We analyze the motion of a {\it massless} and chargeless} particle very near to event horizon. It reveals that radial has exponential growing nature which indicates there is possibility inducing chaos in an integrable system when it comes under influence This being confirmed by investigating Poincar$\acute{e}$ section trajectories with introduction harmonic trap confine particle's motion. Two situations are investigated: (a) any} static, spherically symmetric black hole and, (b) spacetime...

In this paper, we study the motion of a massless, chargeless particle in Schwarzschild-de Sitter spacetime, revealing exponential radial growth and potential chaos an integrable system. Poincar\'e sections show regular Kolmogorov-Arnold-Moser (KAM) tori when black hole cosmological horizons are distant, but distortions emerge as they converge. As coincide, fully contract vanish, marking system's transition to Nariai spacetime. \textit{Our analysis also suggests that, within parameter range...

The classical Hamiltonian for a chargeless and massless particle in very near-horizon region is shown to be of the form $H\ensuremath{\sim}xp$ as long radial motion concerned. This demonstrated explicitly static spherically symmetric black hole also found applicable specific choice trajectories Kerr case. Such feature horizon leads unavoidable ``local instability'' particle's regime We show that at quantum level this provides thermality system. temperature given by Hawking expression....

We revisit our previous proposed conjecture -- horizon creates a local instability which acts as the source of quantum temperature black hole. It is found that chargesless massless particle moving along null trajectory in Eddington-Finkelstein (EF) coordinates feels vicinity horizon. Such observer independent for this motion. Moreover, an associated to EF finds Hamiltonian $xp$ where $p$ canonical momentum corresponding coordinate $x$. Finally, using we notice at level class observers feel...

The ongoing conjecture that the presence of horizon may induce chaos in an integrable system, is further investigated from perspective a uniformly accelerated frame. Particularly, we build up model which consists particle (massless and chargeless) trapped harmonic oscillator frame (namely Rindler observer). Here provides Killing without any intrinsic curvature to system. This makes present observations different previous studies. We observe for some particular values parameters system (like...

The validity of our already proposed conjecture -- {\it horizon creates a local instability which acts as the source quantum temperature black hole} is being tested here for Kerr hole. Earlier this has been explicitly shown spherically symmetric static hole (SSS BH). more realistic situation like spacetime, stationary and axisymmetric, non-trivial example to analyze. We show that chargeless massless particle, near radial motion in SSS BH, can be locally unstable. contribution corresponding...

We compute the Lyapunov exponents for test particles orbiting in unstable circular trajectories around D-dimensional Reissner-Nordström (RN) black holes, scrutinizing instances of chaos bound violation. Notably, we discover that an increase particle angular momentum exacerbates breach bound. Our research centrally investigates correlation between hole thermodynamic phase transitions and breaking limit. Findings suggest can only be transgressed within thermodynamically stable phases holes....

The paper is devoted to a detailed study of the effects quantum corrections on chaotic behaviour in dynamics (massless) probe particle near horizon generalized Schwarzschild black hole. Two possible origins inducing modification hole metric are considered separately; noncommutative geometry inspired (suggested by Nicolini, Smailagic and Spallucci) with field theoretic (derived Donoghue). Our results clearly show that both cases, extensions favour behaviour, namely chaos attained for...

We re-advocated the conjecture of indistinguishability between quantum fluctuation observed from a Rindler frame and real thermal bath, for case free massless scalar field. To clarify robustness how far such is admissible, in this paper, we investigate issue two different non-inertial observers' perspective. A detailed analysis being done to find observable quantities as measured by observers (one another uniformly rotating) on bath Minkowski spacetime. More precisely, compare...

In the studies of quantum field theory in curved spacetime, ambiguous concept vacuum state and particle content is a long-standing debatable aspect. So far it well known to us that background some privileged class observers detect production suitably chosen states matter fields. this work we aim study characteristics behaviour these produced particles de-Sitter (dS) Friedmann-Lama\^{i}tre-Robertson-Walker (FLRW) Universe (both for $(1+1)$ $(3+1)$ dimensions) $(1+1)$-dimensional Schwarzschild...

Dynamical properties of a generic null surface are known to have thermodynamic interpretation. Such an interpretation is completely based on analogy between the usual law thermodynamics and structure gravitational field equation surface. Here we materialize this show that assigning temperature for local observer indeed physically relevant. We find frame, chosen as outgoing massless chargeless particle (or mode), perceives ``local unstable Hamiltonian'' very near Due it has finite quantum...

In this paper, we propose a new analog gravity example---a spinning (or Kerr) black hole in an extended fluid model; the latter was derived earlier work [A. K. Mitra and S. Ghosh, Divergence anomaly Schwinger terms: Towards consistent theory of anomalous classical fluids, Phys. Rev. D 106, L041702 (2022).] by two present authors. The model receives Berry curvature contributions applies to electron dynamics condensed matter lattice systems hydrodynamic limit. We construct acoustic metric for...

We investigate chaos in the dynamics of outgoing massless particles near horizon static spherically symmetric (SSS) black holes two well-motivated models $f(R)$ gravity. In both these models, we probe particle trajectories (under suitable harmonic confinement) vicinity hole horizons, for a set initial conditions. The trajectories, associated Poincar$\acute{e}$ sections, and Lyapunov exponents clearly illustrate role played by growth within specific energy range. demonstrate how this range is...

In this paper, we propose a new Analogue Gravity example - spinning (or Kerr) Black Hole in an extended fluid model. The model receives Berry curvature contributions and applies to electron dynamics Condensed Matter lattice systems the hydrodynamic limit. We construct acoustic metric for sonic fluctuations that obey structurally relativistic wave equation effective curved background. novel approach of dimensional analysis, have derived explicit expressions mass angular momentum per unit (in...

We compute the Lyapunov exponents for test particles orbiting in unstable circular trajectories around D-dimensional Reissner-Nordstr\"om (RN) black holes, scrutinizing instances of chaos bound violation. Notably, we discover that an increase particle angular momentum exacerbates breach bound. Our research centrally investigates correlation between hole thermodynamic phase transitions and breaking limit. Findings suggest can only be transgressed within thermodynamically stable phases holes....

The present paper is based on a previous work (involving two of the authors) where generalized fluid dynamical model was proposed. underlying symplectic structure Lagrangian discrete degrees freedom obeyed Non-Commutative algebra, generated by Berry curvature correction. In an Euler (or Hamiltonian) framework, this manifested as extended algebra between variables, leading to model. Here we study dynamics sonic fluctuations that live in effective analogue gravity spacetime. Interestingly...

This article is devoted to investigate the effects of $f(R)$ theory in dynamics a massless particle near horizon static spherically symmetric (SSS) black hole. Deriving equations motion within gravitational theories, novel solutions for charged and neutral holes are obtained, introducing dimensional parameter $a$ $f(R)=R-2a\sqrt{R}$. Departing from General Relativity, these showcase unique properties reliant on Ricci scalar. Analysis shows that chaos manifests specific energy range, with...