Raj Patil

Research

(Overview)

The observations by Galileo through his telescopes opened new horizons in our understanding of the cosmos. It allowed us to see celestial objects in ways previously unimaginable, revealing moons around Jupiter, the phases of Venus, and much more. Similarly, the first detection of gravitational waves in 2015 has started a new era of astronomical exploration. It allows us to observe cosmic phenomena, such as black hole mergers and neutron star collisions, that were once beyond our reach, fundamentally altering our understanding of the universe.

The question I aim to address is the following: When two objects such as black holes and/or neutron stars, undergo a binary coalescence, they emit gravitational waves. We detect these waves using our amazing detectors. What information can we obtain about the properties of the two colliding objects by analyzing the detected gravitational waves? Specifically, what insights can we gain about their mass, spin, equation of state, their surroundings, and so on?

What are gravitational waves? [LIGO] How are gravitational waves detected? [GW Open Data Workshop]

Image credits: [Link]

One fun excercise is to hear the pleasing melody of graviational waves after converting them into sound waves. Here [Soundofspacetime] you can listen to the sound of gravitational waveforms emitted by various binary sources.
CAUTION! gravitational waves are not sound waves and this is just a fun excercise.

Interesting articles / lectures on gravitational waves:

Massive Black Holes Shown to Act Like Quantum Particles	[Link]	(2022)
Gravitational-wave physics and astronomy in the 2020s and 2030s	[Link]	(2021)
Gravitational waves, Einstein's ripples in spacetime, spotted for first time	[Link]	(2016)
Gravitational Waves: A New Era of Astronomy Begins (Panel discussion at World Science Festival) MODERATOR: Brian Greene, PARTICIPANTS: Barry Barish, Nergis Mavalvala, Frans Pretorius, David Shoemaker, Rai Weiss	[Link]	(2016)

Recent relevant reviews / snowmass papers:

Gravitational Waves and Scattering Amplitudes	[2204.05194]
Post-Minkowskian expansion from Scattering Amplitudes	[2203.13024]
Classical Gravity from Scattering Amplitudes	[2203.13025]

A list of seminal papers in the field of gravity can be found here [link]

Research

(Details)

Currently, I work on the studying astrophysical compact objects and gravitational waves emitted by them using the techniques of quantum field theories and scattering amplitudes. This problem is interesting because the recent direct detections of gravitational waves by LIGO and Virgo observatories have proved to be a probe for the physics of celestial objects like black holes and neutron stars. Such detections have the potential to unravel the mysteries of cosmic origins, equations of state of compact objects and will prove to be a test to the theory of general relativity. On the other hand, the framework of Quantum field theory has proven to be very successful at predicting physical behavior to high accuracy and precision and is the basic language of modern theoretical physics. Moreover, the techniques of scattering amplitudes provide us with several tools which make the calculation of the physical observables systematic and insightful.

In my master's thesis, I studied the method of Effective Field Theories (EFT) used to model the gravitational waves emitted by various binary sources. Such sources, due to their non-relativistic nature, are analytically studied using the techniques of post-Newtonian (PN) approximation by perturbatively expanding in orders of orbital velocity over the speed of light. I followed the calculation of Einstein-Infeld-Hoffmann (EIH) Lagrangian, which is the 1PN correction to the two body gravitational potential. Then, to consider the effects of the electromagnetic charge of the constituents of the binary system, I newly derived the corrections to this 1PN potential by adding photons in the formalism which can be found here [arXiv:2009.11107]. To study the effects of the spin of binary constituents on the waveform, I reviewed the calculation of the Spin-Spin, Spin-Orbit, and Spin-squared effective potentials up to 2PN. I also followed the calculation of the Burke-Thorne radiation reaction force at 2.5 PN, using the Schwinger-Keldysh formalism of open quantum field theories.

Currently, for my Ph.D. thesis, I am working on computing state-of-the-art higher-order effective potentials and fluxes. These potentials and fluxes are important as they are used to compute accurate theoretical waveform templates which are compulsory ingredients for data analysis and reliable physical interpretation of the gravitational wave signals. I am developing a fast and efficient Mathematica routine for the automatic computation of Feynman diagrams and the corresponding integrals using the multi-loop techniques of quantum field theories [Poster at QCDmeetsGravity2022]. Using this I have performed the following analyses:

• Spin-orbit potential at NNNLO (at 4.5PN): [arXiv:2209.00611]
• Quadratic-in-spin potential at NNNLO (at 5PN): [arXiv:2210.09176]

Astrophysical black holes and neutron stars usually have a non-zero angular momentum and this "spin" has a huge impact on the emitted gravitational waves. The effects of spin can be characterised as follows. The spin-orbit sector is analogous to the fine structure correction obtained to the hydrogen atom, which describe the interaction between the orbital angular momentum of the binary and the spin of one of its constituents. Whereas, the quadratic in spin are analogous to the hyperfine structure corrections to the hydrogen atom and describe the interaction between each other/self of the spins of the binary constituents. I have computed the effective Hamiltonians at 4.5PN and 5PN, that describe the effect of spin of the constituents on the binary dynamics, thus on the emitted gravitational waves.

• Dynamic tidal potential at 2PN: [arXiv:2304.02030]
• Dynamic and adiabatic tidal potential at 3PN: [arXiv:2308.01865]
• Adiabatic tidal fluxes at 2PN: [arXiv:2412.01706]

Neutron stars feature a number of oscillation modes, and to understand them we can picture a basic stellar model that consists of the continuity equation (conservation of mass), Euler’s equation (equation of motion for the fluid elements), Poisson’s equation (that determines the gravitational force from the matter distribution), and the equation-of-state (that describes how pressure and density are related). With these elements combined, we can describe a star in equilibrium, which we can then perturb. The lowest frequency normal mode of perturbed oscillation is known as the fundamental mode (f-mode), which is one of the dominant modes in the context of tidal excitation. I have computed the effective Hamiltonians at 2PN and 3PN, that describe the effect of such tidal f-mode oscillations on the binary dynamics, thus on the emitted gravitational waves. When these oscillation frequency is large as compared to the external driving tidal frequency (which happens in the early inspiral), the tides are locked and move adiabatically with the companion object in the binary. For this case of adiabatic tides, I have computed the effective Hamiltonians at 3PN and also computed the energy flux, the angular momentum flux, the mode amplitudes and the mode phase at 2PN.

I am also working on developing SEOBNR-PM [arXiv:2405.19181] which is a bound-orbit waveform model that uses the post-Minkowskian (PM) results in the effective one body (EOB) formalism. A typical time-domain waveform model uses the Hamiltonian (for conservative effects) and Fluxes (for dissipative effects) to evolve the dynamics of the binary system in the inspiral phase when the orbital radius is slowly decaying due to gravitational wave emission. Then when two compact objects collide on each other, a numerical relativity (NR) and black hole perturbation theory informed templated is used to model the merger and the ringdown. In SEOBNR-PM we use the PM scattering angle (upto 4PM for non-spinning and 5PM for spinning) to construct a PM Hamiltonian, which is a new feature of this model. Here is one example of a waveform generated using the model and its comparison to the corresponding NR waveform.