arXiv subjects

Sunandan Gangopadhyay

Publications and source records attributed to Sunandan Gangopadhyay.

At least 109 records · Page 6Linked to original sources

arXiv2021

Holographic insulator/superconductor phase transition by matching method and thermodynamic geometry

In this work, we have analytically analyzed the insulator/superconductor phase transition in the presence of a 5-dimensional $AdS$ soliton background using matching method and thermodynamic geometry approach. We have first employed the matching method to obtain the critical chemical potential. We then move on to investigate the free energy and thermodynamic geometry of this model in 3+1 dimensions. This investigation of the thermodynamic geometry leads to the critical chemical potential of the system from the condition of the divergence of the scalar curvature. We have then compared the value of the critical chemical potential $μ_{c}$ in dimension $d=5$ obtained from these two different methods, namely, the matching method and the thermodynamic geometry procedure. We have also obtained an expression for the condensation operator using the matching method. Our findings agree very well with the numerical findings in the literature.

hep-th↗

arXiv2021

Cosmology with modified continuity equation in asymptotically safe gravity

We study FLRW cosmology, taking into account quantum gravitational corrections in the formalism of the exact renormalization group flow of the effective action for gravity. We calculate the quantum corrected scale factor, energy density, and entropy production at late times, taking different cut-off functions. Our approach differs from previous ones in the way energy-momentum conservation is imposed -- we include the running Newton constant $G(k)$ in the definition of energy-momentum tensor, keeping in mind the covariant conservation identity of the Einstein tensor. The quantum corrections obtained in this approach are different from what are found by letting the conservation equation remain the same as for a scale-independent Newton constant. We also find that for a specific choice of the cut-off scale, the quantum corrected behaviour of the Newton constant and the cosmological constant lead to a bouncing emergent universe solution.

gr-qc↗

arXiv2021

Investigation of circular geodesics in a rotating charged black hole in the presence of perfect fluid dark matter

In this work we have obtained a charged black hole solution in the presence of perfect fluid dark matter (PFDM) and discuss its energy conditions. The metric corresponding to the rotating avatar of this black hole solution is obtained by incorporating the Newman-Janis algorithm. We then compute two types of circular geodesics, namely, the null geodesics and time-like geodesics for this rotating spacetime geometry. For the case of time-like geodesics, we consider both neutral as well as charged massive particles. The effective potentials of the corresponding circular geodesics has also been studied. We then present our results by graphically representing the collective effects of the black hole parameters, namely, the charge of the black hole ($Q$), spin parameter ($a$) and the PFDM parameter ($α$) on the energy ($E$), angular momentum ($L$) and effective potential ($V_{eff}$) of the concerned particle. Finally, we discuss the Penrose process in order to study the negative energy particles having possible existence within the ergosphere, and which in turn leads to the energy gain of the emitted particle.

gr-qc↗

arXiv2020

Generalized uncertainty principle in resonant detectors of gravitational waves

With the direct detection of gravitational waves by advanced LIGO detector, a new "window" to quantum gravity phenomenology has been opened. At present, these detectors achieve the sensitivity to detect the length variation ($δL$), $\mathcal{O} \approx 10^{-17}-10^{-21}$ meter. Recently a more stringent upperbound on the dimensionless parameter $β_0$, bearing the effect of generalized uncertainty principle has been given which corresponds to the intermediate length scale $l_{im}= \sqrt{β_0} l_{pl} \sim 10^{-23} m$. Hence the flavour of the generalized uncertainty principle can be realised by observing the response of the vibrations of phonon modes in such resonant detectors in the near future. In this paper, therefore, we calculate the resonant frequencies and transition rates induced by the incoming gravitational waves on these detectors in the generalized uncertainty principle framework. It is observed that the effects of the generalized uncertainty principle bears its signature in both the time independent and dependent part of the gravitational wave-harmonic oscillator Hamiltonian. We also make an upper bound estimate of the GUP parameter.

gr-qc↗

arXiv2020

Generalized entanglement temperature and entanglement Smarr relation

We observe that in presence of excitation, a thermodynamic Smarr like relation corresponding to a generalized entanglement temperature ($T_g$) can be holographically obtained for the entanglement entropy of a subsystem. Such a relation emerges naturally by demanding that the generalized entanglement temperature produces the exact Hawking temperature as the leading term in the IR limit ($l\rightarrow \infty$). Remarkably, this relation has the same form as the Smarr relation in black hole thermodynamics. We demonstrate this for three spacetime geometries, namely, a background with a nonconformal factor, a hyperscaling violating geometry background, and a charged black hole background which corresponds to a field theory with a finite chemical potential.

hep-th↗

arXiv2020

Universal Pieces of Holographic Entanglement Entropy and Holographic Subregion Complexity

We propose that the definition of holographic subregion complexity (HSC) needs a slight modification for supergravity solutions with warped anti-de Sitter (AdS) factors. Such warp factors can arise due to the nontrivial dilaton profile, for example, in $AdS_6$ solutions of type IIA supergravity. This modified definition ensures that the universal piece of the HSC is proportional to that of the holographic entanglement entropy, as is the case for supergravity solutions without warp factors. This also means that the leading behaviour at large $N$ is the same for both these quantities, as we show for some well-known supergravity solutions (with and without warp factors) in various dimensions. We also show that this relation between the universal pieces suggests "universal" relations between field theoretical analogue of HSC and the sphere partition function or Weyl $a$-anomaly in odd or even dimensions, respectively.

hep-th↗

arXiv2020

Exact solutions of a damped harmonic oscillator in a time dependent noncommutative space

In this paper we have obtained the exact eigenstates of a two dimensional damped harmonic oscillator in time dependent noncommutative space. It has been observed that for some specific choices of the damping factor and the time dependent frequency of the oscillator, there exists interesting solutions of the time dependent noncommutative parameters following from the solutions of the Ermakov-Pinney equation. Further, these solutions enable us to get exact analytic forms for the phase which relates the eigenstates of the Hamiltonian with the eigenstates of the Lewis invariant. We then obtain expressions for the matrix elements of the coordinate operators raised to a finite arbitrary power. From these general results we then compute the expectation value of the Hamiltonian. The expectation values of the energy are found to vary with time for different solutions of the Ermakov-Pinney equation corresponding to different choices of the damping factor and the time dependent frequency of the oscillator.

quant-ph↗

arXiv2020

Holographic computation of Wilson loops in a background with broken conformal invariance and finite chemical potential

In this paper, we follow a `bottom-up' AdS/QCD approach to holographically probe the dynamics of a moving $q\bar{q}$ pair inside a strongly coupled plasma at the boundary. We consider a deformed AdS-Reissner Nordström metric in the bulk in order to introduce nonconformality and finite quark density in the dual field theory. By boosting the gravity solution in a specific direction we consider two extreme cases of orientation, parallel and perpendicular, for the Wilson loop which in turn fixes the relative position of the $q\bar{q}$ pair with respect to the direction of boost in the plasma. By utilizing this set-up, we holographically compute the vacuum expectation value of the time-like Wilson loop in order to obtain real part of the $q\bar{q}$ potential and the effects of nonconformality (deformation parameter $c$), chemical potential $μ$ and rapidity $β$ are observed on this potential. We then compute the in-medium energy loss of the moving parton (jet quenching parameter $q_m$) by setting $β\rightarrow\infty$ which in turn makes the Wilson loop light-like. We also use the jet quenching as an order parameter to probe the strongly-coupled domain of the dual field theory. Finally, we compute the imaginary part of the $q\bar{q}$ potential ($\mathrm{Im}(V_{q\bar{q}})$) by considering the thermal fluctuation (arbitrary long wavelength) of the string world-sheet. It is observed that for fixed values of the chemical potential and rapidity, increase in the nonconformality parameter leads to an increase in the real and imaginary potentials as well as the jet quenching parameter.

hep-th↗

arXiv2020

Phase transitions in Born-Infeld AdS black holes in D-dimensions

In this paper, we have investigated phase transitions in arbitrary spacetime dimensions for Born-Infeld AdS black holes. The phase transition points are characterised from the divergence of heat capacity of the black hole. Two well established techniques, namely, the Ehrenfest scheme and the Ruppeiner state space geometry approach are used to identify the order of phase transition the black hole undergoes. It is observed that the results obtained from these two methods agree with each other. Our analysis reveals that the phase transition is of second order. It is also observed from the variation of the heat capacity with entropy that the small unstable black hole phase becomes more and more stable with increase in the spacetime dimensions. We speculate that this dependence of the stability of the black hole on the spacetime dimension can put an upper limit to the dimension of spacetime from the physical condition of the improbability of the formation of a small stable black hole. We have also derived a Smarr relation in D-spacetime dimensions using scaling arguments and first law of black hole thermodynamics which includes the cosmological constant and the Born-Infeld parameters as thermodynamic variables.

hep-th↗

arXiv2020

Holographic information theoretic quantities for Lifshitz black hole

In this paper, we have investigated the holographic entanglement entropy for a linear subsystem in a $3+1$-dimensional Lifshitz black hole. The entanglement entropy has been analysed in both the infra-red and ultra-violet limits, and has also been computed in the near horizon approximation. The notion of a generalized temperature in terms of the renormalized entanglement entropy has been introduced. This also leads to a generalized thermodynamics like law $E=T_g S_{REE}$. The generalized temperature has been defined in such a way that it reduces to the Hawking temperature in the infra-red limit. We have then computed the holographic subregion complexity. Then the Fisher information metric and the fidelity susceptibility for the same linear subsystem have also been computed using the bulk dual prescriptions. It has been observed that the two metrics are not related to each other.

hep-th↗

arXiv2020

Cosmology of Bianchi type-I metric using renormalization group approach for quantum gravity

We study the anisotropic Bianchi type-I cosmological model at late times, taking into account quantum gravitational corrections in the formalism of the exact renormalization group flow of the effective average action for gravity. The cosmological evolution equations are derived by including the scale dependence of Newton's constant $G$ and cosmological constant $Λ$. We have considered the solutions of the flow equations for $G$ and $Λ$ at next to leading order in the infrared cutoff scale. Using these scale dependent $G$ and $Λ$ in Einstein equations for the Bianchi-I model, we obtain the scale factors in different directions. It is shown that the scale factors eventually evolve into FLRW universe for known matter like radiation. However, for dust and stiff matter we find that the universe need not evolve to the FLRW cosmology in general, but can also show Kasner type behaviour.

gr-qc↗

arXiv2020

Effect of magnetic field on holographic insulator/superconductor phase transition in higher dimensional Gauss-Bonnet gravity

In this paper, we have investigated the effect of magnetic field numerically as well as analytically for holographic insulator/superconductor phase transition in higher dimensional Gauss-Bonnet gravity. First we have analysed the critical phenomena with magnetic field using two different numerical methods, namely, quasinormal modes method and the shooting method. Then we have carried out our calculation analytically using the St$\ddot{u}$rm-Liouville eigenvalue method. The methods show that marginally stable modes emerge at critical values of the chemical potential and the magnetic field satisfying the relation $Λ^2\equivμ^2-B$. We observe that the value of the chemical potential and hence the value of $Λ$ increases with higher values of the Gauss-Bonnet parameter and dimension of spacetime for a fixed mass of the scalar field. This clearly indicates that the phase transition from insulator to superconductor becomes difficult in the presence of the magnetic field for higher values of the Gauss-Bonnet parameter and dimension of spacetime. Our analytic results are in very good agreement with our numerical results.

hep-th↗

arXiv2019

$p$-wave holographic superconductors with massive vector condensate in Born-Infeld electrodynamics

In this paper, we have studied the effect of Born-Infeld electrodynamics in holographic $p$-wave superconductors with massive vector condensation. We have analysed this model in the probe limit using a variational method known as the Stürm-Liouville eigenvalue approach. For this $p$-wave holographic superconductor model, we have calculated the critical temperature $T_{c}$ as well as the value of the condensation operator for two different choices of $m^{2}$. We have also pointed out the similarities and dissimilarities between this model for $m^{2} = 0$ and $p$-wave holographic superconductor model constructed out of Einstein-Yang-Mills theory. We have then computed the conductivity of these holographic superconductor models using a self-consistent approach and have shown that the DC conductivity diverges.

hep-th↗

arXiv2019

Meissner effect in holographic superconductors with Dirac-Born-Infeld electrodynamics

In this paper, we have investigated the Meissner effect of holographic superconductors in the presence of Dirac-Born-Infeld electrodynamics. The matching method is applied to obtain the critical magnetic field and the critical temperature. The critical magnetic field obtained from this investigation shows the effects of the DBI parameter $b$ and differs from that obtained from Born electrodynamics because of the extra $\vec{E}.\vec{B}$ term in the Dirac-Born-Infeld theory. It is observed that the critical magnetic field increases in Dirac-Born-Infeld theory compared to that in the Born theory.

hep-th↗

arXiv2019

Holographic entanglement entropy and generalized entanglement temperature

In this work we study the flow of holographic entanglement entropy in dimensions $d \geq 3$ in the gauge/gravity duality set up. We observe that a generalized entanglement temperature $T_g$ can be defined which gives the Hawking temperature $T_H$ in the infrared region and leads to a generalized thermodynamics like law $E= \left(\frac{d-1}{d}\right)T_g~S_{REE}$, which becomes an exact relation in the entire region of the subsystem size $l$, including both the infrared ($l\rightarrow\infty$) as well as the ultraviolet ($l\rightarrow 0$) regions. Furthermore, in the IR limit, $T_g$ produces the Hawking temperature $T_H$ along with some correction terms which bears the signature of short distance correlations along the entangling surface. Moreover, for $d\geq 3$, the IR limit of the renormalized holographic entanglement entropy gives the thermal entropy of the black hole as the leading term, however, does not have a logarithmic correction to the leading term unlike the BTZ black hole ($d=2$) case. The generalized entanglement temperature $T_g$ also firmly captures the quantum mechanical to thermal crossover in the dual field theory at a critical value $l_c$ of the subsystem size in the boundary which we graphically represent for $AdS_{3+1}$ and $AdS_{4+1}$ black holes. We observe that this critical value $l_c$ where the crossover takes place decreases with increase in the dimension of the spacetime.

hep-th↗

arXiv2019

Photon velocity, power spectrum in Unruh effect with modified dispersion relation

In this paper we propose a new form of generalized uncertainty principle which involves both a linear as well as a quadratic term in the momentum. From this we have obtained the corresponding modified dispersion relation which is compared with the corresponding relation in rainbow gravity. The new form of the generalized uncertainty principle reduces to the known forms in appropriate limits. We then calculate the modified velocity of photons and we find that it is energy dependent, allowing therefore for a superluminal propagation. We then derive the $1+1$-dimensional Klein-Gordon equation taking into account the effects of the modified dispersion relation. The positive frequency mode solution of this equation is then used to calculate the power spectrum arising due to the Unruh effect. The result shows that the power spectrum depends on the energy of the particle owing its origin to the presence of the generalized uncertainty principle. Our results capture the effects of both the simplest form as well as the linear form of the generalized uncertainty principle and also points out an error in the result of the power spectrum up to first order in the generalized uncertainty principle parameter existing in the literature.

physics.gen-ph↗

arXiv2019

Shadow of charged black holes in Gauss-Bonnet gravity

In this paper, we investigate the effect of higher curvature corrections from Gauss-Bonnet gravity on the shadow of charged black holes in both $AdS$ and Minkowski spacetimes. The null geodesic equations are computed in $d=5$ spacetime dimensions by using the directions of symmetries and Hamilton-Jacobi equation. With the null geodesics in hand, we then proceed to evaluate the celestial coordinates ($α, β$) and the radius $R_s$ of the black hole shadow and represent it graphically. The effects of charge $Q$ of the black hole and the Gauss-Bonnet parameter $γ$ on the radius of the shadow $R_s$ is studied in detail. It is observed that the Gauss-Bonnet parameter $γ$ affects the radius of the black hole shadow $R_s$ differently for the $AdS$ black hole spacetime in comparison to the black hole spacetime which is asymptotically flat. In particular the radius of the black hole shadow increases with increase in the Gauss-Bonnet parameter in case of the $AdS$ black hole spacetime and decreases in case of the asymptotically flat black hole spacetime. We then introduce a plasma background in order to observe the change in the silhouette of the black hole shadow due to a change in the refractive index of the plasma medium. Finally, we study the effect of the Gauss-Bonnet parameter $γ$ on the energy emission rate of the black hole which depends on the black hole shadow radius and represent the results graphically.

gr-qc↗

arXiv2019

Signatures of noncommutativity in bar detectors of gravitational waves

The comparison between the noncommutative length scale $\sqrtθ$ and the length variation $δL=h L$, detected in the GW detectors indicate that there is a strong possibility to detect the noncommutative structure of space in the GW detector set up. We therefore explore how the response of a bar detector gets affected due to the presence of noncommutative structure of space keeping terms upto second order in the gravitational wave perturbation ($h$) in the Hamiltonian. Interestingly, the second order term in $h$ shows a transition between the ground state and one of the perturbed second excited states that was absent when the calculation was restricted only to first order in $h$.

gr-qc↗