arXiv subjects

Sajal Mukherjee

Publications and source records attributed to Sajal Mukherjee.

36 records · Page 2Linked to original sources

arXiv2023

Entanglement harvesting for different gravitational wave burst profiles with and without memory

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.

gr-qc↗

arXiv2023

Transition from inspiral to plunge for braneworld EMRI

In the present article, we discuss the late inspiral and then the transition regime to the plunge phase of a secondary, less massive compact object into a more massive braneworld black hole, in the context of an extreme-mass-ratio inspiral. We obtain the approximate expressions for fluxes due to slowly evolving constants of motion, such as the energy and the angular momentum, in the presence of the tidal charge inherited from the higher spacetime dimensions for an extreme-mass-ratio system. These expressions for fluxes are further used to introduce dissipative effects while modeling the inspiral to the plunge phase through the transition regime. Within our setup, we provide a qualitative understanding of how the additional tidal charge present in the braneworld scenario may affect the timescale of the late inspiral to the plunge, in particular, by enhancing the time scale of the transition regime. Finally, we provide an estimate for the tidal charge from the higher dimensions, using the observable aspects of the transition regime from the late inspiral to the plunge by the gravitational wave detectors.

gr-qc↗

arXiv2023

On Elser's conjecture and the topology of $U$-nucleus complex

Dorpalen-Barry et al. proved Elser's conjecture about sign of Elser's number by interpreting them as certain sums of reduced Euler characteristics of an abstract simplicial complex known as $U$-nucleus complex. We prove a conjecture posed by them regarding the homology of $U$-nucleus complex.

math.CO↗

arXiv2023

Resonance crossing of a charged body in a magnetized Kerr background: an analogue of extreme mass ratio inspiral

We investigate resonance crossings of a charged body moving around a Kerr black hole immersed in an external homogeneous magnetic field. This system can serve as an electromagnetic analogue of a weakly non-integrable extreme mass ratio inspiral (EMRI). In particular, the presence of the magnetic field renders the conservative part of the system non-integrable in the Liouville sense, while the electromagnetic self-force causes the charged body to inspiral. By studying the system without the self-force, we show the existence of an approximate Carter-like constant and discuss how resonances grow as a function of the perturbation parameter. Then, we apply the electromagnetic self-force to investigate crossings of these resonances during an inspiral. Averaging the energy and angular momentum losses during crossings allows us to employ an adiabatic approximation for them. We demonstrate that such adiabatic approximation provides results qualitatively equivalent to the instantaneous self-force evolution, which indicates that the adiabatic approximation may describe the resonance crossing with sufficiently accuracy in EMRIs.

gr-qc↗

arXiv2022

Extended bodies moving on geodesic trajectories

This work investigates whether an extended test body obeying the Mathisson-Papapetrou- Dixon equations under the Ohashi-Kyrian-Semerak 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-Semerak 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.

gr-qc↗

arXiv2022

Pure Gauss-Bonnet NUT Black Hole Solution: I

We find a new exact $Λ$-vacuum solution in pure Gauss-Bonnet gravity with NUT charge in six dimension with horizon having product topology $S^{(2)} \times S^{(2)}$. We also discuss its horizon and singularity structure, and consequently arrive at a parameter window for its physical viability. It should be noted that all NUT black hole solutions in higher dimensions have product, instead of spherical, topology. We prove, in general, that it is because of the radial symmetry of the NUT spacetime; i.e. in higher dimensions NUT spacetime cannot maintain radial symmetry unless horizon has $S^{(2)}$ or its product topology. On the way we also prove a general result for spherical symmetry that when null energy condition is satisfied, one has then only to solve a first order equation to get a vacuum or $Λ$-vacuum solution.

gr-qc↗

arXiv2021

Gravitational Wave observatories may be able to detect hyperbolic encounters of Black Holes

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 complimentary 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.

gr-qc↗

arXiv2021

Generalized Larcombe-Fenessey invariants of matrix powers

In this article, we have found significant generalization of the invariance properties of powers of matrices discovered by Larcombe, Fenessey and further explored by Zeilberger. Moreover, we found interesting new results exhibiting similar phenomena in a more general setup.

math.CO↗

arXiv2021

Possible connection between the reflection symmetry and existence of equatorial circular orbit

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.

gr-qc↗

arXiv2021

Pure Gauss-Bonnet NUT black hole with and without non-central singularity

It is known that NUT solution has many interesting features and pathologies like being non-singular and having closed timelike curves. It turns out that in higher dimensions horizon topology cannot be spherical but it has instead to be product of $2$-spheres so as to retain radial symmetry of spacetime. In this letter we wish to present a new solution of pure Gauss-Bonnet $Λ$-vacuum equation describing a black hole with NUT charge. It has three interesting cases: (a) black hole with both event and cosmological horizons with singularity being hidden behind the former, (b) a regular spacetime free of both horizon and singularity, and (c) black hole with event horizon without singularity and cosmological horizon. Singularity here is always non-centric at $r \neq 0$.

gr-qc↗

arXiv2021

Thermal behavior of a radially deformed black hole spacetime

In the present article, we study the Hawking effect and the bounds on greybody factor in a spacetime with radial deformation. This deformation is expected to carry the imprint of a non-Einsteinian theory of gravity, but shares some of the important characteristics of general relativity (GR). In particular, this radial deformation will restore the asymptotic behavior, and also allows for the separation of the scalar field equation in terms of the angular and radial coordinates -- making it suitable to study the Hawking effect and greybody factors. However, the radial deformation would introduce a change in the locations of the horizon, and therefore, the temperature of the Hawking effect naturally alters. In fact, we observe that the deformation parameter has an enhancing effect on both temperature and bounds on the greybody factor, which introduces a useful distinction with the Kerr spacetime. We discuss these effects elaborately, and broadly study the thermal behavior of a radially deformed spacetime.

gr-qc↗

arXiv2020

Multipole moments of compact objects with NUT charge: Theoretical and observational implications

We derive the multipole moments of the Kerr-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.

gr-qc↗

arXiv2020

Resonant orbits for a spinning particle in Kerr spacetime

In the present article, we study the orbital resonance corresponds to an extended object approximated up to the dipole order term in Kerr spacetime. We start with the Mathisson-Papapetrou equations under the linear spin approximation and primarily concentrate on two particular events. First, when the orbits are nearly circular and executing a small oscillation about the equatorial plane and second, a generic trajectory confined on the equatorial plane. While in the first case, all the three fundamental frequencies, namely, radial $Ω_r$, angular $Ω_θ$, azimuthal $Ω_ϕ$ can be commensurate with each others and give rise to the resonance phenomenon, the later is only accompanied with the resonance between $Ω_r$ and $Ω_ϕ$ as we set $θ=π/2$. We provide a detail derivation in locating the prograde resonant orbits in either of these cases and also study the role played by the spin of the black hole. The implications related to spin-spin interactions between the object and black hole are also demonstrated.

gr-qc↗

arXiv2019

On some novel features of the Kerr-Newman-NUT Spacetime

In this work we have presented a special class of Kerr-Newman-NUT black hole, having its horizon located precisely at $r=2M$, for $Q^{2}=l^{2}-a^{2}$, 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 $l^2 > a^2$, 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.

gr-qc↗

arXiv2018

Off-equatorial stable circular orbits for spinning particles

In 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 Mathission-Papapetrau's 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 $S^{a} = \left(0,S^r,S^θ,0\right)$ , there exists an unique circular orbit at $(r_c,θ_c)$ 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 non-equatorial plane. We further establish that the location ($r_c,θ_c$) of the ISCO for a given spinning particle depends on the radial component of the spin vector ($S^r$) as well as the angular momentum of the black hole ($J$). The implications of using different spin supplementary conditions are investigated.

gr-qc↗

arXiv2018

Horndeski theories confront the Gravity Probe B experiment

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.

gr-qc↗

arXiv2015

Carter Constant and Angular Momentum

We investigate the carter like constant for a particle in a non relativistic dipolar field. This special case is a missing link between carter constant in stationary axially symmetric spacetime such as Kerr solution and its possible Newtonian counterpart. We use this system to carry over the definition of angular momentum from Newtonian mechanics to relativistic stationary axially symmetric stationary spacetime.

gr-qc↗

arXiv2011

Architecture of A Scalable Dynamic Parallel WebCrawler with High Speed Downloadable Capability for a Web Search Engine

Today World Wide Web (WWW) has become a huge ocean of information and it is growing in size everyday. Downloading even a fraction of this mammoth data is like sailing through a huge ocean and it is a challenging task indeed. In order to download a large portion of data from WWW, it has become absolutely essential to make the crawling process parallel. In this paper we offer the architecture of a dynamic parallel Web crawler, christened as "WEB-SAILOR," which presents a scalable approach based on Client-Server model to speed up the download process on behalf of a Web Search Engine in a distributed Domain-set specific environment. WEB-SAILOR removes the possibility of overlapping of downloaded documents by multiple crawlers without even incurring the cost of communication overhead among several parallel "client" crawling processes.

cs.IR↗