Research

From perturbation theory to fully nonlinear black hole dynamics

Numerical relativity (NR) accurately describes comparable-mass black hole mergers but becomes increasingly expensive at large mass ratios. Black-hole perturbation theory (BHPT), by contrast, is computationally less expensive but formally applies when one black hole is much lighter than the other. I helped uncover a surprising connection between these regimes: a simple two-parameter rescaling of time and amplitude brings linear BHPT waveforms remarkably close to fully nonlinear NR waveforms, even for comparable-mass binaries. This relationship, known as the α–β scaling, reveals an unexpected simplicity in relativistic binary dynamics and provides a practical foundation for waveform modeling across mass ratios.

Building on this connection, I developed gwTeukolsky, a modular, tiered perturbative framework for investigating which physical corrections matter at different stages of binary evolution. By systematically comparing perturbative calculations incorporating different dynamical components against fully nonlinear numerical relativity simulations, I study how finite-mass-ratio effects shape the inspiral and merger, and where different perturbative approximations succeed or break down. This work also introduces the Vishveshwara Catalog, the first public catalog of black-hole perturbation theory waveforms, comprising 1,525 simulations across 346 binary configurations, including precessing binaries.

Universal waveform structure, higher harmonics, and observable eccentricity

Orbital eccentricity carries important clues about how binary black holes form, particularly through dynamical interactions in dense astrophysical environments. Yet eccentric mergers produce complex, highly oscillatory gravitational-wave signals whose higher harmonics are difficult to model accurately. I developed the methodology underlying the first numerical relativity surrogate model (NRSur2dq1Ecc) for eccentric binary black hole mergers. Using numerical relativity simulations, I subsequently discovered a remarkably simple structure: in non-precessing eccentric binaries, the eccentric modulations of different gravitational-wave modes follow approximately universal relationships. This discovery underpins gwNRHME, a computationally inexpensive framework that reconstructs higher harmonics from the eccentric modulation of the dominant quadrupole mode, allowing existing eccentric waveform models to be readily extended beyond the quadrupole.

Building on this discovery, I developed a post-Newtonian-theory-inspired framework for characterizing orbital eccentricity directly from the universal modulation patterns in gravitational waveforms, providing a gauge-independent definition of eccentricity. I also collaborated with the IAS group to develop gwharmone, a data-driven surrogate model for eccentric binary black hole waveforms that decomposes each spherical-harmonic mode into its constituent eccentric harmonics. Together, these developments connect the underlying physics of eccentric mergers to efficient waveform modeling and the interpretation of gravitational-wave observations.

The lingering imprint of spacetime curvature after black hole ringdown

The gravitational radiation from a merging black hole does not simply decay through exponentially damped quasinormal modes. At sufficiently late times, waves scattered by the curvature of spacetime produce slowly decaying, power-law tails. These signatures provide a complementary probe of black hole dynamics beyond the conventional ringdown description. However, late-time tails are generally expected to become prominent only long after merger, beyond the time spans typically covered by numerical relativity simulations.

Using black-hole perturbation theory simulations, I investigated the physical origin and phenomenology of late-time tails in highly eccentric binary black hole mergers. I demonstrated that orbital eccentricity can significantly enhance these tails and cause them to emerge much earlier than in quasi-circular mergers, potentially bringing them within reach of numerical relativity simulations. These findings subsequently motivated follow-up numerical relativity investigations, which identified late-time tails in simulations of eccentric black hole mergers.

The final mass, spin, and recoil velocity of a merger remnant provide a direct connection between the relativistic dynamics of black hole mergers and their astrophysical consequences. I have developed analytical models of these remnant properties by combining physical insights with numerical relativity and black-hole perturbation theory simulations. These models span a broad range of binary configurations, from comparable to extreme mass ratios, including aligned-spin, precessing, and eccentric binaries.

I use these models to investigate the astrophysical consequences of black hole mergers, particularly gravitational-wave recoil. The anisotropic emission of gravitational radiation imparts a velocity kick to the remnant, sometimes large enough to eject it from its host environment. Using gravitational-wave observations, we found evidence for substantial recoil kicks in GW200129 and GW191109. Extending this investigation to electromagnetic observations, I used HST and JWST imaging together with relativistic recoil models to constrain the possible progenitor binary of RBH-1, a candidate runaway supermassive black hole.

Dense star clusters are natural environments for the dynamical formation of binary black holes. Through repeated gravitational encounters, black holes can form binaries and merge, while remnants that remain gravitationally bound to their host clusters can undergo subsequent mergers, building progressively more massive black holes. Whether these remnants are retained depends critically on their gravitational-wave recoil kicks. Using my relativistic recoil models, I investigated the astrophysical consequences of black hole mergers across different environments. Applying these models to events in the GWTC catalogs, I estimated the retention probabilities of merger remnants in globular clusters, nuclear star clusters, and galaxies. I also performed thousands of dense star cluster simulations to investigate how recoil prescriptions influence hierarchical black hole growth. These simulations showed that older, simplified recoil models can underestimate hierarchical merger rates, demonstrating that accurate relativistic modeling is essential for predicting the assembly of black hole populations.

Beyond population-level studies, individual gravitational-wave events can provide clues about their formation environments. I investigated two asymmetric binary black hole mergers from the IAS catalog, GW190711_030756 and GW200114_020818, exploring their possible astrophysical formation pathways and what their inferred properties reveal about dynamical assembly.

I developed gwAgent, a physics-informed AI framework that uses large language model agents to discover compact, interpretable analytical surrogate models of gravitational-wave signals. By combining symbolic expressions, numerical experiments, and iterative validation, gwAgent searches for physically meaningful representations rather than relying exclusively on black-box approximations. On the benchmarks considered, it achieves competitive performance against conventional machine-learning and symbolic-regression approaches while retaining interpretable analytical expressions.

I also developed gwBenchmarks, a framework for evaluating AI systems on realistic gravitational-wave research tasks requiring domain-specific reasoning, computational tools, and multi-step scientific workflows. Rather than measuring performance solely through question answering, gwBenchmarks evaluates whether agents can carry out scientific calculations and produce results that can be independently checked. Together, these projects investigate both the potential of AI for scientific model discovery and the reliability of AI systems as research assistants.

Can AI coding agents accelerate the development of sophisticated numerical physics software without compromising scientific reliability? I investigated this question through the development of gwKerrDynamics and gwTeukolsky, two complementary computational frameworks for black hole dynamics and gravitational-wave generation. Developed over approximately five weeks with extensive use of AI coding agents, the packages grew to roughly 34,000 lines of code across 120 modules, supported by 623 tests, and enabled the production of 1,525 perturbative waveforms for the Vishveshwara Catalog. The agents assisted with implementation, testing, numerical experiments, and debugging, while the physical formulations, conventions, validation criteria, and scientific interpretation were specified and assessed by the researchers.

A central lesson of this work is that generating complex scientific code is not the same as establishing its physical correctness. AI agents can produce plausible implementations and explanations even when calculations contain subtle errors that survive conventional test suites. We therefore developed a validation-driven workflow that challenges generated results against independent calculations, published data, analytic limits, and physical symmetries. This approach enabled the systematic development of increasingly sophisticated perturbative calculations while revealing both the capabilities and limitations of agentic scientific programming. More broadly, it demonstrates how AI-assisted software development can accelerate computational research when coupled to rigorous, physics-based verification.

Numerical relativity and black hole perturbation theory provide accurate descriptions of merging black holes, but their computational cost makes direct use in gravitational-wave parameter estimation impractical. I develop reduced-order surrogate waveform models that learn from a limited set of high-fidelity simulations and rapidly predict waveforms across a much larger range of binary parameters. By exploiting the structure and smooth dependence of gravitational-wave signals on the underlying physical parameters, these models can reproduce expensive calculations at a fraction of their original computational cost.

My work spans several complementary approaches, including numerical relativity surrogates for eccentric binary black holes, BHPTNRSurrogate models that connect perturbation theory with numerical relativity across mass ratios, and EMRISurrogate models for extreme-mass-ratio systems. Together, these efforts aim to make accurate waveform predictions accessible across different binary configurations and dynamical regimes, enabling their use in gravitational-wave inference and astrophysical studies.

Accurate waveform models are only part of the challenge in gravitational-wave astronomy. Extracting the physical properties of merging black holes requires exploring high-dimensional parameter spaces, often with strong degeneracies and multiple likelihood peaks. I have worked on making Bayesian parameter estimation both faster and more reliable, including methods for reducing parameter degeneracies and improving the efficiency of posterior sampling.

In particular, I developed factorized parameter estimation, an approach designed to accelerate gravitational-wave inference toward real-time source characterization, and contributed to Cogwheel, a framework for efficient Bayesian parameter estimation. I have also carried out extensive analyses of gravitational-wave observations using high-fidelity numerical relativity surrogate models, including a study of GWTC-3 with fully precessing waveforms. These efforts connect advances in statistical inference with increasingly accurate descriptions of black hole mergers, allowing us to extract more information from gravitational-wave observations while keeping the computational cost manageable.

Before gravitational waves, I tested alternatives to general relativity, including Weyl conformal gravity, MOG and MOND-like theories, against the dynamics of globular clusters, the Milky Way, ultra-diffuse galaxies such as NGC1052-DF2, and the white dwarf mass-radius relation.

Much of this work is joint. Frequent collaborators include:

• IAS group. Tejaswi Venumadhav, Matias Zaldarriaga, Digvijay Wadekar, Javier Roulet, Barak Zackay, Ajit Kumar Mehta, Jonathan Mushkin
• Surrogate models and SXS. Scott Field, Vijay Varma, Harald Pfeiffer, Lawrence Kidder, Mark Scheel, Matthew Giesler
• Perturbation theory. Gaurav Khanna, Scott Hughes, Niels Warburton, Barry Wardell, Adam Pound, Maarten van de Meent, Alessandra Buonanno, Steven Liebling
• Data analysis. Rory Smith, Carl-Johan Haster, Avi Vajpeyi
• Tests of GR. Parameswaran Ajith, B. S. Sathyaprakash, Abhirup Ghosh
• Modified gravity. Koushik Dutta