the quasinormal-mode spectrum of horizonless compact objects in spinning configurations at first order in the spin. The work generalizes the black-hole membrane paradigm to horizonless compact objects, providing a consistent framework to compute their ringdown frequencies and identifying observable deviations from the Kerr spectrum. This establishes a key theoretical tool to probe the presence (or absence) of horizons through gravitational-wave observations. Moreover, I have extended the membrane paradigm to calculate the tidal deformability of horizonless compact objects in the inspiral and ringdown stages of a compact binary coalescence.
WP2 - First constraints on the location of the horizon of black holes from current GW observations: I co-developed a parametrized spin-precessing inspiral–merger–ringdown waveform model for tests of general relativity named Parametrized Effective One Body (pSEOB). The extension of the framework included the addition of spin-induced orbital precession and higher-order modes in the gravitational waveform. The model enables theory-agnostic tests of general relativity in the highly dynamical and nonlinear regime, constraining possible extensions of general relativity. The model was applied to the analysis of several gravitational-wave events such as GW150914, GW200129, GW230814 and GW250114. These are loud signals that are optimal probes for testing the event horizon of black holes.
WP3 - Estimation of the prospects of detectability of horizons with next-generation detectors: I am working on a project to constrain the horizon of black holes from future observations of massive binaries with LISA. The research project extends the results in Toubiana et at., Phys. Rev. D 109, 104019 (2024) by providing constraints on the compactness and the reflectivity of compact objects from the observations of the ringdown of massive remnants with a Bayesian analysis. I am supervising a PhD student who is implementing a fully Bayesian code the theory-motivated waveforms developed in WP1. Motivated by the results obtained on the gravitational-wave events in WP2, I have been working on identifying possible false deviations from general relativity expected to arise for current and future gravitational-wave detectors.
WP1 - Derivation of the quasinormal modes of horizonless objects in the spinning configuration: I derived the quasinormal-mode spectrum of horizonless compact objects in spinning configurations at first order in the spin. The work generalizes the black-hole membrane paradigm to horizonless compact objects, providing a consistent framework to compute their ringdown frequencies and identifying observable deviations from the Kerr spectrum. This establishes a key theoretical tool to probe the presence (or absence) of horizons through gravitational-wave observations. Moreover, I have extended the membrane paradigm to calculate the tidal deformability of horizonless compact objects in the inspiral and ringdown stages of a compact binary coalescence.
WP2 - First constraints on the location of the horizon of black holes from current GW observations: I co-developed a parametrized spin-precessing inspiral–merger–ringdown waveform model for tests of general relativity named Parametrized Effective One Body (pSEOB). The extension of the framework included the addition of spin-induced orbital precession and higher-order modes in the gravitational waveform. The model enables theory-agnostic tests of general relativity in the highly dynamical and nonlinear regime, constraining possible extensions of general relativity. The model was applied to the analysis of several gravitational-wave events such as GW150914, GW200129, GW230814 and GW250114. These are loud signals that are optimal probes for testing the event horizon of black holes.
WP3 - Estimation of the prospects of detectability of horizons with next-generation detectors: I am working on a project to constrain the horizon of black holes from future observations of massive binaries with LISA. The research project extends the results in Toubiana et at., Phys. Rev. D 109, 104019 (2024) by providing constraints on the compactness and the reflectivity of compact objects from the observations of the ringdown of massive remnants with a Bayesian analysis. I am supervising a PhD student who is implementing a fully Bayesian code the theory-motivated waveforms developed in WP1. Motivated by the results obtained on the gravitational-wave events in WP2, I have been working on identifying possible false deviations from general relativity expected to arise for current and future gravitational-wave detectors.
WP1: I extended the membrane paradigm to slowly rotating horizonless compact objects. I showed that the axial–polar isospectrality is broken, and the spin can drive instabilities in reflective ultracompact configurations—making spinning horizonless objects more distinguishable from black holes in the prompt ringdown. I developed a model-agnostic framework based on the membrane paradigm to expresses the tidal Love numbers of compact objects in terms of frequency-dependent viscosity coefficients—encompassing neutron stars and horizonless objects such as thin-shell gravastars. The results recovered known ultracompact behaviors and uncovered novel quasi-universal relations for neutron stars with different viscosities depending on the equations of state.
WP2: Within the parametrized effective-one-body framework, I analyzed several GW events. The analysis of GW250114 constrained for the first time the frequency of the ℓ = m = 4 quasinormal mode and set the strongest bounds to date on the fundamental ℓ = m = 2 mode, providing percent-level constraints on deviations from the Kerr solution. Other interesting events which indpendently provided a 10%-level constrain on the ringdown are GW150914 and GW200129. The analysis of GW230814 (currently under proof stage) revelead the possibility of having false deviations from general relativity due to detector's noise and waveform systematics. Additional work is required to develop strategies for mitigating false deviations of general relativity. The analysis of GW200129 demonstrated that false deviations from general relativity from induced spin-precession can be mitigated if modeled in the waveform. Moreover, I analyzed the population of compact objects detected up to 2024 finding that no more than 20% of the binary population can host totally reflective horizonless compact objects.
WP3: I produced an extensive list of possible causes for deviations from general relativity with future gravitational wave events. I identified noise artifacts from single gravitational-wave detectors as one of the most likely sources for biases. I also highlighted the importance of missing physics (spin-precession) and higher-order modes for parametrized tests of general relativity. I have furtherly forecasted the constraints that we will be able to set with Einstein Telescope on the fraction of totally reflecting horizonless compact objects in binary coalescences, finding that in just one day of observation we will be able to set an upper limit to this fraction down to 5% (as opposed to 20% currently achieved with about 2 years of observations).
WP2: Within the parametrized effective-one-body framework, I analyzed several GW events. The analysis of GW250114 constrained for the first time the frequency of the ℓ = m = 4 quasinormal mode and set the strongest bounds to date on the fundamental ℓ = m = 2 mode, providing percent-level constraints on deviations from the Kerr solution. Other interesting events which indpendently provided a 10%-level constrain on the ringdown are GW150914 and GW200129. The analysis of GW230814 (currently under proof stage) revelead the possibility of having false deviations from general relativity due to detector's noise and waveform systematics. Additional work is required to develop strategies for mitigating false deviations of general relativity. The analysis of GW200129 demonstrated that false deviations from general relativity from induced spin-precession can be mitigated if modeled in the waveform. Moreover, I analyzed the population of compact objects detected up to 2024 finding that no more than 20% of the binary population can host totally reflective horizonless compact objects.
WP3: I produced an extensive list of possible causes for deviations from general relativity with future gravitational wave events. I identified noise artifacts from single gravitational-wave detectors as one of the most likely sources for biases. I also highlighted the importance of missing physics (spin-precession) and higher-order modes for parametrized tests of general relativity. I have furtherly forecasted the constraints that we will be able to set with Einstein Telescope on the fraction of totally reflecting horizonless compact objects in binary coalescences, finding that in just one day of observation we will be able to set an upper limit to this fraction down to 5% (as opposed to 20% currently achieved with about 2 years of observations).