arXiv subjects

Satadal Datta

Publications and source records attributed to Satadal Datta.

At least 19 recordsLinked to original sources

arXiv2026

Dynamical Love numbers of analogue rotating black and white holes

We calculate the dynamical tidal response coefficients (TRCs) of 2+1D analogue black and white holes generated by draining and fountaining bathtub flows, respectively. The parameter space is characterized by the frequency and azimuthal number of the Fourier modes and the rotation of the analogue black or white hole. In general, the TRC is a complex-valued function of these parameters. Its real and imaginary parts are defined as the tidal Love number (TLN) and the tidal dissipation coefficient (TDC), respectively. The TRC of the analogue black hole (ABH) exhibits several interesting features. At certain points in the parameter space, including the static case of vanishing perturbation frequency, the TLN exhibits logarithmic running, while the TDC vanishes. Unlike in Einstein gravity, fluid dynamics allows for the physical existence of an analogue white hole (AWH) event horizon. Time-independent, torque-free, barotropic, inviscid, axisymmetric fluid dynamical equations can yield a pair of transonic background flow solutions. The solutions in the pair, corresponding to an ABH-AWH pair, share the same angular momentum and Bernoulli constant but have opposite mass flow rates, all of which are conserved quantities. For such an ABH-AWH pair, the TRC of the AWH is the complex conjugate of the TRC of the ABH.

gr-qc↗

arXiv2024

Probing Penrose-type singularities in sonic black holes

Addressing the general question whether Penrose singularities physically exist inside black holes, we investigate the problem in the context of an analogue system, a flowing laboratory liquid, for which the governing equations are at least in principle known to all relevant scales, and in all regions of the effective spacetime. We suggest to probe the physical phenomena taking place close to the singularity in the interior of a $2+1$D analogue black hole arising from a polytropic, inviscid, irrotational, and axisymmetric steady flow, and propose to this end an experimental setup in a Bose-Einstein condensate. Our study provides concrete evidence, for a well understood dynamical system, that the Einstein equations are not necessary for a singularity to form, demonstrating that Penrose-type spacetime singularities can potentially also exist in non-Einsteinian theories of gravity. Finally, we demonstrate how the singularity is physically avoided in our proposed laboratory setup.

gr-qc↗

arXiv2023

Petrov classification of analogue spacetimes

In an effort to invariantly characterize the conformal curvature structure of analogue spacetimes built from a nonrelativistic fluid background, we determine the Petrov type of a variety of laboratory geometries. Starting from the simplest examples, we increase the complexity of the background, and thereby determine how the laboratory fluid symmetry affects the corresponding Petrov type in the analogue spacetime realm of the sound waves. We find that for more complex flows isolated hypersurfaces develop, which are of a Petrov type differing from that of the surrounding fluid. {Finally, we demonstrate that within the incompressible background approximation, as well as for all compressible quasi-one-dimensional flows, the only possible Petrov types are the algebraically general type I and the algebraically special types O and D.

gr-qc↗

arXiv2023

Dispersive censor of acoustic spacetimes with a shock-wave singularity

A dispersionless shock wave in a fluid without friction develops an acoustic spacetime singularity which is naked (not hidden by a horizon). We show that this naked nondispersive shock-wave singularity is prohibited to form in a Bose-Einstein condensate, due to the microscopic structure of the underlying ${\rm a}\!{\rm e}$ther and the resulting effective trans-Planckian dispersion. Approaching the instant of shock $t_{\rm shock}$, rapid spatial oscillations of density and velocity develop around the shock location, which begin to emerge already slightly before $t_{\rm shock}$, due to the quantum pressure in the condensate. These oscillations render the acoustic spacetime structure completely regular, and therefore lead to a removal (censoring) of the spacetime singularity. Thus, distinct from the cosmic censorship hypothesis of Penrose formulated within Einsteinian gravity, the quantum pressure in Bose-Einstein condensates censors (prohibits) the formation of a naked shock-wave singularity, instead of hiding it behind a horizon.

gr-qc↗

arXiv2022

A Revisit to Lorentz Transformation without Light

We derive rotation free Lorentz Transformation (LT) between two inertial reference frames without using the second postulate of Einstein, i.e., we do not assume the invariant speed of light (in vacuum) under LT. We find a general transformation rule between two inertial frames where a speed, invariant under that transformation, arises naturally. This idea first came into light by Mathematician Ignatowski [1] around the year, 1910. Without loss of novelty, here we present our derivation while reviewing more recent literature in this subject.

physics.class-ph↗

arXiv2022

Inherent nonlinearity of fluid motion and acoustic gravitational wave memory

We consider the propagation of nonlinear sound waves in a perfect fluid at rest. By employing the Riemann wave equation of nonlinear acoustics in one spatial dimension, it is shown that waves carrying a constant density perturbation at their tails produce an acoustic analogue of gravitational wave memory. For the acoustic memory, which is in general $nonlinear$, the nonlinearity of the effective spacetime dynamics is not due to the Einstein equations, but due to the nonlinearity of the perfect fluid equations. For concreteness, we employ a box-trapped Bose-Einstein condensate, and suggest an experimental protocol to observe acoustic gravitational wave memory.

gr-qc↗

arXiv2021

Analogue gravitational field from nonlinear fluid dynamics

The dynamics of sound in a fluid is intrinsically nonlinear. We derive the consequences of this fact for the analogue gravitational field experienced by sound waves, by first describing generally how the nonlinearity of the equation for phase fluctuations back-reacts onto the definition of the background providing the effective space-time metric. Subsequently, we use the the analytical tool of Riemann invariants in one-dimensional motion to derive source terms of the effective gravitational field stemming from nonlinearity. Finally, we show that the consequences of nonlinearity we derive can be observed with Bose-Einstein condensates in the ultracold gas laboratory.

gr-qc↗

arXiv2020

Simulating gravity in rotational flow

We consider classical fluids in non-relativistic framework. The flow is considered to be barotropic, inviscid and rotational. We study the linear perturbations over a steady state background flow. We find the acoustic metric from the conservation equation of a current constructed from linear perturbation of first order derivatives (in position and time coordinate) of Bernoulli's constant (scalar field) and vorticity (a vector field). We have rather shown that the conservation equation of current reduces to a massless scalar field equation in the high frequency limit. In contrast to the contemporary works, our work shows that even if we can not find a wave equation (in rotational flow) which is structurally similar to a massless scalar field equation in curved space-time, but still an analogue space-time exists through a conservation equation. Considering velocity potential and Clebesch coefficients, we find that only for some specific systems current conservation equation can be found yielding the same analogue space-time. We conclude that for rotational flows, it is wise to study linear perturbation of Bernoulli's constant over the velocity potential and Clebsch coefficients.

gr-qc↗

arXiv2020

Higher Dimensional Limit Cycles and Coupling Induced Synchronization in Dynamical Systems

Limit cycles (attractors for neighbouring periodic orbits in a dissipative dynamical system) have been widely studied but the corresponding generalization for quasi periodic orbits have rarely been discussed. Here we investigate "higher dimensional limit cycles" by analysing a pair of coupled non identical Van der Pol oscillators and also the Kuznetsov oscillator. We find that the renormalization group based approach introduced by Chen, Goldenfeld and Oono is ideally suited for analysing the quasi periodic analogues of limit cycles. We also address entrainment issues in a pair of forced and coupled Van der Pol oscillators. Our principle finding there is that if two such independent oscillators one with frequency entrainment and the other without are coupled linearly, then it is possible to produce an entrained state via the coupling.

nlin.CD↗

arXiv2019

Lagrangian Description of Accreting Black Hole Systems in the Context of Emergent Spacetime

We make use of the Lagrangian description of fluid motion to highlight certain features in the context of spacetime geometry as emergent phenomena in fluid systems. By using Lagrangian Perturbation Theory (LPT), we find that if the flow is not barotropic it will not be locally irrotational, and as a result, emergent gravity can not be realised for such flow. Our work gives a new perspective of examining the perturbations in a fluid from a different approach (other than Eulerian approach) which is the way of using Lagrangian Perturbation Theory. We make use of Lagrangian description of motion to examine the propagation of Eikonal wave (wave having very short wavelength) from the reference frame of the observer moving with the background flow. We find that waves of ultra short wavelength propagate similar to waves in a static uniform medium in the near vicinity of the observer. We restrict ourselves to nonrelativistic flows in astrophysical black hole accretion.

gr-qc↗

arXiv2019

Lagrangian Description in the context of Emergent spacetime

We make use of the Lagrangian description of fluid motion to highlight certain features in the context of spacetime geometry as emergent phenomena in fluid systems. We find by using Lagrangian Perturbation Theory (LPT), that not all kind of perturbations on a steady state flow can produce analogue spacetime effect. We also explore the manifold structure of emergent spacetime by using the Lagrangian description of fluid motion. We restrict ourselves to nonrelativistic flows.

gr-qc↗

arXiv2019

Instabilities in nonrelativistic spherically symmetric self-gravitating accretion

We consider time dependent problem in perturbative approach for a nonrelativistic inviscid spherically symmetric accretion model where the effect of the gravity of the medium is considered in Newtonian gravity framework. We consider spherically symmetric nonrelativistic accretion, i.e. Bondi accretion with self-gravity. Our approach is perturbative in the linear order of perturbation regime. We introduce linear perturbation over the existing steady state solution of the system. The analysis has two features, one is that the linear perturbation in mass accretion rate in such irrotational inviscid model of accretion gives rise to emergent gravity and on the other hand, we get some significant insights about instabilities in the flow due to the effect of gravity in the medium, whereas the instabilities are absent in the absence of self-gravity.

astro-ph.HE↗

arXiv2018

Acoustic Analogue of Gravitational Wave

We explore nonlinear perturbations in different static fluid systems. We find that the equations, corresponding to the perturbation of the integrals of motion, i.e; Bernoulli's constant and the mass flow rate, satisfy massless scalar field equation in a time dependent acoustic metric. When one is interested up to the second order behaviour of the perturbations, the emergent time dependent acoustic metric of the system, derived from the massless scalar field equations of the perturbations of the integrals of motion, has some astounding similarities with the metric describing gravitational wave in Minkowski spacetime.

gr-qc↗

arXiv2018

Acoustic geometry obtained through the perturbation of the Bernoulli's constant

For accretion onto astrophysical black holes, we demonstrate that linear perturbation of Bernoulli's constant defined for an inviscid irrotational adiabatic flow of perfect ideal fluid gives rise to phenomena of analogue gravity. The formulation of our work is done in the Newtonian framework and also within the General relativistic framework, i.e., considering a static spacetime background, as well. The resulting structure of the analogue acoustic metric is similar to the acoustic metric found in perturbing velocity potential and mass accretion rate.

gr-qc↗

arXiv2017

Amplitude death by delay induced position coupling in a system of two coupled Van der Pol Oscillators

We consider a system of two interacting identical Van der Pol Oscillators in a simple harmonic potential well. The position coupling term between the oscillators is such that there is a finite delay, i.e; each system takes a finite time to react to the other one. We investigate the amplitude death in the presence of such interaction and we find out the amplitude death regions in the corresponding parameter space.

nlin.CD↗

arXiv2017

Bifurcations of a Van der Pol oscillator in a double well

We study the changes in the phase portrait of a Van der Pol oscillator in a double well with the change in the shape of the well. Both the symmetric and asymmetric double wells are considered. We find that the shape of the well plays a very important role in the dynamics of the oscillator such as with the change in shape of the well, the stability of the fixed points of the system changes as well as limit cycles appear and are being destroyed.

nlin.CD↗

arXiv2017

Analogue tachyon in Jeans Cloud

We study the linear perturbations in a stable Jeans cloud, i.e; the dimension of the cloud is less than the Jeans length. We find that the linear perturbation of density in such a system obeys a wave equation in acoustic analogue of Minkowski space-time which is similar to Klein-Gordon equation for tachyon field in Minkowski space-time, i.e; Klein-Gordon equation with negative mass-squared term in a flat space time background. We further find the analogy with tachyon field for linear perturbation of density by studying linear perturbations in a stable cloud made of Bose-Einstein condensate as dark matter.

gr-qc↗

arXiv2017

A parametric model to study the mass radius relationship of stars

In static and spherically symmetric spacetime, we solve the Einstein Maxwell equations. The effective gravitational potential and the electric field for charged anisotropic fluid are defined in terms of two free parameters. For such configuration, the mass of the star as a function of stellar radius is found in terms of two aforementioned parameters, subjected to certain stability criteria. For various values of these two parameters one finds that such mass radius relationship can model stellar objects located at various regions of Hertzsprung-Russel diagram.

astro-ph.SR↗