arXiv subjects

Arpan Krishna Mitra

Publications and source records attributed to Arpan Krishna Mitra.

15 recordsLinked to original sources

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↗

arXiv2026

Non-Commutative fluid: an alternative source of cosmic acceleration

We present a novel formulation for the Hubble parameter derived from Newtonian cosmology, incorporating non-commutative fluid dynamics through a deformed Poisson bracket structure. This approach introduces a new cosmological parameter, denoted by $σ$, which emerges naturally from the underlying non-commutative framework. It gives rise to a source term in the background fluid continuity equation, thereby leading to an apparent type of matter creation picture through the resulting non-conservation. Remarkably, the resulting Hubble function accounts for the observed accelerated expansion of the universe without invoking any external dark energy component or cosmological constant. Instead, the parameter $σ$ effectively serves as the driver of acceleration. We further examine the observational constraints on $σ$ using current cosmological data, including the recent Dark Energy Spectroscopic Instrument(DESI) dataset, demonstrating its viability as an alternative explanation for late-time cosmic acceleration within a non-commutative cosmological model.

gr-qc↗

arXiv2025

Relativistic Fluid Dynamics in Curved Spacetime: a Novel Effective Hamiltonian Approach

We present a comprehensive Eulerian (Hamiltonian) framework for relativistic fluid dynamics in curved spacetimes, with emphasis on Schwarzschild geometry. The key innovation lies in the consistent use of density and three-velocity fields, all defined in coordinate (Newtonian) time, while fully incorporating relativistic and curvature effects. {\it We stress that the entire dynamics is developed in coordinate (Eulerian) time, from the viewpoint of a static Eulerian observer.} In the non-relativistic regime, it is well known that Poisson brackets between the density $ρ(\vec{x}, t)$ and velocity fields $v^i(\vec{x}, t)$, together with an appropriate Hamiltonian, yield the continuity and Euler equations as Hamiltonian equations of motion. These field-theoretic Poisson brackets can be derived from canonical phase-space brackets defined on Lagrangian variables $(x_i, p_j)$, mapped to Eulerian fields $(ρ, v^i)$. We extend this framework to curved spacetime by constructing a relativistic version of the Eulerian Poisson algebra and proposing a corresponding Hamiltonian. This yields relativistic continuity and Euler equations valid in generic spacetimes, with evolution in coordinate time. Applying this to the Schwarzschild metric, we obtain exact stationary background solutions for radial flows and perform a perturbative stability analysis. We also introduce a generalised vorticity and examine its effect on perturbations over irrotational backgrounds, revealing its role in flow stability. This work offers a unified, first-principles Hamiltonian formulation of relativistic fluid dynamics in curved geometries, forming a foundation for further study of astrophysical and cosmological fluid phenomena.

gr-qc↗

arXiv2025

Dynamical analog spacetimes from nonlinear perturbations in a topological material

Emergent spacetime analogs in condensed matter systems have opened a fascinating window into simulating aspects of gravitational physics in controlled laboratory environments. In this work, we develop a comprehensive nonlinear analog gravity framework within a topological material, incorporating the impact of Berry curvature on the hydrodynamic flow of electrons. Unlike prevalent studies in existing literature limited to linear perturbations, we derive and analyze a fully nonlinear wave equation governing radial perturbations of density and velocity fields, which dynamically generate an effective acoustic metric. Taking the example of graphene as a representative system, and calculating its properties from first principles, we numerically demonstrate the formation of evolving acoustic horizons and quantify analog Hawking temperatures in experimentally accessible regimes. Our findings suggest that topological materials can serve as versatile platforms to probe rich gravitational phenomena, including horizon dynamics and quasi-thermal emission, beyond conventional linear approximations. This work lays the groundwork for exploring nonlinear emergent spacetime in a broad class of quantum materials, bridging condensed matter physics and gravitational analogs.

gr-qc↗

arXiv2024

Spinning Black Hole in a Fluid

In this paper, we propose a new Analogue Gravity example - a spinning (or Kerr) Black Hole in an extended fluid model. The fluid model receives Berry curvature contributions and applies to electron dynamics in Condensed Matter lattice systems in the hydrodynamic limit. We construct the acoustic metric for sonic fluctuations that obey a structurally relativistic wave equation in an effective curved background. In a novel approach of dimensional analysis, we have derived explicit expressions for effective mass and angular momentum per unit mass in the acoustic metric (in terms of fluid parameters), to identify with corresponding parameters of the Kerr metric. The spin is a manifestation of the Berry curvature-induced effective noncommutative structure in the fluid. Finally we put the Kerr Black Hole analogy in a robust setting by revealing explicitly the presence of horizon and ergo-region for a specific background fluid velocity profile. We also show that near horizon behavior of the phase-space trajectory of a probe particle agrees with Kerr Black Hole analogy. In fluid dynamics perspective, presence of a horizon signifies the wave blocking phenomenon.

gr-qc↗

arXiv2024

Barrow Holographic Dark Energy in Brane World Cosmology

Cosmological features of Barrow Holographic Dark Energy (BHDE), a recent generalization of original Holographic dark energy with a richer structure, are studied in the context of DGP brane, RS II brane-world, and the cyclic universe. It is found that a flat FRW scenario with pressure less dust and a dark energy component described as BHDE can accommodate late time acceleration with Hubble horizon considered as infrared cut off even in the absence of interaction between the dark sectors. Statefinder diagnostic reveals that these model resemble $ΛCDM$ cosmology in future. It is found that BHDE parameter $Δ$, despite its theoretically constrained range of values, is significant in describing the evolution of the universe, however, a classically stable cosmological model cannot be obtained in the RS-II and DGP brane. Viability of the models is also probed with observed Hubble data.

gr-qc↗

arXiv2023

Acoustic Kerr Metric in Analogue Gravity

The present paper is based on a previous work (involving two of the present authors) where a generalized fluid dynamical model was proposed. The underlying symplectic structure of the Lagrangian discrete degrees of freedom obeyed a Non-Commutative algebra, generated by Berry curvature correction. In an Euler (or Hamiltonian) framework, this is manifested as an extended algebra between the fluid variables, leading to the extended fluid model. Here we study the dynamics of sonic fluctuations that live in this effective analogue gravity spacetime. Interestingly enough, the effective metric resembles that of a spinning Black Hole; the spin is induced by the underlying Non-Commutative structure. The effective mass and spin parameters of the Black Hole, in terms of fluid parameters, are also identified. The connection of our model with anomalous Hall systems may lead to observable signatures of the analogue black hole in physical systems.

gr-qc↗

arXiv2022

Divergence Anomaly and Schwinger Terms: Towards a Consistent Theory of Anomalous Classical Fluid

Anomaly, a generic feature of relativistic quantum field theory, is shown to be present in non-relativistic classical ideal fluid. A new result is the presence of anomalous terms in current algebra, an obvious analogue of Schwinger terms present in quantum field theory. We work in Hamiltonian framework where Eulerian dynamical variables obey an anomalous algebra (with Schwinger terms) that is inherited from modified Poisson brackets, with Berry curvature corrections, among Lagrangian discrete coordinates. The divergence anomaly appears in the Hamiltonian equations of motion. A generalized form of fluid velocity field can be identified with the "anomalous velocity" of Bloch band electrons appearing in quantum Hall effect in condensed matter physics. We finally show that the divergence anomaly and Schwinger terms satisfy well known Adler consistency condition. Lastly we mention possible scenarios where this new anomalous fluid theory can impact.

hep-th↗

arXiv2022

Multi-criticality and related bifurcation in accretion discs around non-rotating black holes -- an analytical study

Low angular momentum, general relativistic, axially symmetric accretion of hydrodynamic fluid onto Schwarzschild black holes may undergo more than one critical transition. To obtain the stationary integral solutions corresponding to such multi-critical accretion flow, one needs to employ numerical solutions of the corresponding fluid dynamics equations. In the present work, we develop a {\it{completely analytical}} solution scheme which may be used to find several trans-critical flow behaviours of aforementioned accretion, without explicitly solving the flow equations numerically. We study all possible geometric configurations of the flow profile, governed by all possible thermodynamic equations of state. We use Sturm's chain algorithm to find out how many physically acceptable critical points the accretion flow can have, and discuss the transition from the mono to the multi-critical flow profile, and related bifurcation phenomena. We thus illustrate, completely analytically, the application of certain aspects of the dynamical systems theory in the field of large scale astrophysical flow under the influence of strong gravity. Our work may possibly be generalized to calculate the maximal number of equilibrium points certain autonomous dynamical systems can have in general.

astro-ph.HE↗

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↗

arXiv2018

Noncommutative fluid and Growing Modes of Inhomogeneity in (Newtonian) Cosmology

Time evolution of modes of density contrast, in particular the growing modes, dictate the structure formation in Universe. In this paper we explicitly show how (spatial) Non-Commutativity (NC) can affect the behavior of the modes, that is we compute NC corrected power law profiles of the density contrast modes. We develop a generalized fluid model that lives in NC space. The dynamical equations of fluid, namely the continuity and Euler equations receive NC contributions. When mapped to comoving coordinates these generate the NC extended versions of continuity and Friedmann equations for cosmology. Introducing cosmological perturbations finally yield the NC corrected evolution of density contrast modes. The construction of the NC fluid model from first principles and development of the formal aspects of its Hamiltonian formulation have been presented in the first part.

hep-th↗

arXiv2018

On the equivalence among stress tensors in a gauge-fluid system

In this paper we bring out the subtleties involved in the study of a first order relativistic field theory with auxiliary field variables playing an essential role. In particular we discuss the nonisentropic Eulerian (or Hamiltonian) fluid model. Interactions are introduced by coupling the fluid to a {\it dynamical} Maxwell ($U(1)$) gauge field. This dynamical nature of the gauge field is crucial in showing the equivalence, on the physical subspace, of the stress tensor derived from two definitions, {\it{ie.}} the canonical (Noether) one and the symmetric one. In the conventional equal-time formalism, we have shown that the generators of the spacetime transformations obtained from these two definitions agree, modulo the Gauss constraint. This equivalence in the physical sector has been achieved only because of the dynamical nature of the gauge fields. Subsequently we have explicitly demonstrated the validity of the Schwinger condition. A detailed analysis of the model in lightcone formalism has also been done where several interesting features are revealed.

hep-th↗

arXiv2016

Canonical formulation for nonrelativistic Euler fluids and Schwinger type conditions

We present a new approach, based on Noether's energy-momentum tensor, to construct the lagrangian for nonrelativistic nonisentropic Euler fluids. An advantage of this approach is that it naturally provides a generalised Clebsh decomposition for the fluid velocity. This is used to develop a hamiltonian formulation inolving a noncanonical algebra. This algebra is very simply obtained from the symplectic structure. It is used to show that the components of the Noether's energy-momentum tensor satisfy certain Schwinger-type relations. These relations, which are reminiscent of corresponding relations in relativistic field theory, are new.

hep-th↗

arXiv2015

Hamiltonian analysis of interacting fluids

Ideal fluid dynamics is studied as a relativistic field theory with particular importance on its hamiltonian structure. The Schwinger condition, whose integrated version yields the stress tensor conservation, is explicitly verified both in equal-time and light-cone coordinate systems. We also consider the hamiltonian formulation of fluids interacting with an external gauge field. The complementary roles of the canonical(Noether) stress tensor and the symmetric one obtained by metric variation are discussed. Finally, a non-relativistic reduction of the system in light-cone coordinates has been carried out which reproduces results found earlier in the literature.

hep-th↗

arXiv2014

Two dimensional hydrodynamics with gauge and gravitational anomalies

We present a new approach to discuss two dimensional chiral and non-chiral hydrodynamics with gauge and gravitational anomalies. Exact constitutive relations for the stress tensor and charge current are obtained. For the chiral theory, the constitutive relations may be put in the ideal (chiral) fluid form whereas the constitutive relations corresponding to non-chiral case do not take the ideal fluid form. The constitutive relations in the presence of both gravity and gauge sectors are new. These expressions, in the absence of the gauge sector, reproduce the results obtained in the gradient expansion approach.

hep-th↗