arXiv subjects

Suman Kumar Panja

Publications and source records attributed to Suman Kumar Panja.

17 recordsLinked to original sources

arXiv2026

Vacuum fluctuations in Rainbow space-time: Study of Casimir effect

We investigate the Casimir effect in rainbow space-time, focusing on leading-order corrections to the Casimir energy and force. Starting with the scalar field Lagrangian in rainbow space-time, with parallel plates introduced through delta-function potentials, we find the corresponding energy-momentum tensor. We obtain the vacuum expectation value of this energy-momentum tensor by expressing it as a quadratic operator acting on the Green's function. By solving the Euler-Lagrange equation of a scalar field in rainbow space-time, we obtain the Green's function solutions. Employing these Green's function solutions in the vacuum expectation value of the energy-momentum tensor, we obtain the modified Casimir energy and Casimir force expressions in rainbow space-time. We study the variation of the deformed Casimir force and energy with the distance between the plates for different choices of rainbow functions. Our results show that for two choices of rainbow functions, the absolute value of the Casimir energy and force is decreasing or increasing, whereas for one specific choice of rainbow functions, it remains the same as the standard result in Minkowski space-time. Comparing our result with experimentally measured value of Casimir force, we obtain the bound on the rainbow parameter dependent terms to be of the order of 10^-24.

hep-th↗

arXiv2026

How a minimal length scale modifies thermodynamics of RN AdS Black Holes?

We investigate the thermodynamic modifications of the Reissner-Nordstroem anti-de Sitter (RN AdS) black hole induced by a minimal length scale,which naturally emerges in $\kappa$-deformed space-time. By constructing the modified metric via phase-space commutation relations,we derive the deformed Hawking temperature, entropy, and enthalpy. We analyze the thermal stability through the heat capacity and study the P-V criticality, revealing that the black hole undergoes a small-to-large phase transition analogous to the Van der Waals system, albeit with a critical ratio slightly lowered by non-commutativity. Furthermore, we examine the Joule-Thomson expansion and find that the non-commutative (NC) parameter expands the cooling region in the temperature-pressure plane. Our results demonstrate that while the overall thermodynamic analogy with the Van der Waals fluid persists, the minimal length scale systematically deform the coexistence region and inversion curves, offering potential observational signatures for quantum gravity.

gr-qc↗

arXiv2026

Thermal Casimir effect in $κ$-Minkowski space-time

We study the finite temperature Casimir effect for parallel plates in the $κ$-Minkowski space-time. Using the Matsubara formalism and imposing the Dirichlet boundary conditions on a massless $κ$-scalar field, we compute the $κ$-deformed corrections to thermal Casimir free energy, pressure, entropy, and internal energy. Our results demonstrate that space-time non-commutativity enhances the attractive nature of the thermal Casimir force while preserving thermodynamic consistency; the system satisfies the Nernst theorem and laws of thermodynamics remain intact in $κ$-deformed space-time. Our analysis yields an upper bound on the deformation parameter as $a\leq10^{-18}m$. Furthermore, our results indicate that non-commutative effects become experimentally observable in Casimir effect studies when the ratio of the non-commutative scale to plate separation satisfies $a/L\leq 10^{-12}$. We also obtain the expression for Stefan-Boltzmann's law in $κ$-Minkowski space-time.

hep-th↗

arXiv2025

High-temperature plasma in Casimir physics

We present a short review of an unusual but important application for a high-temperature charged plasma. The unorthodox proposition was made by Ninham concerning a contribution from Casimir forces across high-temperature electron-positron plasma in nuclear interactions. The key message in the current work is how high temperatures ($\sim10^{11}$ \,K) pop out as essential. Clearly, classical, semi-classical, and quantum considerations for the background media impact both the Casimir effect and the physics of stars and the Universe.

cond-mat.mtrl-sci↗

arXiv2024

Centripetal force on Casimir energies in $κ$-deformed rotating frame

We investigate the implications of a fundamental length scale on the centripetal force on a rotating Casimir apparatus in $κ$-space-time. We model the Casimir apparatus rotating with constant angular speed using appropriate $κ$-deformed coordinates. We find the $κ$-deformed centripetal force on a single plate, as well as for parallel plates. We show that the Casimir energy, including the divergent part (self energies of the plates) experiences centripetal forces like a conventional mass. We also find centripetal force on oriented parallel plates rotating with constant angular speed in $κ$-space-time. Results show that the mass-energy equivalence principle holds in the $κ$-space-time.

hep-th↗

arXiv2024

Non-commutative correction of ideal gas thermodynamics

In this study, we investigate the thermodynamics of a relativistic ideal within the context of $κ$-deformed space-time and Rainbow gravity background. To achieve this, we construct a modified partition function by considering a deformed Hamiltonian and incorporating corrections based on the time-invariant phase-space volume. We explore the implications of our model on the modified black body radiation spectrum and the modified Debye theory of specific heat in $κ$-deformed space-time and Rainbow gravity background.

gr-qc↗

arXiv2024

Geodesic motion of particles in the vicinity of the $κ$-deformed Schwarzchild Black Hole

In this study, we investigate the geodesic motion of a test particle around the Schwarzchild black hole in a $κ$-deformed space-time. We compute a modified Lagrangian to obtain the $κ$-deformed effective potential and find the particle trajectories based on the constants of motion. For the same value of angular momentum, we obtain a significant deformation in the orbits of the particles due to the non-commutativity of the $κ$-deformed space-time. The deformation parameter becomes more significant for higher values of the angular momentum. The radius of the individual trajectories become smaller and their velocities decrease compared to the commutative case. The radius of the innermost stable circular orbit ($r_{ISCO}$) is also found using the modified effective potential. Though the equations get modified due to the non-commutativity of the $κ$-deformed space-time, the $r_{ISCO}$ remains the same. We then study a large number of freely streaming particles moving in this $κ$-deformed space-time and analyze the movement of these particles around the black hole due to the non-commutativity of the space-time. We concentrate on particles with different angular momentum moving around the black hole. We find that the motion of the particles are modified due to the non-commutativity of the space-time. The particles move slower along their respective trajectories in the deformed space-time. So, they remain closer to the black hole for a longer period of time, indicating that the accretion of freely streaming particles around the black hole would be modified by the non-commutativity of the space-time.

gr-qc↗

arXiv2024

Maximal acceleration in Rainbow gravity

In this paper, we derive maximal acceleration of a massive particle in Rainbow gravity. Using eight-dimensional phase-space metric compatible with Rainbow gravity, we obtain the maximal acceleration, valid up to first order in the Rainbow gravity parameter $η$. Using the positivity condition on maximal acceleration, we find the upper bound on the Rainbow gravity parameter is of the order of $~10^{22}$ for positron and $10^{-44}$ for a black hole. After obtaining the expression for maximal acceleration for different choices of Rainbow functions, we derive corresponding modifications to Unruh temperature. Comparing with the observational value of the Unruh temperature, we find the upper bound on $η$ as $~10^{32}$ for positron radiation. %and of the order of $10^{-100}$ for radiation from a black hole. We then derive geodesic equations for different choices of Rainbow functions and also obtain Newtonian limit of these geodesic equations. We find that the changes in the value of maximum acceleration, maximum temperature and Newtonian force equation are dependent on the choices of Rainbow functions.

gr-qc↗

arXiv2024

How does Casimir energy fall in $κ$-deformed space-time?

We investigate the response of Casimir energies to fluctuations in a scalar field in a weak gravitational field in the $κ$-deformed space-time. We model the Casimir plates in a gravitational field by $κ$-deformed Rindler coordinates and calculate the Casimir energy using the $κ$-deformed scalar field. We show that the Casimir energy accelerates in a weak gravitational field like a mass. Thus, our calculations show that the mass-energy equivalence principle holds in $κ$-deformed space-time even though a length scale is introduced through space-time non-commutativity.

hep-th↗

arXiv2024

Influence of the cosmological constant on $κ$-deformed Neutron Star

We study a model of the neutron star in $κ$-deformed space-time in the presence of the cosmological constant ($Λ$). The Einstein tensor and the energy-momentum tensor are generalized to $κ$-deformed space-time and we construct the field equations with the cosmological constant. Considering the interior of the star to be a perfect fluid as in the commutative case, we find the Tolman-Oppenheimer-Volkoff equations with the inclusion of the cosmological constant in $κ$-deformed space-time. The behavior of the maximum allowed mass of the star and its radius are studied with the variation in the cosmological constant as well as the deformation parameter. We see that the non-commutativity enhances the mass of the star and its maximum mass increases with a decrease in the cosmological constant. The maximum mass varies from $3.44M_{\odot}$ to $3.68M_{\odot}$ as $Λ$ varies from $10^{-10}m^{-2}$ to $10^{-15}m^{-2}$. We also obtain the compactness factor and surface redshift of the star. We observe that the compactness of the star increases as the cosmological constant decreases, whereas the surface redshift of the star decreases with a decrease in the cosmological constant. The compactness factor and surface redshift corresponding to the maximum mass of the neutron star remains almost constant as $Λ$ decreases.

gr-qc↗

arXiv2024

Neutron Star in Quantized-space-time

We construct and analyze a model of the neutron star in the k deformed space-time. This is done by first deriving the k deformed generalization of the Einstein tensor, starting from the non-commutative generalization of the metric tensor. By generalizing the energy momentum tensor to the non-commutative space-time and exploiting the k deformed dispersion relation, we then set up Einstein's field equations in the kdeformed space time. As we adopt a realization of the non commutative coordinates in terms of the commutative coordinates and their derivatives, our model is constructed in terms of commutative variables. Using this, we derive the kdeformed generalization of the Tolman Oppenheimer Volkoff equation. Now, by treating the interior of the star to be a perfect fluid as in the commutative space-time, we investigate the modification of the neutron star's mass due to non commutativity of the space time, valid up to first order in the deformation parameter. We show that the non-commutativity of the space time enhances the mass limit of the neutron star. We show that the radius and maximum mass of the neutron star depend on the deformation parameter. Further, our study shows that the mass increases as the radius increases for fixed values of the deformation parameter. We show that maximum mass and radius increase as the deformation parameter increases. We find that the mass varies from 0.26Ms to 3.68Ms as radius changes from 8.45km to 18.66km. Using the recent observational limits on the upper bound of the mass of a neutron star, we find the deformation parameter is approximately $10^{-44}m$. We also show that the compactness and surface redshift of the neutron star increase with its mass.

gr-qc↗

arXiv2023

Newtonian cosmology and Evolution of kappa-deformed universe

Considering space--time to be non-commutative, we study the evolution of the universe employing the approach of Newtonian cosmology. Generalizing the conservation of energy and the first law of thermodynamics to $κ$-deformed space--time, we derive the modified Friedmann equations, valid up to the first order, in the deformation parameter. Analyzing these deformed equations, we derive the time evolution of the scale factor in cases of radiation-dominated, matter-dominated, and vacuum (energy)-dominated universes. We show that the rate of change of the scale factor in all three situations is modified by the non-commutativity of space--time, and this rate depends on the sign of the deformation parameter, indicating a possible explanation for the observed Hubble tension. We undertake this investigation for two different realizations of non-commutative space--time coordinates. In both cases, we also argue for the existence of bounce in the evolution of the universe.

gr-qc↗

arXiv2022

Casimir effect in DFR space-time

Non-Commutative space-time introduces a fundamental length scale suggested by approaches to quantum gravity. Here we report the analysis of the Casimir effect for parallel plates separated by a distance of $L$ using a Lorentz invariant scalar theory in a non-commutative space-time (DFR space-time), both at zero and finite temperatures. This is done in two ways; one when the additional space-dimensions introduced in DFR space-time are treated as extra dimensions but on par with usual space-dimension and in the second way, the additional dimensions are treated as compact dimensions. Casimir force obtained in the first approach coincides with the result in the extra-dimensional commutative space-time and this is varying as $\frac{1}{L^5}$. In the second approach, we derive the corrections to the Casimir force, which is dependent on the separation between the plate, $L$ and on the size of the extra compactified dimension, $R$. Since correction terms are very small, keeping only the most significant terms of these corrections, we show that for certain values of the R, the corrections due to non-commutativity makes the force between the parallel plates more attractive, and using this, we find lower bound on the value of $R$. We show here that the requirement of the Casimir force and the energy to be real, impose the condition that the weight function used in defining the DFR action has to be a constant. At zero temperature, we find correction terms due to non-commutativity, depend on $L$ and $R$ dependent modified Bessel functions $K_{1}$ and $K_{2}$, with coefficients that vary as $\frac{1}{LR^3}$ and $\frac{1}{L^2R^2}$, respectively . For finite temperature, the Casimir force has correction terms that scale as $\frac{1}{L}$ and $\frac{1}{L^3}$ in high-temperature limit and as $\frac{1}{L^2}$ and $\frac{1}{L^4}$ in the low-temperature limit.

hep-th↗

arXiv2022

Maximal acceleration in a Lorentz invariant non-commutative space-time

In this paper, we derive the non-commutative corrections to the maximal acceleration in the Doplicher-Fredenhagen-Roberts (DFR) space-time and show that the effect of the non-commutativity is to decrease the magnitude of the value of the maximal acceleration in the commutative limit. We also obtain an upper bound on the acceleration along the non-commutative coordinates using the positivity condition on the magnitude of the maximal acceleration in the commutative space-time. From the Newtonian limit of the geodesic equation and Einstein's equation for linearised gravity, we derive the explicit form of Newton's potential in DFR space-time. By expressing the non-commutative correction term of the maximal acceleration in terms of Newton's potential and applying the positivity condition, we obtain a lower bound on the radial distance between two particles under the gravitational attraction in DFR space-time. We also derive modified uncertainty relation and commutation relation between coordinates and its conjugate, due to the existence of maximal acceleration.

hep-th↗

arXiv2021

Application of regularization maps to quantum mechanical systems in 2 and 3 dimensions

We extend the Levi-Civita (L-C) and Kustaanheimo-Stiefel (K-S) regularization methods that maps the classical system where a particle moves under the combined influence of $\frac{1}{r}$ and $r^2$ potentials to a harmonic oscillator with inverted sextic potential and interactions to corresponding quantum mechanical counterparts, both in 2 and 3 dimensions. Using the perturbative solutions of the Schrödinger equation of the later systems, we derive the eigen spectrum of the Hydrogen atom in presence of an additional harmonic potential. We have also obtained the mapping of a particle moving in the shifted harmonic potential to H-atom using Bohlin-Sundman transformation, for quantum regime. Exploiting this equivalence, the solution to the Schrödinger equation of the former is obtained from the solutions of the later.

math-ph↗

arXiv2021

Regularization of central forces with damping in two and three-dimensions

Regularization of damped motion under central forces in two and three-dimensions are investigated and equivalent, undamped systems are obtained. The dynamics of a particle moving in $\frac{1}{r}$ potential and subjected to a damping force is shown to be regularized a la Levi-Civita. We then generalize this regularization mapping to the case of damped motion in the potential $r^{-\frac{2N}{N+1}}$. Further equation of motion of a damped Kepler motion in 3-dimensions is mapped to an oscillator with inverted sextic potential and couplings, in 4-dimensions using Kustaanheimo-Stiefel regularization method. It is shown that the strength of the sextic potential is given by the damping co-efficient of the Kepler motion. Using homogeneous Hamiltonian formalism, we establish the mapping between the Hamiltonian of these two models. Both in 2 and 3-dimensions, we show that the regularized equation is non-linear, in contrast to undamped cases. Mapping of a particle moving in a harmonic potential subjected to damping to an undamped system with shifted frequency is then derived using Bohlin-Sudman transformation.

math-ph↗

arXiv2019

Time-space noncommutativity and Casimir effect

We show that the Casimir force and energy are modified in the kappa-deformed space-time. This is analysed by solving the Green's function corresponding to kappa-deformed scalar field equation in presence of two parallel plates, modelled by delta-function potentials. Exploiting the relation between energy-momentum tensor and Green's function, we calculate the correction to Casimir force, valid up to second order in the deformation parameter. The Casimir force is shown to get corrections which scale as $L^{-4}$ and $L^{-6}$ and both these types of corrections produce attractive forces. Using the measured value of Casimir force, we show that the deformation parameter should be below $10^{-23}$m.

hep-th↗