arXiv subjects

Tapas K. Das

Publications and source records attributed to Tapas K. Das.

At least 19 recordsLinked to original sources

arXiv2026

Emergent gravity from Michel flow with position dependent adiabatic index

Spherically symmetric, general relativistic Bondi accretion is known as the Michel flow. The stationary integral transonic solutions for the Michel flow has been constructed for multi-component accretion described by an equation of state where the adiabatic index varies with the radial distance along which the streamlines are studied, and the corresponding phase portrait spanned by such radial distance and the flow Mach number has been obtained. Borrowing the techniques used in the dynamical systems theory, the nature of the transonic points of the aforementioned flow has been classified. The steady state flow has been perturbed to study the stability of the stationary solutions, and it has been found that such flows are stable under the (linear) radial perturbation. As a consequence of the stability analysis, the corresponding acoustic space time embedded within the accreting matter has been obtained, and the horizon of the metric of such sonic space time has been identified by constructing the causal structure with the help of the Carter-Penrose diagrams. In this way, the accreting black hole systems in the general relativistic set up has been investigated from various different perspectives - from its astrophysical aspects, from the dynamical systems point of view, as well as within the realm of the classical analogue gravity phenomena.

astro-ph.HE↗

arXiv2026

Emergent gravity from nonlinear perturbation of spherical accretion with variable adiabatic index

The main aim of the present work is to demonstrate that the analogue gravity phenomena are not an artifact of linear perturbation, rather gravity-like effects emerge through the non linear higher order perturbation of transonic fluid as well. To establish that fact, a spherically accreting astrophysical system has been considered where the hydrodynamic accretion with a relativistic, multi-component equation of state with position dependent adiabatic index onto compact astrophysical objects has been considered. By extending the acoustic metric formalism beyond the linear regime, it has been shown that the aforementioned perturbations satisfy a covariant wave equation in an effective acoustic spacetime with non-linear corrections, making the analogue geometry dynamical. As a consequence, the acoustic horizon can shift (inward or outward), depending on the relative amplitudes of density, temperature, and mass accretion-rate fluctuations. This provides a more realistic framework to investigate the dynamics of the non-linear analogue spacetime in astrophysically relevant accretion flows.

gr-qc↗

arXiv2026

On the spin dependence of the emergent gravity phenomena as observed in axially symmetric black hole accretion with spatially varying adiabatic index

The present work addresses an axisymmetrically accreting black hole system from three perspectives: the astrophysical, the dynamical systems, and the emergent gravity standpoint. Steady-state equations governing low angular momentum axially symmetric accretion under a pseudo-Kerr potential are formulated for a multi-species flow with a spatially varying adiabatic index. The resulting transonic solutions are shown to be multi-transonic and may accommodate a stationary shock. Critical points are classified via perturbative dynamical systems methods, and linear stability analysis confirms that the stationary solutions remain stable under radial perturbation. The ensuing acoustic geometry harbours acoustic black holes at the sonic points and an acoustic white hole at the shock location, whose causal structure is constructed via the Carter--Penrose diagram. The surface gravity associated with each acoustic horizon is computed using a generalized expression that accounts for the spatial variation of the local sound speed.

astro-ph.HE↗

arXiv2025

Gravity as emergent phenomena for spherically symmetric black hole accretion of multi-component flow with relativistic equation of state

We investigate analogue gravity phenomena arising as a result of the linear perturbation of the spherically symmetric accretion flows onto non rotating black holes, where the gravitational field is determined by a set of post Newtonian pseudo Schwarzschild black hole potentials and the infaling matter is described by a relativistic multi-species equation of state. The stationary transonic integral accretion solutions corresponding to the steady state of aforementioned type of accreting systems are constructed and the stability analysis of such solutions are performed through the time dependent linear perturbation of the accretion flow. Such linear stability analysis leads to the formation of a black hole like sonic metric embedded within the infalling matter. The acoustic horizons are then identified by constructing the causal structure, i.e., the Carter-Penrose diagrams. The variation of the analogue surface gravity corresponding to the aforementioned sonic metric has been studied as a function of various parameters governing the accretion flow.

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arXiv2025

Effect of spin on the dynamics of multi-component trans-relativistic accretion flows around Kerr black holes

We investigate the axially symmetric accretion of low angular momentum hydrodynamic matter onto a rotating black hole. The gravitational field under consideration is assumed to be described by a pseudo-Newtonian Kerr potential. The accreting matter consists of different species defined by a relativistic equation of state with a variable adiabatic index.We construct and solve the hydrodynamical conservation equations governing such a flow, and find out the corresponding stationary integral solutions. We find that depending on the values of initial boundary conditions, accretion flow may exhibit multi-transonic behaviour, and a standing shock may form. We investigate, in minute detail, how the spin angular momentum of the black hole, as well as the composition of the accreting matter influence the dynamics of accretion flow and the astrophysics of shock formation in the aforementioned accreting black hole systems.

astro-ph.HE↗

arXiv2025

Spherical accretion in the Schwarzschild spacetime in the Newtonian analogous construct

The velocity-dependent Newtonian analogous potentials (NAPs) corresponding to general relativistic (GR) spacetimes accurately capture most of the relativistic features, including all classical tests of GR, effectively representing spacetime geometries in Newtonian terms. The NAP formulated by Tejeda \& Rosswog (TR13) for Schwarzschild spacetime has been applied to the standard thin accretion disk around a black hole (BH) as well as in the context of streamlines of noninteracting particles accreting onto a Schwarzschild BH, showing good agreement with the exact relativistic solutions. As a further application, here we explore the extent to which TR13 NAP could describe a transonic hydrodynamical spherical accretion flow in Schwarzschild spacetime within the framework of standard Newtonian hydrodynamics. Instead of obtaining a typical single "saddle-type" sonic transition, a "saddle-spiral pair" is produced, with the inner sonic point being an (unphysical) "spiral type" and the outer being a usual "saddle type." The Bondi accretion rate at outer sonic radii, however, remains consistent with that of the GR case. The primary reason for the deviation of our findings from the classical Bondi solution is likely due to the inconsistency between the Euler-type equation in the presence of velocity-dependent TR13 NAP within the standard Newtonian hydrodynamics framework, and the corresponding GR Euler equation, regardless of the fluid's energy. Our study suggests that a (modified) hydrodynamical formalism is needed to effectively implement such potentials in transonic accretion studies that align with the spirit of TR13-like NAP, while remaining consistent with the GR hydrodynamics. This could then essentially circumvent GR hydrodynamics or GR magnetohydrodynamics equations.

gr-qc↗

arXiv2024

Bondi Flow from Various Perspectives

Realization of the stationary integral solutions of steady state transonic accretion flow in spherical symmetry helps to understand accretion phenomena on various astrophysical objects. In recent years, attempts have been made to study accreting black hole systems as an example of autonomous dynamical systems. The fixed point analysis is used to study the transonic properties of accretion flow onto an astrophysical black hole, hence the nature of the phase orbits for the transonic flow solutions can be understood without constructing the integral solutions. Since a large-scale astrophysical fluid flow is vulnerable to external perturbation, one needs to ensure that the stationary accretion solutions are stable under perturbation. By adopting a time-dependent stability analysis scheme for the accretion flow, one demonstrates under which condition the perturbation will not diverge. It has also been observed that a space-time metric, dubbed the sonic metric, can be constructed to describe the propagation of the perturbation embedded within the accreting fluid, which mimics a black hole like spacetime within the accreting fluid, where the transonic surfaces can be identified with a black hole like horizons. Such identification is accomplished using the theory of causal structure - by constructing Carter-Penrose diagrams. An accreting black hole system, thus, can be perceived as a classical analogue gravity model naturally found in the universe. Hence, accretion phenomena onto astrophysical black holes can be looked upon from three apparently non-overlapping perspectives - astrophysical processes, theory of dynamical systems, and emergent gravity (alternatively, the analogue gravity) phenomena, respectively. The present article illustrates, by taking the simplest possible accretion flow model, how one can study astrophysical accretion processes from the aforementioned perspectives (Abridged).

astro-ph.HE↗

arXiv2024

Tacit algorithmic collusion in deep reinforcement learning guided price competition: A study using EV charge pricing game

Players in pricing games with complex structures are increasingly adopting artificial intelligence (AI) aided learning algorithms to make pricing decisions for maximizing profits. This is raising concern for the antitrust agencies as the practice of using AI may promote tacit algorithmic collusion among otherwise independent players. Recent studies of games in canonical forms have shown contrasting claims ranging from none to a high level of tacit collusion among AI-guided players. In this paper, we examine the concern for tacit collusion by considering a practical game where EV charging hubs compete by dynamically varying their prices. Such a game is likely to be commonplace in the near future as EV adoption grows in all sectors of transportation. The hubs source power from the day-ahead (DA) and real-time (RT) electricity markets as well as from in-house battery storage systems. Their goal is to maximize profits via pricing and efficiently managing the cost of power usage. To aid our examination, we develop a two-step data-driven methodology. The first step obtains the DA commitment by solving a stochastic model. The second step generates the pricing strategies by solving a competitive Markov decision process model using a multi-agent deep reinforcement learning (MADRL) framework. We evaluate the resulting pricing strategies using an index for the level of tacit algorithmic collusion. An index value of zero indicates no collusion (perfect competition) and one indicates full collusion (monopolistic behavior). Results from our numerical case study yield collusion index values between 0.14 and 0.45, suggesting a low to moderate level of collusion.

cs.LG↗

arXiv2024

Joint operation of a fast-charging EV hub with a stand-alone independent battery storage system under fairness considerations

The need for larger-scale fast-charging electric vehicle (EV) hubs is on the rise due to the growth in EV adoption. Another area of power infrastructure growth is the proliferation of independently operated stand-alone battery storage systems (BSS), which is fueled by improvements and cost reductions in battery technology. Many possible uses of the stand-alone BSS are being explored including participation in the energy and ancillary markets, load balancing for renewable generations, and supporting large-scale load-consuming entities like hospitals. In this paper, we study a novel usage of the stand-alone BSS whereby in addition to participating in the electricity reserve market, it allows an EV hub to use a part of its storage capacity, when profitable. The hub uses the BSS storage capacity for arbitrage consequently reducing its operating cost. We formulate this joint operation as a bi-objective optimization model. We then reformulate it into a second-order cone Nash bargaining problem, the solution of which guarantees fairness to both the hub and the BSS. A sample numerical case study is formulated using actual prices of electricity and simulated data for the reserve market and EV charging demand. The Nash bargaining solution shows that both participants can benefit from the joint operation.

eess.SY↗

arXiv2023

Deep PackGen: A Deep Reinforcement Learning Framework for Adversarial Network Packet Generation

Recent advancements in artificial intelligence (AI) and machine learning (ML) algorithms, coupled with the availability of faster computing infrastructure, have enhanced the security posture of cybersecurity operations centers (defenders) through the development of ML-aided network intrusion detection systems (NIDS). Concurrently, the abilities of adversaries to evade security have also increased with the support of AI/ML models. Therefore, defenders need to proactively prepare for evasion attacks that exploit the detection mechanisms of NIDS. Recent studies have found that the perturbation of flow-based and packet-based features can deceive ML models, but these approaches have limitations. Perturbations made to the flow-based features are difficult to reverse-engineer, while samples generated with perturbations to the packet-based features are not playable. Our methodological framework, Deep PackGen, employs deep reinforcement learning to generate adversarial packets and aims to overcome the limitations of approaches in the literature. By taking raw malicious network packets as inputs and systematically making perturbations on them, Deep PackGen camouflages them as benign packets while still maintaining their functionality. In our experiments, using publicly available data, Deep PackGen achieved an average adversarial success rate of 66.4\% against various ML models and across different attack types. Our investigation also revealed that more than 45\% of the successful adversarial samples were out-of-distribution packets that evaded the decision boundaries of the classifiers. The knowledge gained from our study on the adversary's ability to make specific evasive perturbations to different types of malicious packets can help defenders enhance the robustness of their NIDS against evolving adversarial attacks.

cs.CR↗

arXiv2022

Dependence of acoustic surface gravity on disc thickness for accreting astrophysical black holes

For axially symmetric accretion maintained in hydrostatic equilibrium along the vertical direction, we investigate how the characteristic features of the embedded acoustic geometry depends on the background Kerr metric, and how such dependence is governed by three different expressions of the thickness of the matter flow. We first obtain the location of the sonic points and stationary shock between the sonic points. We then linearly perturb the flow to obtain the corresponding metric elements of the acoustic space-time. We thus construct the causal structure to establish that the sonic points and the shocks are actually the analogue black hole type and white hole type horizons, respectively. We finally compute the value of the acoustic surface gravity as a function of the spin angular momentum of the rotating black hole for three different flow thicknesses considered in the present work. We find that for some flow models, the intrinsic acoustic geometry, although in principle may be extended up to the outer gravitational horizon of the astrophysical black hole, cannot be constructed beyond a certain truncation radius as imposed by the expressions of the thickness function of the corresponding flow.

astro-ph.HE↗

arXiv2022

Carter-Penrose diagrams for emergent spacetime in axisymmetrically accreting black hole systems

For general relativistic, inviscid, axisymmetric flow around Kerr black hole one may choose different flow thickness. The stationary flow equations can be solved using methods of dynamical system to get transonic accretion flows , i.e, flow infalling in the blackhole that turns supersonic from subsonic with decreasing radial distance, or vice versa. This transonic flows are obtained by choosing the particular flow passing through critical points of phase portrait. For certain flow thickness like the one maintaining conical shape, the sonic point coincide with the critical point. But there are certain flows maintaining hydrostatic equilibrium, such as the one described by Novikov-Thorne, where the sonic point is not same as the critical point. We perturb the flow for both kind of flow and study the behaviour of linear perturbation which behaves like massless scalar field in some curved spacetime, known as, analogue space time. We draw the compactified causal structure, i.e, Penrose Carter diagram for both kind of analogue metric and prove that for both cases critical points are the acoustic horizons, whereas in the case where sonic points do not coincide with critical points, the sonic points are not the acoustic horizon, as one may expect from the definition of sound speed.

gr-qc↗

arXiv2021

Dynamical analogue spacetimes in non-relativistic flows

Analogue gravity models describe linear fluctuations of fluids as a massless scalar field propagating on stationary acoustic spacetimes constructed from the background flow. In this paper, we establish that this paradigm generalizes to arbitrary order nonlinear perturbations propagating on dynamical analogue spacetimes. Our results hold for all inviscid, spherically symmetric and barotropic non-relativistic flows in the presence of an external conservative force. We demonstrate that such fluids always admit a dynamical description governed by a coupled pair of wave and continuity equations. We provide an iterative approach to solve these equations about any known stationary solution to all orders in perturbation. In the process, we reveal that there exists a dynamical acoustic spacetime on which fluctuations of the mass accretion rate propagate. The dynamical acoustic spacetime is shown to have a well defined causal structure and curvature. In addition, we find a classical fluctuation relation for the acoustic horizon of the spacetime that admit scenarios wherein the horizon can grow as well as recede, with the latter being a result with no known analogue in black holes. As an example, we numerically investigate the Bondi flow accreting solution subject to exponentially damped time dependent perturbations. We find that second and higher order classical perturbations possess an acoustic horizon that oscillates and changes to a new stable size at late times. In particular, the case of a receding acoustic horizon is realized through `low frequency' perturbations. We discuss our results in the context of more general analogue models and its potential implications on astrophysical accretion flows.

gr-qc↗

arXiv2021

Emergent gravity through non-linear perturbation

As of now, all analogue gravity models available in the literature deal with the emergence of an acoustic geometry through linear perturbations of transonic fluids only. It has never been investigated whether the analogue gravity phenomena is solely a consequence of linear perturbations, or rather a generic property of arbitrary perturbations of inhomogeneous, inviscid and irrotational fluids. In the present work, for the first time in the literature, we demonstrate that acoustic spacetimes may be formed through higher order non-linear perturbations, and thus establish that analogue gravity phenomena is rather more general than what was thought before. We consider spherically accreting astrophysical systems as a natural classical analogue gravity model, and develop a formalism to investigate non-linear perturbations of such accretion flows to arbitrary order. Our iterative approach involves a coupled set of equations for the mass accretion rate and the density of the fluid. In particular, we demonstrate that the wave equation for the mass accretion rate involves an acoustic metric which can be perturbatively constructed to all orders. We numerically solve the coupled equations about the leading transonic Bondi flow solution. This analysis uses boundary conditions set to the original unperturbed values, with the time dependence of the mass accretion rate perturbation taken to be exponentially damped. The perturbed solutions indicate that second order and higher perturbations of the metric generically cause the original acoustic horizon to oscillate and change in size. We explain this phenomenon in detail and its implications on non-linear perturbations of accretion flows in general.

gr-qc↗

arXiv2020

Influence of flow thickness on general relativistic low angular momentum accretion around spinning black holes

General relativistic, axisymmetric flow of low angular momentum accretion around a Kerr black hole can have certain geometric configuration where the flow is maintained in hydrostatic equilibrium along the vertical direction (direction orthogonal to the equatorial plane of the flow). The flow thickness for such accretion models becomes a function of the local radial distance measured from the black hole horizon. There are three types of functions defined in the literature which resemble the thickness of the flow for such a configuration. We formulate the equations governing the steady state astrophysical accretion characterized by both the polytropic as well as the isothermal equation of state in classical thermodynamics. We solve the equations within the framework of such geometric configuration for three different thickness functions, to obtain the multi-transonic, shocked, stationary integral accretion solutions. Such solutions enable us to study how flow thickness influences the dependence of the properties of post-shock flows on black hole spin angular momentum, i.e., the Kerr parameter. For temperature-preserving standings shocks, we find that the post-shock part of the disc can become luminous and considerable amount of gravitational energy carried by the accreting fluid can get liberated at the shock. We find which kind of thickness function produces the maximum liberated energy, making the disc most luminous.

astro-ph.HE↗

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↗

arXiv2018

Effect of matter geometry on low angular momentum black hole accretion in the Kerr metric

This work illustrates how the formation of energy-preserving shocks for polytropic accretion and temperature-preserving shocks for isothermal accretion are influenced by various geometrical configurations of general relativistic, axisymmetric, low-angular-momentum flow in the Kerr metric. Relevant pre- and post-shock states of the accreting fluid, both dynamical and thermodynamic, have been studied comprehensively. Self-gravitational back-reaction on the metric has not been considered in the present context. An elegant eigenvalue-based analytical method has been introduced to provide qualitative descriptions of the phase-orbits corresponding to stationary transonic accretion solutions, without resorting to involved numerical schemes. Effort has been made to understand how the weakly-rotating flow behaves in close proximity of the event horizon and how such `quasi-terminal' quantities are influenced by the black hole spin for different matter geometries. Our main purpose is thus to mathematically demonstrate that for non-self-gravitating accretion, separate matter geometries, in addition to the corresponding space-time geometry, control various shock-induced phenomena observed within black hole accretion discs. This work is expected to reveal how such phenomena observed near the horizon depend on physical environment of the source harbouring a supermassive black hole at its centre. It is also expected to unfold correspondences between the dependence of accretion-related parameters on flow geometries and on black hole spin. Temperature-preserving shocks in isothermal accretion may appear bright as substantial amount of rest-mass energy of the infalling matter gets dissipated at the shock surface, and the prompt removal of such energy to maintain isothermality may power the X-ray/IR flares emitted from our Galactic centre.

astro-ph.HE↗

arXiv2018

Second Order Perturbative Effects on the Acoustic Geometry

In this work, we have studied the effect of higher order perturbations, particularly the second order in details, on the sonic horizon. We have considered two different schemes of perturbations which are velocity potential perturbation and mass acceleration rate perturbation. These two schemes give us qualitatively similar behaviour. We have found that the analogue gravity formalism also holds for the higher order perturbations.

gr-qc↗