arXiv subjects

Anirban Saha

Publications and source records attributed to Anirban Saha.

At least 19 recordsLinked to original sources

arXiv2026

Probing the massive scalar mode in the levitated sensor detector of gravitational wave

Owing to the mass scale associated with it the scalar longitudinal polarization mode of gravitational wave predicted in various modified theories of gravity should propagate at a subluminal speed and thus arrive with a time delay (for burst signals) or a phase difference (for persistent signals) at the detector site compared to the massless tensor polarization modes which move at the speed of light and are present in both standard general relativity and modified theories. The longitudinal massive scalar mode interacts non-trivially with detectors along the signal propagation direction in contrast to massless the tensor modes which interact only in the transverse plane. Identifying the signature of these distinctive features in a gravitational wave signal can provide observational evidence in favour of modified theories of gravity over general relativity. In this work we argue that owing to its compact design and tunability of operational frequency the recently proposed levitated sensor detectors \cite{Aggarwal} that works on the principle of gravitational wave induced resonant oscillation of a optically trapped \cite{Ashkin_1970} dielectric nanosphere sensor \cite{Geraci} can be useful in this regard. We demonstrate that the dynamics of the levitated sensor mass obeys a geodesic deviation equation in the proper detector frame and construct a quantum mechanical description of this system in modified gravity framework to compute the probabilities of resonant transitions in response to incoming gravitational wave signals of both periodic and aperiodic kind.

gr-qc↗

arXiv2025

Exploring density dependent B as a suitable parameter in higher dimensional approach with a non-linear equation of state

In this investigation, we present a singularity free interior solution of the Einstein field equation for a class of anisotropic compact objects in dimensions $D\geq4$. In accordance with the concept of Vaidya and Tikekar, the geometry of the physical $(D-1)$-space of a star corresponding to $t=constant$ hypersurface is assumed to be of a $(D-1)$ spheroid. For the fulfilment of causality condition, a limit of the spheroidal parameter ($λ$) is noted depending on the values of amount of anisotropy ($α$) and space-time dimensions ($D$). We note that by switching off the extra parameters ($α$ and $D$), previously obtained limit of $λ$ can be generated. To validate our findings, we compare the results obtained from our model with observational data of PSR J1614-2230 (mass=$1.908^{+0.016}_{-0.016}M_{\odot}$, radius=$11.93^{+0.50}_{-0.50}km$). It is noted that the best fit equation of state corresponds to polynomial equation of state of the order of five. We use this finding to develop a density dependent MIT bag model which seems to be useful for the correct description of compact object in our model. The mass radius relation shows that our model mimics a wide range of recently observed pulsars in four and higher dimensions. Furthermore, we also found that our model exhibits stability according to Generalised TOV equation, Herrera cracking condition, and the adiabatic index.

gr-qc↗

arXiv2025

Testing Multipole Moments of compact objects beyond Kerr paradigm

Multipole moments are related to the physical properties of compact gravitating objects; therefore, understanding their structure is useful in accessing the nature of compact objects. We look into gravitational wave observables for black holes with charge, black holes on the brane, black holes with torsion, and regular black holes to see if and how they are correlated to the black hole hairs, which are related to the multipole moments. We find that the gravitational wave observables are indeed related to the hairs of non-vacuum spacetimes (for instance, charge $Q$ in the case of Kerr-Newman black holes). We also constrain the black hole hairs for change in gravitational wave phasing to see if the dependencies are significant and can be observed. The results from the analysis imply that the charge $Q$ in Kerr-Newman black holes should be detectable; thus, we provide a constraint to $Q^2/M^2$ given the spin and mass ratio of an ideal EMRI system for which future detectors like LISA can detect the change in gravitational wave observables. We also look into an analytical approach to find multipole moments of non-vacuum black hole spacetimes, mainly using the Improved Twist Vector approach for the Geroch-Hansen multipole moments and the Thorne formalism. The necessary analytics are computed, and the multipole moments are obtained for various non-vacuum spacetimes. However, the multipole moments don't contain any information about the black hole hairs, and we have commented on this observation in our paper.

gr-qc↗

arXiv2025

Dirac equation in a gauge-field background in the Moyal plane

Starting with the Dirac equation for an electron in a constant electromagnetic background on a noncommutative (NC) plane, we obtain a gauge invariant description of the system. Surprisingly, the dynamics of the system is dictated by the standard form of Lorentz force law, once the effective magnetic and electric fields $\left( B^{NC}, \, E^{NC} \right)$ correct up to leading order in the NC parameter are identified. The Hall effect is studied using the NC corrected fields in the non-relativistic (NR) limit. This shows that noncommutativity affects the cyclotron frequency, but leaves the Hall conductivity unaffected at least to first order in the NC parameter. Owing to the NC corrected magnetic field, the hyperfine splitting of Hydrogen atom spectrum also shows a first order correction which helps establish an upper bound on the spatial NC parameter.

hep-th↗

arXiv2023

Energy momentum tensor of a non-minimally coupled scalar from the equivalence of the Einstein and Jordan frames

Unlike the minimally coupled gravity theory where matter is coupled with gravity in such a manner so that one can differentiate the matter and gravity sector uniquely, the non-minimally coupled theories (NMCT) are distinguished by the intermingling of two. As a consequence of this the calculation of the energy momentum tensor (EMT) in NMCT is beset with an arbitrariness. In this paper we provide an algorithm based on the well known equivalence between Jordan frame and Einstein frame formulations which enables us to construct the EMT for NMCT in a unique way.

gr-qc↗

arXiv2022

Quantum mechanical interaction of matter with the scalar mode of gravitational wave in modified gravity theories

We study the interaction of a quantum mechanical particle with gravitational wave (GW) in the framework of modified theory of gravity (MTG) where apart from the two standard tensorial modes of polarization of GW there exists another massless scalar mode. The purpose of using the MTG framework in our study is to uncover key features in matter's response to GWs that, if observed in actual GW data, can serve as observational evidence in favor of MTG over standard General Relativity.

gr-qc↗

arXiv2022

Generalized uncertainty principle in bar detectors of gravitational waves

At present the gravitational waves detectors achieve the sensitivity to detect the length variation ($δL$), $\mathcal{O} \approx 10^{-17}-10^{-21}$ meter. Recently a more stringent upperbound on the dimensionless parameter $β_0$, bearing the effect of generalized uncertainty principle has been given which corresponds to the intermediate length scale $l_{im}= \sqrt{β_0} l_{pl} \sim 10^{-23} m$. Hence it becomes quite obvious to search for the generalized uncertainty principle by observing the response of the vibrations of phonon modes in such resonant detectors in the near future. Therefore, we calculate the resonant frequencies and transition rates induced by the incoming gravitational waves on these detectors in the generalized uncertainty principle framework. This presentation is based on the work published in \cite{sb2}.

gr-qc↗

arXiv2020

Generalized uncertainty principle in resonant detectors of gravitational waves

With the direct detection of gravitational waves by advanced LIGO detector, a new "window" to quantum gravity phenomenology has been opened. At present, these detectors achieve the sensitivity to detect the length variation ($δL$), $\mathcal{O} \approx 10^{-17}-10^{-21}$ meter. Recently a more stringent upperbound on the dimensionless parameter $β_0$, bearing the effect of generalized uncertainty principle has been given which corresponds to the intermediate length scale $l_{im}= \sqrt{β_0} l_{pl} \sim 10^{-23} m$. Hence the flavour of the generalized uncertainty principle can be realised by observing the response of the vibrations of phonon modes in such resonant detectors in the near future. In this paper, therefore, we calculate the resonant frequencies and transition rates induced by the incoming gravitational waves on these detectors in the generalized uncertainty principle framework. It is observed that the effects of the generalized uncertainty principle bears its signature in both the time independent and dependent part of the gravitational wave-harmonic oscillator Hamiltonian. We also make an upper bound estimate of the GUP parameter.

gr-qc↗

arXiv2019

Signatures of noncommutativity in bar detectors of gravitational waves

The comparison between the noncommutative length scale $\sqrtθ$ and the length variation $δL=h L$, detected in the GW detectors indicate that there is a strong possibility to detect the noncommutative structure of space in the GW detector set up. We therefore explore how the response of a bar detector gets affected due to the presence of noncommutative structure of space keeping terms upto second order in the gravitational wave perturbation ($h$) in the Hamiltonian. Interestingly, the second order term in $h$ shows a transition between the ground state and one of the perturbed second excited states that was absent when the calculation was restricted only to first order in $h$.

gr-qc↗

arXiv2018

Footprint of spatial noncommutativity in resonant detectors of gravitational wave

The present day gravitational wave (GW) detectors strive to detect the length variation $δL = h L$, which, owing to the smallness of the metric perturbation $\sim h$, is an extremely small length $\mathcal{O} \sim 10^{-18} - 10^{-21}$ meter. The recently proposed noncommutative structure of space has a characteristic length-scale $\sqrtθ$ which has an estimated upper-bound in similar length-scale range. We therefore propose that GW data can be used as an effective probe of noncommutative structure of space and demonstrate how spatial noncommutativity modifies the responding frequency of the resonant mass detectors of GW and also the corresponding probabilities of GW induced transitions that the phonon modes of the resonant mass detectors undergo. In this paper we present the complete perturbative calculation involving both time-independent and time-dependent perturbation terms in the Hamiltonian.

gr-qc↗

arXiv2018

A field theoretic approach to the energy momentum tensor for theories coupled with gravity

We provide a field-theoretic algorithm of obtaining energy momentum tensor (EMT) for gravitationally coupled theories. The method is based on an auxiliary field theory and equally applicable to both minimal and non-minimal coupling. The algorithm illuminates the connection between the EMT, obtained by functional variation of the metric, and local balance of energy and momentum. Our method is of cardinal value for the proper identification of the EMT in context of non-minimally coupled gravity theories.

gr-qc↗

arXiv2017

Equivalence principle in context of large uniform acceleration - a quantum mechanical perspective

We study the effect of large acceleration of an uniformly accelerated frame on the validity of weak equivalence principle. Specifically we demonstrate how the behaviour of free quantum particle, as observed by an observer with large uniform acceleration, completely changes from that of a quantum particle emmarsed in a uniform gravitational field. We also extend our analysis to the simplest noncommutative space scenario to show that while spatial noncommutativity does not affect the quantum particle in a gravitational field, it does alter the energy eigenvalues of a quantum particle as seen from a frame with very large uniform acceleration.

quant-ph↗

arXiv2016

Emergent Universe with particle production

The possibility of an emergent universe solution to Einstein's field equations allowing for an irreversible creation of matter at the expense of the gravitational field is shown. With the universe being chosen as spatially flat FRW spacetime together with equation of state proposed in [17], the solution exists when the ratio of the phenomenological matter creation rate to the number density times the Hubble parameter is a number $β$ of the order of unity and independent of time. The thermodynamic behaviour is also determined for this solution. Interestingly, we also find that an emergent universe scenario is present with usual equation of state in cosmology when the matter creation rate is chosen to be a constant. More general class of emergent universe solutions are also discussed.

gr-qc↗

arXiv2016

Non-minimally coupled quintessence DE model with a cubic galileon term --A Dynamical System Analysis

We consider a scalar field which is generallly non-minimally coupled to gravity and has a characteristic cubic Galilean-like term in the kinetic part of the action, in presence of a generic self-interaction as a candidate Dark Energy model. The system is dynamically analyzed and novel fixed points with perturbative stability are demonstrated. Evolution of the system is numerically studied near a novel fixed point which owes its existance to the Galileon character of the model. It turns out that demanding the stability of this novel fixed points puts strong restriction on the allowed non-minimal coupling and the choice of the self-interaction. The evolutions of the system is charted out on a $r-s$ diagram. The evolution of the equation of state parameter is studied which shows that our model predicts accelerated universe throughout and the phantom limit is only approached closely but never crossed. Our result thus extends the findings of of \cite{Cubic_Galileon_NMC} for more general NMC than linear and quadratic couplings.

gr-qc↗

arXiv2016

Response of simple quantum systems to different polarizations of gravitational waves in noncommutative phase-space

Owing to the extreme smallness of any noncommutative scale that may exist in nature, both in the spatial and momentum sector of the quantum phase-space, a credible possibility of their detection lies in the present day gravitational wave detector set-ups, which effectively detects the relative length-scale variations ${\cal{O}}\left[10^{-23} \right]$. With this motivation, we have considered how a free particle and harmonic oscillator in a quantum domain will respond to linearly and circularly polarized gravitational waves if the given phase-space has a noncommutative structure. The results show resonance behaviour in the responses of both free particle and HO systems to GW with both kind of polarizations. We critically analyze all the responses, and their implications in possible detection of noncommutativity. We use the currently available upper-bound estimates on various noncommutative parameters to anticipate the relative size of various response terms. We also argue how the quantum harmonic oscillator system we considered here can be very relevant in context of the resonant bar detectors of GW which are already operational currently.

hep-th↗

arXiv2015

Resonant-bar detectors of gravitational wave as possible probe of the noncommutative structure of space

We report the plausibility of using quantum mechanical transitions, induced by the combined effect of Gravitational wave (GW) and noncommutative (NC) structure of space, among the states of a 2-dimensional harmonic oscillator, to probe the spatial NC geometry. The phonon modes excited by the passing GW within the resonant bar-detector are formally identical to forced harmonic oscillator and they represent a length variation of roughly the same order of magnitude as the characteristic length-scale of spatial noncommutativity estimated from the phenomenological upper bound of the NC parameter. This motivates our present work. We employ various GW wave-forms that are typically expected from possible astronomical sources. We find that the transition probablities are quite sensitive to the nature of polarization of the GW. We also elaborate on the particular type of sources of GW, radiation from which can induce transitions that can be used as effective probe of the spatial noncommutative structure.

gr-qc↗

arXiv2015

On the Landau system in noncommutative phase-space

We consider a charged particle moving in a two dimensional plane in the presence of a background magnetic field perpendicular to the plane, i.e. the Landau system in a phase-space where the coordinates and momenta both follow canonical noncommutative algebra. A set of generalized transformations is derived in this paper which maps the NC problem to an equivalent commutative problem. In this set up, we study the Aharonov-Bohm effect and the Landau levels. For the Aharonov-Bohm effect, the phase-shift is found to contain corrections due to phase-space noncommutativity and also depends on the scaling parameter appearing in the generalized transformations. The result agrees with those in the literature upto first order in the noncommutative parameters when proper choice of the scaling parameter is taken. We then obtain the magnetic length and degeneracy of the Landau levels, both are seen to admit NC corrections. The Landau levels are seen to get altered due to phase-space noncommutativity as well. This energy spectrum of the Landau system is computed from two different perspectives, namely the explicit NC variable approach and the commutative-equivalent approach. The results match exactly, solidifying the evidence in favour of the equivalence of the two approaches.

hep-th↗

arXiv2014

Interaction of a circularly polarised gravitational wave with a charged particle in a static magnetic background

Interaction of a charged particle in a static magnetic background, i.e., a Landau system with circularly polarised gravitational wave (GW) is studied quantum mechanically in the long wavelength and low velocity limit. We quantize the classical Hamiltonian following \cite{speli}. The rotating polarization vectors of the circularly polarized GW are employed to form a unique directional triad which served as the coordinate axes. The Schrodinger equations for the system are cast in the form of a set of coupled linear differential equations. This system is solved by iterative technique. We compute the time-evolution of the position and momentum expectation values of the particle. The results show that the resonance behaviour obtained earlier\cite{emgw_classical} by classical treatements of the system has a quantum analogue not only for the linearly polarized GW \cite{emgw_1_lin}, but for circularly polarized GW as well.

gr-qc↗