Browsing by Author "Mukherjee, Sajal"

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Analytical model of precessing binaries using post-Newtonian theory in the extreme mass-ratio limit I: General Formalism
(ARXIV, 2024-02) Mukherjee, Sajal
We develop a fully analytical waveform model for precessing binaries with arbitrary spin vectors using post-Newtonian theory in the extreme mass-ratio limit and a hierarchical multi-scale analysis. Although the post-Newtonian series poorly converges in this limit, our results can be used to estimate how precession affects the measurability of certain binary parameters, and to inform and compare with other waveform approximants, such as effective-one-body models, hybrid waveforms, and self-force calculations.
Can extended bodies follow geodesic trajectories?
(ARXIV, 2023-11) Mukherjee, Sajal
We provide an extension of the analysis on whether an extended test body can follow a geodesic trajectory given by Mukherjee, S., Lukes-Gerakopoulos, G. and Nayak, R. K. (2022), Extended bodies moving on geodesic trajectories, General Relativity and Gravitation, 54(9), 113, arXiv: 1907.05659. In particular, we consider a test body in a pole-dipole-quadrupole approximation under the Ohashi-Kyrian-Semerák spin supplementary condition moving in the Schwarzschild and Kerr background. Using orbital setups under which a pole-dipole body can follow geodesic motion, we explore under which conditions this can take place also in the pole-dipole-quadrupole approximation, when only the mass quadrupole is taken into account. For our analysis we employ the assumption that the dipole contribution and the quadrupole contribution vanish independently.
Carter constant and angular momentum
(World Scientific, 2018) Mukherjee, Sajal
We investigate the Carter-like constant in the case of a particle moving in a nonrelativistic dipolar potential. This special case is a missing link between the Carter constant in stationary and axially symmetric spacetimes (SASS) such as Kerr solution and its possible Newtonian counterpart. We use this system to carry over the definition of angular momentum from the Newtonian mechanics to the relativistic SASS.
Collisional Penrose process and jets in Kerr naked singularity
(Springer, 2018-07) Mukherjee, Sajal
In this article, we investigate the possibilities of energy extraction from an over-spinning Kerr spacetime using collisional Penrose process. This phenomenon can produce a high-energy ejecta of particles under certain favourable conditions. Unlike black holes, in this case, the particles endowed with higher energy can escape to infinity. We use this model to explore various possibilities of jet formation in an over-spinning geometry. Primarily we concentrate on the energy extraction associated with collisions taking place on the off-equatorial planes and find the signature of jets from them. We also apply this formalism to a toy model which could be useful in practical astrophysical scenarios. This is motivated from the atomic model where we have considered the decay of a circular orbit because of energy extraction via Penrose mechanism.
Collisional Penrose process with spinning particles
(Elsevier, 2018-03) Mukherjee, Sajal
In this article, we have investigated collisional Penrose process (CPP) using spinning particles in a Kerr spacetime. Recent studies have shown that the collision between two spinning particles can produce a significantly high energy in the center of mass frame. Here, we explicitly compute the energy extraction and efficiency as measured by an observer at infinity. We consider the colliding particles as well as the escaping particles may contain spins. It has been shown that the energy extraction is larger than the non-spinning case and also their possibility to escape to infinity is wider than the geodesics.
The curious case of parabolic encounters: gravitational waves with linear & non-linear memory
(2025-11) Mukherjee, Sajal
The memory effect is known to introduce a permanent displacement in the gravitational wave (GW) detectors after the passage of a GW signal. While the linear memory adheres to the source properties, the non-linear memory is a secondary effect sourced by the GW itself. In the present work, we discuss GW signals with both these kinds of memory effects, while focusing on the parabolic limit of an encounter. This special case is theoretically intriguing and emerges as a limiting situation for both eccentric and hyperbolic events. However, in this paper, we argue that a simple extrapolation of memory calculations for eccentric or hyperbolic cases to the parabolic case may lead to incorrect estimations. Therefore, we treat the parabola as a special case and use an intrinsic parameterization, with which we calculate gravitational wave signals and their energy spectrum via an effective field theory formalism. Unlike the hyperbolic case, which is known to have linear memory, we notice that parabolic encounters bring out new features in the zero frequency limit (ZFL). Our work highlights some of the key challenges and salient aspects of these encounters, and paves the way to study such binary evolution with nonzero memory.
Detectability of gravitational wave stochastic background from weakly hyperbolic encounters
(ARXIV, 2023-11) Mukherjee, Sajal
We compute the stochastic gravitational wave (GW) background generated by black hole-black hole (BH-BH) hyperbolic encounters with eccentricities close to one and compare them with the respective sensitivity curves of planned GW detectors. We use the Keplerian potential to model the orbits of the encounters and the quadrupole formula to compute the emitted GWs. We take into account hyperbolic encounters that take place in clusters up to redshift 5, with BH's masses spanning from 5M⊙ to 55M⊙. We assume the clusters to be virialized and we study several cluster models with different mass and virial velocity, and finally, provide an accumulative result to display the background in an average sense. Using the maxima and the minima of our accumulative result for each frequency, we provide analytical expressions for both optimistic and pessimistic scenarios. Our results imply that the background from these encounters are likely to be detected by the third generation detectors Cosmic explorer, and Einstein telescope, while the tail section at lower frequencies intersects with DECIGO -- making it a possible source for both ground and space based future GW detectors
Discrete Morse theory and the topology of matching complexes of complete graphs
(ARXIV, 2024-01) Mukherjee, Sajal
We denote the matching complex of the complete graph with n vertices by Mn. Bouc first studied the topological properties of Mn in connection with the Quillen complex. Later Björner, Lovász, Vrećica, and Živaljević showed that Mn is homotopically (νn−1)-connected, where νn=⌊n+13⌋−1, but in general the topology of Mn is not very well-understood even for smaller natural numbers. Forman developed discrete Morse theory, which has various applications in diverse fields of studies. In this article, we develop a discrete Morse theoretic technique to capture deeper structural topological properties of Mn. We show that Mn is \emph{geometrically} (νn−1)-connected, where the notion of geometrical k-connectedness as defined in this article, is stronger than that of homotopical k-connectedness. Previously, Björner et al. showed that M8 is simply connected, but not 2-connected. The technique developed here helped us determine that M8 is in fact homotopy equivalent to a wedge of 132 spheres of dimension 2.
Entanglement harvesting for different gravitational wave burst profiles with and without memory
(ARXIV, 2023-09) Mukherjee, Sajal
In the present article, we study how different gravitational wave (GW) burst profiles in linearized gravity, with and without the asymptotic memory, may influence the harvesting between two static Unruh-DeWitt detectors. To this end, we investigate the following burst profiles -- Gaussian, sech-squared, Heaviside step function, and tanh. Out of these, the first two bursts contain no memory, while the latter two consist of a non-vanishing memory effect. We find that in all of these cases, entanglement harvesting is possible, and it decreases with the increasing distance between detectors and the detector transition energy. We observe that the harvesting differs qualitatively based on the presence or absence of the memory, which is prominent in a low transition energy regime. With memory, the harvesting keeps increasing with decreasing transition energy, while without memory, it tends to reach finite values. Furthermore, for the two burst profiles without memory, longer bursts correspond to greater harvesting in the low detector transition energy regime, and this characteristic is reversed for larger transition energy. Meanwhile, for the tanh-type profile with memory, harvesting is always greater for shorter bursts. We discuss various implications of our findings.
Extended bodies moving on geodesic trajectories
(Springer, 2022-09) Mukherjee, Sajal
This work investigates whether an extended test body obeying the Mathisson–Papapetrou–Dixon equations under the Ohashi–Kyrian–Semerák spin supplementary condition can follow geodesic trajectories in curved spacetimes. In particular, we explore what are the requirements under which pole-dipole and pole-dipole-quadrupole approximated bodies moving in the Schwarzschild or Kerr spacetimes can follow equatorial geodesic trajectories. We do this exploration thoroughly in the pole-dipole case, while we focus just on particular trajectories in the pole-dipole-quadrupole case. Using the Ohashi–Kyrian–Semerák spin supplementary condition to fix the center of the mass of a pole-dipole body has the advantage that the hidden momentum is eliminated. This allows the four-velocity to be parallel to the four-momentum, which provides a convenient framework for our investigation. We discuss how this feature can be recovered at a pole-dipole-quadrupole approximation and what are the consequences.
Gravitational wave observatories may be able to detect hyperbolic encounters of black holes
(OUP, 2021-09) Mukherjee, Sajal
Gravitational wave (GW) astronomy promises to observe different kinds of astrophysical sources. Here, we explore the possibility of detection of GWs from hyperbolic interactions of compact stars with ground-based interferometric detectors. It is believed that a bound compact cluster, such as a globular cluster, can be a primary environment for these interactions. We estimate the detection rates for such events by considering local geometry within the cluster, accounting for scattering probability of compact stars at finite distances, and assuming realistic cluster properties guided by available numerical models, their formation times, and evolution of stars inside them. We find that, even in the conservative limit, it may be possible to detect such black hole encounters in the next few years by the present network of observatories with the ongoing sensitivity upgrades and one to few events per year with the next-generation observatories. In practice, actual detection rates can significantly surpass the estimated average rates, since the chances of finding outliers in a very large population can be high. Such observations (or, no observation) may provide crucial constraints to estimate the number of isolated compact stars in the universe. These detections will be exciting discoveries on their own and will be complementary to observations of binary mergers, bringing us one step closer to address a fundamental question: How many black holes are there in the observable universe?
Horndeski theories confront the Gravity Probe B experiment
(APS, 2018-06) Mukherjee, Sajal
In this work we have investigated various properties of a spinning gyroscope in the context of Horndeski theories. In particular, we have focused on two specific situations—(a) when the gyroscope follows a geodesic trajectory and (b) when it is endowed with an acceleration. In both these cases, besides developing the basic formalism, we have also applied the same to understand the motion of a spinning gyroscope in various static and spherically symmetric spacetimes pertaining to Horndeski theories. Starting with the Schwarzschild de Sitter spacetime as a warm up exercise, we have presented our results for two charged Galileon black holes as well as for a black hole in scalar coupled Einstein-Gauss-Bonnet gravity. In all these cases we have shown that the spinning gyroscope can be used to distinguish black holes from naked singularities. Moreover, using the numerical estimation of the geodetic precession from the Gravity Probe B experiment, we have constrained the gauge/scalar charge of the black holes in these Horndeski theories. Implications are also discussed.
Impact of a third body on binary neutron star tidal interactions
(2025-11) Mukherjee, Sajal
For waveform modelling of compact binary coalescence, it is conventionally assumed that the binary is in isolation. In this work, we break that assumption and introduce a third body at a distance. The primary goal is to understand how the distant third body would affect the binary dynamics. However, in the present work, we treat the three-body problem perturbatively and study tidal interaction in the binary due to the third body's presence. We introduce appropriate modifications to the equations governing the orbital motions and the evolution equations of the binary component's quadrupole moment. Further, we obtain the radiated energy and accumulated dephasing for the binary. We show that for b-EMRI, the effect is weak in the tidal sector, while for systems such as b-IMRIs, it would be most relevant to study these effects.
Multipole moments of compact objects with NUT charge: Theoretical and observational implications
(APS, 2020-12) Mukherjee, Sajal
We derive the multipole moments of the Kerr-Newman-Unti-Tamburino (NUT) black hole spacetime using the Geroch-Hansen formalism, even though the spacetime is not asymptotically flat. Intriguingly, in the presence of the NUT charge, the absence of reflection symmetry about the equatorial plane leads to mass and spin multipole moments of all orders, in stark contrast to Kerr-like spacetimes. This leads to a drastic departure of the multipolar structure of a compact object with NUT charge, whose implications for gravitational wave observations have been explored. Our analysis of multipole moments for the Kerr-NUT spacetime is also in tune with the Thorne’s approach.
Observation of W Z γ production and constraints on new physics scenarios in proton-proton collisions at √s = 13 TeV
(APS, 2025-07) Mukherjee, Sajal
A measurement of the 𝑊⁢𝑍⁢𝛾 triboson production cross section is presented. The analysis is based on a data sample of proton-proton collisions at a center-of-mass energy of √𝑠 =13 TeV recorded with the CMS detector at the LHC, corresponding to an integrated luminosity of 138 fb−1 . The analysis focuses on the final state with three charged leptons, ℓ±⁢𝜈⁢ℓ+⁢ℓ− , where ℓ =𝑒 or 𝜇 , accompanied by an additional photon. The observed (expected) significance of the 𝑊⁢𝑍⁢𝛾 signal is 5.4 (3.8) standard deviations. The cross section is measured in a fiducial region, where events with an ℓ originating from a tau lepton decay are excluded, to be 5.48 ±1.11 fb , which is compatible with the prediction of 3.69 ±0.24 fb at next-to-leading order in quantum chromodynamics. Exclusion limits are set on anomalous quartic gauge couplings and on the production cross sections of massive axionlike particles.
Off-equatorial stable circular orbits for spinning particles
(APS, 2018-10) Mukherjee, Sajal
n this article, we investigate the motion of a spinning particle at a constant inclination, different from the equatorial plane, around a Kerr black hole. We mainly explore the possibilities of stable circular orbits for different spin supplementary conditions. The Mathisson-Papapetrou equations are extensively applied and solved within the framework of linear spin approximation. We explicitly show that for a given spin vector of the form Sa=(0,Sr,Sθ,0), there exists a unique circular orbit at (rc, θc) defined by the simultaneous minima of energy, angular momentum, and Carter constant. This corresponds to the innermost stable circular orbit (ISCO) which is located on a nonequatorial plane. We further establish that the location (rc, θc) of the ISCO for a given spinning particle depends on the radial component of the spin vector (Sr) as well as the angular momentum of the black hole (J). The implications of using different spin supplementary conditions are investigated.
On some novel features of the Kerr–Newman-NUT spacetime
(Springer, 2019-02) Mukherjee, Sajal
In this work we have presented a special class of Kerr–Newman-NUT black hole, having its horizon located precisely at , for , where M, l, a and Q are respectively mass, NUT, rotation and electric charge parameters of the black hole. Clearly this choice radically alters the causal structure as there exists no Cauchy horizon indicating spacelike nature of the singularity when it exists. On the other hand, there is no curvature singularity for , however it may have conical singularities. Furthermore there is no upper bound on specific rotation parameter a / M, which could exceed unity without risking destruction of the horizon. To bring out various discerning features of this special member of the Kerr–Newman-NUT family, we study timelike and null geodesics in the equatorial as well as off the equatorial plane, energy extraction through super-radiance and Penrose process, thermodynamical properties and also the quasi-periodic oscillations. It turns out that the black hole under study radiates less energy through the super-radiant modes and Penrose process than the other black holes in this family.
Periastron shift for a spinning test particle around naked singularities
(APS, 2018-06) Mukherjee, Sajal
In the present article, we investigate the Periastron precession for a spinning test particle moving in nearly circular orbits around naked singularities. We consider two well-known solutions that can produce a spacetime with naked singularity—(a) first, the Reissner-Nordström metric, which is a static charged solution with spherical symmetry, and (b) second, the stationary, axisymmetric Kerr metric. For simplicity, we only consider the motion confined on the equatorial plane in both these cases and solve exactly the Mathisson-Papapetrou equations. In addition, we analytically compute the Periastron precession within the framework of linear spin approximation. The inclusion of the spin parameter modifies the results with nonspinning particles and also reflects some interesting properties of the naked geometries. Furthermore, we carried out a numerical approach without any assumptions to probe the large order spin values. The implication of the spin-curvature coupling in connection with the naked geometries is also discussed.
Possible connection between the reflection symmetry and existence of equatorial circular orbit
(APS, 2021-05) Mukherjee, Sajal
We study a viable connection between the circular-equatorial orbits and reflection symmetry across the equatorial plane of a vacuum stationary axis-symmetric spacetime in general relativity. The behavior of the circular equatorial orbits in the direction perpendicular to the equatorial plane is studied, and different outcomes in the presence and in the absence of the reflection symmetry are discussed. We conclude that in the absence of the equatorial reflection symmetry neither stable nor unstable circular orbit can exist on the equatorial plane. Moreover, to address the observational aspects, we provide two possible examples relating gravitational wave astronomy and the thin accretion disk which can put constraints on the symmetry breaking parameters.
Pure Gauss–Bonnet NUT black hole solution: I
(Springer, 2022-04) Mukherjee, Sajal
We obtain an exact -vacuum solution in the pure Gauss–Bonnet gravity with NUT charge in six dimension, with horizon having the product topology of . We discuss its horizon and singularity structure, and consequently arrive at parameter windows for its physical viability. It turns out that for the curvatures to remain function of r alone for NUT black hole spacetime, horizon topology has to be product of spheres. This is true for Einstein as well as for pure Gauss–Bonnet gravity, and perhaps would hold good for higher order pure Lovelock as well.