arXiv subjects

Malay K. Nandy

Publications and source records attributed to Malay K. Nandy.

36 records · Page 2Linked to original sources

arXiv2024

Nonlinear Dynamics of the Inner Horizon in Reissner-Nordström Black Holes: Insights into Mass Inflation

The well-known instability of the inner horizon of a Reissner-Nordström black hole, first suggested by Simpson and Penrose, although studied extensively, has remained illusive so far as several studies led to varied conclusions about the dynamical nature of the inner horizon. In this work, we therefore focus upon the dynamic nature of the inner horizon in the course of mass inflation. We model this phenomenon with a massive chargeless scalar field minimally coupled with the Reissner-Nordström spacetime. Employing the Einstein-Maxwell field equation coupled with the Klein-Gordon equation, we obtain a nonlinear dynamical equation for the inner horizon coupled with the dynamics of the mass function and the scalar field. In the S-wave approximation, we develop a perturbative solution about the dynamic inner horizon and obtain an analytical solution as a polynomial of twelfth degree. Our detailed analysis shows that the inner horizon moves inward in the course of mass inflation. Higher the mass of the scalar field, faster are the shrinking rate of the inner horizon and the rate of mass inflation. Our solution for dynamic shrinking of the inner horizon suggests that a Reissner-Nordström spacetime tends towards a Schwarzschild-like geometry, in the infinite advanced time limit.

gr-qc↗

arXiv2024

Charged black holes in Eddington-inspired Born-Infeld gravity: An in-depth analysis of the structure of spacetime geometry

In this paper, we focus upon the behaviour of spacetime of charged black holes described by Eddington-inspired Born-Infeld (EiBI) gravity. With a static and spherically symmetric metric, we solve the ensuing field equations obtained from the EiBI-Maxwell action in the Palatini formalism. Consequently we carry out, for the first time, an in-depth analysis of the structure of spacetime geometry in several regions of the charged EiBI black hole. In particular, we consider the analytical behaviours of the metric coefficients and the Kretschmann scalar by probing their asymptotic nature {\em analytically} in different regions of the black hole spacetime, such as, near the center, in the intermediate region, and near the horizon, for both positive and negative EiBI coupling. These analyses give a thorough understanding of the nature of spacetime of EiBI-Maxwell black holes. In order to aide our understanding further, we solve the EiBI-Maxwell field equation numerically with different values of the parameters involved. We find close agreement between the analytical behaviours and those obtained from numerical integration of the EiBI-Maxwell field equation.

gr-qc↗

arXiv2024

Stability of charged scalar hair on a Reissner-Nordström black hole

The Israel-Carter theorem (also known as the "no-hair theorem") puts a restriction on the existence of parameters other than mass, electric charge, and angular momentum of a black hole. In this context, Bekenstein proposed no-hair theorems in various black hole models with neutral and electrically charged scalar fields. In this paper, we take the Einstein-Maxwell-charged scalar model with an electrically charged scalar field gauge-coupled to the Maxwell field surrounding a charged black hole with a static spherically symmetric metric. In particular, we consider a quadratic scalar potential without any higher order terms and we do not impose any restriction on the magnitude of the scalar charge with respect to the black hole charge. With this setting, we ascertain the validity of all energy conditions coupled with the causality condition, suggesting the possibility of existence of charged hairy solutions. Consequently, we obtain, by exact numerical integration, detailed solutions of the field equations that incorporate backreaction on the spacetime due to the presence of the charged scalar field. The solutions exhibit damped oscillatory behaviours for the charged scalar hair. We also find that the electric potential is a monotonic function of the radial coordinate, as required by electrodynamics. In order to ascertain the existence of our charged hairy solutions, we carry out dynamic stability analyses against time-dependant perturbations about the static solutions. For a definite conclusion, we employ two different methodologies. The first methodology involves a Sturm-Liouville equation, whereas the second methodology employs a Schrödinger-like equation, for the dynamic perturbations. We find that our solutions are stable against time-dependant perturbations by both methodologies, confirming the existence of the charged hairy solutions.

gr-qc↗

arXiv2024

Maximal mass of the neutron star with a deconfined quark core

The nature of equation of state for the matter in the neutron star plays an important role in determining its maximal mass. In addition, it must comply with the condition of causality. Noting that the central density of a maximally massive neutron star is well above the nuclear saturation density, a deconfined quark core in the central region is motivated in this paper. We analyze this scenario by employing the MIT bag model to represent the core region and one of the unified equations of state for the region outside the core. Such combination is found to solve the problem of causality violation. In each case of the combined equations of state, the radial profile of $ρr^2$ displays a peak and dominant contribution to the total mass of the star comes from the region around the peak value of $ρr^2$, whereas the contribution is small from the regions near the center and the surface. This peak occurs in the region of hadronic matter for the combinations considered in this paper. Importantly, we find that the position of the peak in $ρr^2$ is well-correlated with the maximal mass -- the highest value of $1.98\ M_\odot$ obtains for the case with the peak occurring farthest from the center. This gravitational threshold being obtained for a non-rotating neutron star, we expect the threshold to lie well above 2 $ M_\odot$ for a rapidly rotating neutron star, that may explain the existance of massive pulsars from recent astronomical observations.

astro-ph.HE↗

arXiv2024

Emergent spin and clock variable in Bianchi type-I quantum cosmology

We consider the Bianchi type-I model of the universe in the Wheeler-DeWitt quantization scheme with the matter degree of freedom represented by a scalar field. As a consequence, the quantum mechanical equation of the universe is obtained in the minisuperspace consisting of the Misner variables and the scalar field. Employing Dirac factorization, we find that the volume parameter makes a suitable choice for the clock variable whereas the matter clock leads to various inconsistencies. We further find that the minisuperspace orbital angular momentum operator does not commute with the Hamiltonian in the Dirac-type equation. We therefore find the missing part of the angular momentum whereby the total angular momentum commutes with the Hamiltonian. We interpret this missing part as the spin of the quantum universe during its early stage of evolution. The emergence of the three-component spin vector is owing to the presence of anisotropy in the Bianchi type-I model of the universe which is absent in the quantization of isotropic models.

gr-qc↗

arXiv2024

Mass Superinflation from Enhanced Cauchy Horizon Singularity in a Reissner-Nordström Black Hole

Ever since Penrose and Simpson contradicted Novikov's prediction that an infalling passenger would emerge into an asymptotically flat universe, there have been a continued interest in predicting the nature of singularity at the Cauchy horizon of a Reissner-Nordstrom blackhole. This prediction was first confirmed by Poisson and Israel using cross-stream of massless particles, suggesting the phenomenon of mass inflation. Ori however obtained a weaker singularity using a null shell of radiation. In this work, we consider a massive scalar field coupled to the Reissner-Nordstrom geometry and analyze the nature of singularity at the Cauchy horizon. To study the asymptotic behavior of the mass function and the scalar field near the Cauchy horizon, we perturbatively solve the coupled dynamical equations emplyoing the Adomian decomposition method. Our analysis shows that the mass function exhibits a very rapid and unbounded double-exponential growth, called herein mass superinflation, which is enormously stronger than previously obtained singularities. The scalar field is also found to undergo a very strong blueshift near the Cauchy horizon.

gr-qc↗

arXiv2023

Primordial reheating in $f(R)$ cosmology by spontaneous decay of scalarons

We employ a viable $f(R)$ gravity model capable of giving an inflationary phase in order to study the subsequent reheating phase due to particle creation at the expense of energy in the scalaron field. Since quantum mechanics is expected to play a dominant role in particle creation, we formulate a plausible scenario of reheating obeying Heisenberg's uncertainty principle that imposes constraints on the particles created in the configuration space. We show that, so long as the energy available in the scalaron field is sufficient to populate the entire configuration space, the energy density of the particles grows, attaining a maximum value giving an efficient reheating. Beyond this maximum, the available energy becomes insufficient to populate the entire configuration space leading to a declining energy density. We further find that there is a negligible growth of energy density in the inflationary phase that lasts for $\sim 10^7 \, t_{\rm P}$, although particles are constantly created in this phase. The subsequent reheating phase spans for $\sim10^{11} \, t_{\rm P}$ and it begins with a well-defined preheating stage lasting for $\sim 10^{5} \, t_{\rm P}$, making a cross-over to a thermilization regime. The temperature at the beginning of the thermilization is found to be $T_{\rm th}\sim 10^{12}$ GeV, whereas the reheating temperature is estimated as $T_{r}\sim10^{13}$ GeV. Importantly, these estimates follow from a single parameter, the scalaron mass, $M\sim10^{-5} \, M_{\rm P}$.

gr-qc↗

arXiv2020

Stellar structure of quark stars in a modified Starobinsky gravity

We propose a form of gravity-matter interaction given by $ωRT$ in the framework of $f(R,T)$ gravity and examine the effect of such interaction in spherically symmetric compact stars. Treating the gravity-matter coupling as a perturbative term on the background of Starobinsky gravity, we develop a perturbation theory for equilibrium configurations. For illustration, we take the case of quark stars and explore their various stellar properties. We find that the gravity-matter coupling causes an increase in the stable maximal mass which is relevant for recent observations on binary pulsars.

gr-qc↗

arXiv2019

Prospect of Chandrasekhar's limit against modified dispersion relation

Newtonian gravity predicts the existence of white dwarfs with masses far exceeding the Chandrasekhar limit when the equation of state of the degenerate electron gas incorporates the effect of quantum spacetime fluctuations (via a modified dispersion relation) even when the strength of the fluctuations is taken to be very small. In this paper, we show that this Newtonian "super-stability" does not hold true when the gravity is treated in the general relativistic framework. Employing dynamical instability analysis, we find that the Chandrasekhar limit can be reassured even for a range of high strengths of quantum spacetime fluctuations with the onset density for gravitational collapse practically remaining unaffected.

gr-qc↗

arXiv2017

Effect of minimal length uncertainty on the mass-radius relation of white dwarfs

Generalized uncertainty relation that carries the imprint of quantum gravity introduces a minimal length scale into the description of space-time. It effectively changes the invariant measure of the phase space through a factor $(1+β\mathbf{p}^2)^{-3}$ so that the equation of state for an electron gas undergoes a significant modification from the ideal case. It has been shown in the literature (Rashidi 2016) that the ideal Chandrasekhar limit ceases to exist when the modified equation of state due to the generalized uncertainty is taken into account. To assess the situation in a more complete fashion, we analyze in detail the mass-radius relation of Newtonian white dwarfs whose hydrostatic equilibria are governed by the equation of state of the degenerate relativistic electron gas subjected to the generalized uncertainty principle. As the constraint of minimal length imposes a severe restriction on the availability of high momentum states, it is speculated that the central Fermi momentum cannot have values arbitrarily higher than $p_{\rm max}\simβ^{-1/2}$. When this restriction is imposed, it is found that the system approaches limiting mass values higher than the Chandrasekhar mass upon decreasing the parameter $β$ to a value given by a legitimate upper bound. Instead, when the more realistic restriction due to inverse $β$-decay is considered, it is found that the mass and radius approach the values close to $1.45$ M$_{\odot}$ and $600$ km near the legitimate upper bound for the parameter $β$. On the other hand, when $β$ is decreased sufficiently from the legitimate upper bound, the mass and radius are found to be approximately $1.46$ M$_{\odot}$ and $650$ km near the neutronization threshold.

gr-qc↗

arXiv2017

Renormalized cumulants and velocity derivative skewness in Kolmogorov turbulence

We apply a renormalized perturbative scheme on the Navier-Stokes equation for an incompressible isotropic turbulent velocity field. This allows us to obtain the renormalized expressions for second- and third-order cumulants of the velocity derivative directly from the corresponding Feynman diagrams. The resulting expressions are integrated numerically by excluding and including the dissipation range assuming Kolmogorov and Pao's phenomenological expressions for the energy spectrum. The ensuing values for skewness are found to be $S=-0.647$ (when the dissipation range is excluded) and $\mathcal{S}=-0.682$ (when the dissipation is included). These estimated values are compared with various experimental, numerical, and theoretical results.

cond-mat.stat-mech↗

arXiv2017

General Relativistic Calculations for White Dwarf Stars

The mass-radius relations for white dwarf stars are investigated by solving the Newtonian as well as Tolman-Oppenheimer-Volkoff (TOV) equations for hydrostatic equilibrium assuming the electron gas to be non-interacting. We find that the Newtonian limiting mass of $1.4562M_\odot$ is modified to $1.4166M_\odot$ in the general relativistic case for $^4_2$He (and $^{12}_{\ 6}$C) white dwarf stars. Using the same general relativistic treatment, the critical mass for $^{56}_{26}$Fe white dwarf is obtained as $1.2230M_\odot$. In addition, departure from the ideal degenerate equation of state (EoS) is accounted for by considering Salpeter's EoS along with the TOV equations yielding slightly lower values for the critical masses, namely $1.4081M_{\odot}$ for $^4_2$He, $1.3916M_{\odot}$ for $^{12}_{\ 6}$C and $1.1565M_{\odot}$ for $^{56}_{26}$Fe white dwarfs. We also compare the critical densities for gravitational instability with the neutronization threshold densities to find that $^4_2$He and $^{12}_{\ 6}$C white dwarf stars are stable against neutronization with the critical values of $1.4081M_\odot$ and $1.3916M_{\odot}$, respectively. However the critical masses for $^{16}_{\ 8}$O, $^{20}_{10}$Ne, $^{24}_{12}$Mg, $^{28}_{14}$Si, $^{32}_{16}$S and $^{56}_{26}$Fe white dwarf stars are lower due to neutronization. Corresponding to their central densities for neutronization thresholds, we obtain their maximum stable masses due to neutronization by solving the TOV equation coupled with the Salpeter EoS.

astro-ph.SR↗

arXiv2016

Steady-state skewness and kurtosis from renormalized cumulants in $(2+1)$-dimensional stochastic surface growth

The phenomenon of stochastic growth of a surface on a two-dimensional substrate occurs in Nature in a variety of circumstances and its statistical characterization requires the study of higher order cumulants. Here, we consider the statistical cumulants of height fluctuations governed by the $(2+1)$-dimensional KPZ equation for flat geometry. We follow a diagrammatic scheme to derive the expressions for renormalized cumulants up to fourth order in the stationary state. Assuming a value for the roughness exponent from reliable numerical predictions, we calculate the second, third and fourth cumulants, yielding skewness $S=0.2879$ and kurtosis $Q=0.1995$. These values agree well with the available numerical estimations.

cond-mat.stat-mech↗

arXiv2016

Reply to Comment on Nonlocal quartic interactions and universality classes in perovskite manganites

Comment [arXiv:cond-mat.stat.mech., 1602.02087v1 (2016)] has raised questions claiming that the nonlocal model Hamiltonian presented in [Phys. Rev. E 92, 012123 (2015)] is equivalent to the standard (short-ranged) Φ^4 theory. These claims are based on a low momentum expansion of the interaction vertex that cannot be applied to the vertex factors containing both low and high momenta inside the loop-integrals. Elaborating upon the important steps of the momentum shell decimation scheme, employed in the renormalization-group calculation, we explicitly show the interplay of internal (high) and external (low) momenta determining the loop integrals for self-energy and vertex functions giving rise to corrections (to the bare parameters) different from those of the standard (short-ranged) Φ^4 theory. Employing explicit mathematical arguments, we show that this difference persists when the range of interaction is assumed to be long (short) ranged with respect to the lattice constant (correlation-length), yielding the critical exponents as given in the original paper.

cond-mat.stat-mech↗

arXiv2015

A Renormalization Scheme and Skewness of Height Fluctuations in $(1+1)$-dimensional VLDS Dynamics

We study the $(1+1)$-dimensional Villain, Lai, and Das Sarma (VLDS) equation driven by a Gaussian white noise and implement a renormalization scheme without rescaling at one-loop order. Using a diagrammatic method, we calculate the renormalized second and third moments in the large-scale and long-time limits. The ensuing skewness value is $S=-0.0441$. This (negative) value is consistent with the numerical prediction of Das Sarma \emph{et al.} [Phys. Rev. E {\bf 53} 359 (1996)].

cond-mat.stat-mech↗

arXiv2015

Hyperskewness of $(1+1)$-dimensional KPZ Height Fluctuations

We evaluate the fifth order normalized cumulant, known as hyperskewness, of height fluctuations dictated by the $(1+1)$-dimensional KPZ equation for the stochastic growth of a surface on a flat geometry in the stationary state. We follow a diagrammatic approach and invoke a renormalization scheme to calculate the fifth cumulant given by a connected loop diagram. This, together with the result for the second cumulant, leads to the hyperskewness value $\widetilde{S} = 0.0835$.

cond-mat.stat-mech↗

arXiv2015

Kurtosis of height fluctuations in $(1+1)$ dimensional KPZ Dynamics

We study the fourth order normalized cumulant of height fluctuations governed by $1+1$ dimensional Kardar-Parisi-Zhang (KPZ) equation for a growing surface. Following a diagrammatic renormalization scheme, we evaluate the kurtosis $Q$ from the connected diagrams leading to the value $Q=0.1523$ in the large-scale long-time limit.

cond-mat.stat-mech↗

arXiv2015

Skewness in (1+1)-dimensional Kardar-Parisi-Zhang-type growth

We use the $(1+1)$-dimensional Kardar-Parisi-Zhang equation driven by a Gaussian white noise and employ the dynamic renormalization-group of Yakhot and Orszag without rescaling [J.~Sci.\ Comput.~{\bf 1}, 3 (1986)]. Hence we calculate the second and third order moments of height distribution using the diagrammatic method in the large scale and long time limits. The moments so calculated lead to the value $S=0.3237$ for the skewness. This value is comparable with numerical and experimental estimates.

cond-mat.stat-mech↗