arXiv subjects

Vishnu Rajagopal

Publications and source records attributed to Vishnu Rajagopal.

16 recordsLinked to original sources

arXiv2026

Joule Thomson expansion of $\kappa$-deformed Schwarzschild-AdS black hole

We investigate the Joule-Thomson expansion of a non-commutative Schwarzschild-AdS black hole, whose space-time geometry is described by the Lie-algebraic $\kappa$-deformed space-time, and show that the $\kappa$-deformation parameter induces Joule-Thomson expansion in an uncharged-AdS black hole. We find the ratio of minimum inversion temperature to critical temperature $T_i^{(min)}/T_c \simeq 0.493$, is independent of the deformation parameter, and is in close agreement with the value for Reissner-Nordstrom black hole. Furthermore, we show the existence of a minimum black hole mass (depending on the $\kappa$-deformation parameter) below which the Joule-Thomson expansion vanishes.

gr-qc↗

arXiv2026

Modified Mukhanov-Sasaki equation and primordial perturbations in $\kappa$-deformed non-commutative space-time

We study the inflationary primordial perturbations in $\kappa$-Minkowski non-commutative space-time, a Lie-algebraic type deformation of canonical space-time motivated by quantum gravity scenarios. Employing the $\kappa$-deformed star product formalism, we construct the bilinear action for curvature perturbations and derive the $\kappa$-deformed Mukhanov-Sasaki equation and obtain the perturbative solutions. Further, we compute the primordial power spectrum and spectral index, showing that the leading order corrections to the power spectrum induces scale-dependent term proportional to $(\ln k)^2$. The spectral index also exhibits an explicit $\ln k$ dependence, which persists even when the slow-roll parameters are constant. We also perform a Bayesian MCMC analysis using ACT DR6 data and constrain the $\kappa$-deformation length scale to $\lambda=6.32^{+6.00}_{-4.30}\times10^{-30}m$ at $1\sigma$ CL, approximately four orders of magnitude larger than the Planck scale, demonstrating that the $\kappa$-deformed space-time offers a potential window into quantum gravity phenomenology through precision cosmology.

gr-qc↗

arXiv2026

Thermodynamics and phase transitions of $\kappa$-deformed Schwarzschild-AdS black holes

We investigate the thermodynamics of the Schwarzschild-AdS black hole in the framework of $\kappa$-deformed non-commutative geometry by constructing an effective $\kappa$-deformed Schwarzschild-AdS metric from the $\kappa$-deformed Newtonian potential. In the extended phase space, we derive a modified first law and the corresponding Smarr relation by treating the $\kappa$-deformation parameter as an additional thermodynamic variable and identifying its conjugate potential. Our analysis shows that $\kappa$-deformation induces critical behaviour and phase transitions in an uncharged Schwarzschild-AdS black hole, with a critical ratio $P_c v_c/T_c \simeq 0.370$ that is independent of the deformation parameter and close to the Van der Waals value.

gr-qc↗

arXiv2025

Thermal Casimir effect in $\kappa$-Minkowski space-time

We study the finite temperature Casimir effect for parallel plates in the $\kappa$-Minkowski space-time. Using the Matsubara formalism and imposing the Dirichlet boundary conditions on a massless $\kappa$-scalar field, we compute the $\kappa$-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 $\kappa$-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 $\kappa$-Minkowski space-time.

hep-th↗

arXiv2025

Search for possible signals of space-time non-commutativity from ACT DR6

The non-commutative geometry offers an effective framework for describing physics at the Planck scale, incorporating generic quantum-gravitational effects through an intrinsic minimal length and the $\kappa$-deformed space-time stands out as a particularly well-developed model based on a Lie-algebraic type non-commutative space-time structure. We investigate the inflationary paradigm and the associated primordial perturbations within the framework of $\kappa$-deformed non-commutative space-time. By constructing a scalar field theory invariant under the $\kappa$-Poincar\'e algebra, we derive the deformed oscillator algebra for the field modes of the primordial perturbations resulting in the non-trivial scale dependent modification of both the scalar and tensor power spectra. Further, we compute the corresponding $\kappa$-deformed corrections to the scalar spectral index and its running, finding that the $\kappa$-deformation naturally provides a higher value for spectral index which offers a potential resolution to the discrepancy between the values reported by PLANCK and ACT. Finally we perform a comprehensive Bayesian analysis using the latest ACT DR6 data, constraining the $\kappa$-deformed non-commutative length scale to $\lambda=2.17^{+2.33}_{-1.53}\times 10^{-30}m$ at the $1\sigma$ confidence level, suggesting the precision cosmology as a powerful probe of quantum gravity phenomenology.

hep-th↗

arXiv2025

Entropic force and bouncing behaviour in $\kappa$-Minkowski space-time

We generalise the entropic force description of gravity into $\kappa$-Minkowski space-time and derive the $\kappa$-deformed corrections to the Newton's gravitational force. Using this we show the appearance of logarithmic correction as the first order $\kappa$-deformed correction term to Bekenstein-Hawking entropy. Further we also derive the $\kappa$-deformed Friedmann equations and study the evolution of scale factor in $\kappa$-deformed space-time. Finally we show that the $\kappa$-deformation parameter avoids the initial singularity in early universe by providing a bounce behaviour for the case of spatially flat and closed universe.

gr-qc↗

arXiv2024

Unruh effect using Doppler shift method in DSR framework

We study the Unruh effect in doubly special relativity (DSR) framework by generalising the Doppler-shift method to DSR. For both the scalar and Dirac particles, we observe a deviation in the power spectrum of Unruh radiation from the standard Bose-Einstein and Fermi-Dirac distributions, respectively, due to the presence of the frame independent length scale of DSR. We further show that this deviation results in the modification of Unruh temperature which then depends non-linearly on the proper acceleration in DSR.

gr-qc↗

arXiv2023

$\kappa$-deformed power spectrum and modified Unruh temperature

In this paper, we study the power spectrum of the uniformly accelerating scalar field, obeying the $\kappa$-deformed Klein-Gordon equation. From this we obtain the $\kappa$-deformed corrections to the Unruh temperature, valid up to first order in the $\kappa$-deformation parameter $a$. We also show that in the small acceleration limit, this expression for the Unruh temperature in $\kappa$-deformed space-time is in exact agreement with the one derived from the $\kappa$-deformed uncertainty relation. Finally, we obtain an upper bound on the deformation parameter $a$.

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

Quantisation of Lorentz invariant scalar field theory in non-commutative space-time and its consequence

Quantisation of Lorentz invariant scalar field theory in Doplicher-Fredenhagen-Roberts (DFR) space-time, a Lorentz invariant, non-commutative space-time is studied. Absence of a unique Lagrangian in non-commutative space-time necessitates us to use an approach to quantisation that is based on the equations of motion alone. Using this we derive the equal time commutation relation between Doplicher-Fredenhagen-Roberts-Amorim (DFRA) scalar field and its conjugate, which has non-commutative dependent modifications, but the corresponding creation and annihilation operators obey usual algebra. We show that imposing the condition that the commutation relation between the field and its conjugate is same as that in the commutative space-time leads to a deformation of the algebra of quantised oscillators. Both these deformed commutation relations derived are valid to all orders in the non-commutative parameter. By analysing the first non-vanishing terms which are $θ^3$ order, we show that the deformed commutaton relations scale as $1/λ^4$, where $λ$ is the length scale set by the non-commutativity of the space-time. We also derive the conserved currents for DFRA scalar field. Further, we analyse the effects of non-commutativity on Unruh effect by analysing a detector coupled to the DFRA scalar field, showing that the Unruh temperature is not modified but the thermal radiation seen by the accelerated observer gets correction due to the non-commutativity of space-time.

hep-th↗

arXiv2020

Maximal acceleration in non-commutative space-time and its implications

In this paper, we derive the non-commutative corrections to the maximal acceleration of a massive particle. Using the eight-dimensional kappa-deformed phase-space metric, we obtain the kappa-deformed maximal acceleration, valid up to first order in the deformation parameter. We then derive the kappa-deformed geodesic equation and obtain its Newtonian limit and from this obtain a bound on the deformation parameter. After re-expressing the kappa-deformed Schwarzschild metric in terms of maximal acceleration, we analyse the motion of a particle in this space-time, and also study the modifications to Hawking radiation. We also derive the kappa-deformed corrections to maximal acceleration using kappa-deformed generalised uncertainty principle.

hep-th↗

arXiv2020

Quantisation of $κ$-deformed Dirac equation

In this paper, we study the quantisation of Dirac field theory in the $κ$-deformed space-time. We adopt a quantisation method that uses only equations of motion for quantising the field. Starting from $κ$-deformed Dirac equation, valid up to first order in the deformation parameter $a$, we derive deformed unequal time anti-commutation relation between deformed field and its adjoint, leading to undeformed oscillator algebra. Exploiting the freedom of imposing a deformed unequal time anti-commutation relations between $κ$-deformed spinor and its adjoint, we also derive a deformed oscillator algebra. We show that deformed number operator is the conserved charge corresponding to global phase transformation symmetry. We construct the $κ$-deformed conserved currents, valid up to first order in $a$, corresponding to parity and time-reversal symmetries of $κ$-deformed Dirac equation also. We show that these conserved currents and charges have a mass-dependent correction, valid up to first order in $a$. This novel feature is expected to have experimental significance in particle physics. We also show that it is not possible to construct a conserved current associated with charge conjugation, showing that the Dirac particle and its anti-particle satisfy different equations in $κ$-space-time.

hep-th↗

arXiv2020

Emergence of maximal acceleration from non-commutativity of space-time

In this paper, we show that the causally connected $4$-dimensional line element of the $\kappa$-deformed Minkowski space-time induces an upper cut-off on the proper acceleration and derive this maximal acceleration, valid up to first order in the deformation parameter. We find a contribution to maximal acceleration which is independent of $\hbar$ and thus signals effect of the non-commutativity alone. We also construct the $\kappa$-deformed geodesic equation and obtain its $\kappa$-deformed Newtonian limit, valid up to first order in deformation parameter. Using this, we constrain non-commutative parameters present in the expression for maximal acceleration. We analyse different limits of the maximal acceleration and also discuss its implication to maximal temperature. We also obtain a bound on the deformation parameter.

hep-th↗

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↗

arXiv2019

Quantisation of Klein-Gordon field in $κ$ space-time: deformed oscillators and Unruh effect

In this paper we study the quantisation of scalar field theory in $κ$-deformed space-time. Using a quantisation scheme that use only field equations, we derive the quantisation rules for deformed scalar theory, starting from the $κ$-deformed equations of motion. This scheme allows two choices; (i)a deformed commutation relation between the field and its conjugate which leads to usual oscillator algebra, (ii) an undeformed commutation relation between field and its conjugate leading to a deformed oscillator algebra. This deformed oscillator algebra is used to derive modification to Unruh effect in the $κ$-space-time.

hep-th↗

arXiv2019

Superdense star in a space-time with minimal length

In this paper we generalise core-envelope model of superdense star to a non-commutative space-time and study the modifications due to the existence of a minimal length, predicted by various approaches to quantum gravity. We first derive Einstein's field equation in $κ$-deformed space-time and use this to set up non-commutative version of core-envelope model describing superdense stars. We derive $κ$-deformed law of density variation, valid up to first order approximation in deformation parameter and obtain radial and tangential pressures in $κ$-deformed space-time. We also derive $κ$-deformed strong energy conditions and obtain a bound on the deformation parameter.

gr-qc↗