arXiv subjects

Rajesh Karmakar

Publications and source records attributed to Rajesh Karmakar.

At least 19 recordsLinked to original sources

arXiv2026

Analytical solution of traversable wormholes in the presence of positive cosmological constant

The construction of traversable wormholes with a cosmological constant, $Λ$, introduces significant challenges and leads to non-trivial modifications of the spacetime geometry. In this work, we obtain an analytical solution describing a locally traversable wormhole for $Λ>0$ following a perturbative approach. Starting from the Ellis-Bronnikov wormhole geometry, we derive the metric deformation induced by the cosmological constant at linear order, assuming $Λr^2_0\ll 1$, where $r_0$ represents the throat of the Ellis-Bronnikov wormhole. We further identify the radial domain of validity of the perturbative solution, which is restricted to $r\ll\sqrt{3/Λ}$. Within this domain, we find that the Ellis-Bronnikov wormhole is modified by the cosmological constant; interestingly, the shape function takes a de Sitter-like form. Nevertheless, we verify that the flare-out condition holds at the deformed throat and find a violation of the null energy condition in its vicinity, as required for traversable WHs. Traversability is further analyzed by evaluating tidal forces and deriving constraints on the velocity required for safe human passage. Additionally, we discuss the possibility of constructing a global extension by matching the perturbative wormhole solution to a Schwarzschild-de Sitter exterior spacetime. Given the recent advances in the observational study of astrophysical compact objects, together with a variety of astrophysical and cosmological observations indicating the existence of a positive cosmological constant, the analytical solution presented here may be of considerable phenomenological interest.

gr-qc↗

arXiv2026

Canonical quantization of massive vector field in Schwarzschild black hole background

We perform a first-principles canonical quantization of a massive vector field, often referred to as the Proca field, in a Schwarzschild spacetime background. While scalar, fermionic, and electromagnetic fields are well studied in this context, the Proca field requires a more nuanced treatment because of the physical nature of the longitudinal polarization mode and the constrained dynamics of the field variables. By implementing the Dirac bracket formalism to treat the constraints inherent in the Proca action, we derive a consistent framework for the commutator algebra of creation and annihilation operators. Following this construction, we define the usual Boulware, Unruh, and Hartle-Hawking vacua. Using the Unruh vacuum, we derive and analyze the Hawking spectrum of the Proca field. Furthermore, we numerically evaluate the Proca condensate constructed from the two-point correlation function $\langle A_μ(x) A_ν(x') \rangle$, defined on all three vacuum states. We find that the condensate becomes significant near the boundary of the future horizon. Our results highlight the interplay among the different polarization modes and the significance of the Proca mass in quantum observables.

gr-qc↗

arXiv2026

Absorption cross section of a Schwarzschild black hole for a massive vector field

In the present work, we study the absorption cross section of a Schwarzschild black hole for a massive vector field over arbitrary frequencies. Working in the Frolov-Krtouš-Kubizňák-Santos (FKKS) basis, we show how the conserved flux of the normalized Proca field naturally leads to the usual definitions of the absorption cross section in terms of the reflection and transmission coefficients. We then numerically compute these quantities over arbitrary frequencies. In contrast to the massless (photon) case, massive vector bosons exhibit new features arising from the field mass. In particular, the mass term introduces a longitudinal degree of freedom in addition to the transverse modes. Furthermore, it leads to a scalar-type branch in the even parity transverse modes, thereby breaking the usual degeneracy with the odd parity sector found in the massless case. We illustrate how these characteristics manifest themselves in the transmission and absorption spectrum. Given the recent developments in the study of ultralight bosonic fields in black hole spacetimes, the present analysis of the transmission properties of massive vector bosons bears particular significance.

gr-qc↗

arXiv2026

Resonant transmission of scalar waves through rotating traversable wormhole

The viability of traversable wormholes as exotic compact objects requires the identification of signatures that distinguish them from other compact objects. Given recent advances in observing rotating black hole signatures, identifying characteristic imprints that reflect the absence of an event horizon and the presence of a throat structure is of considerable significance. Motivated by this, in the present work, we analyze the propagation of a massless scalar field in a rotating traversable wormhole spacetime described by Teo's class of solutions. We numerically compute the transmission (greybody) factor and the corresponding absorption spectrum across a broad range of frequencies. The spectrum exhibits a series of sharp peaks in the amplitudes, which we identify as Breit-Wigner-type resonances. The emergence of such peaks can be attributed to the scalar modes temporarily trapped within the potential well formed by barriers on either side of the throat. These resonant features, previously identified in static wormhole backgrounds, persist in the rotating case. In particular, for Teo's class of wormholes, we find that rotation enhances the strength of the resonances. Overall, our results demonstrate the role of rotation in shaping the resonance effect and indicate these features as characteristic signatures of wormhole geometries.

gr-qc↗

arXiv2026

When Primordial Black Holes Absorb During the Early Universe

We study the evolution of primordial black holes (PBHs) formed in the early universe in the presence of a surrounding thermal bath. By incorporating the effects of thermal absorption, we show that PBHs can undergo significant mass growth, leading to extended lifetimes and substantial deviations from the standard Hawking evaporation scenario. We find a critical collapse efficiency, $γ_{\rm c} \simeq 0.395$, above which the PBH mass grows without bound. This correction has profound implications for both PBH-induced reheating and dark matter (DM) production. Specifically, we find that the reheating temperature can be suppressed, and the DM parameter space for the PBH reheating scenario can undergo $\mathcal{O}(10)$-$\mathcal{O}(10^4)$ corrections, depending on the PBH formation mass and collapse efficiency. Moreover, our results significantly shift the parameter space in which PBHs can account for the entirety of the DM. To the best of our knowledge, this is the first comprehensive phenomenological study to incorporate thermal absorption into PBH evolution and quantify its impact on cosmological observables.

astro-ph.CO↗

arXiv2025

Impact of general relativistic accretion on primordial black holes

We demonstrate that general relativistic corrections to the accretion of relativistic matter onto primordial black holes (PBHs) can significantly enhance their mass growth during the early Universe. Contrary to previous Newtonian treatments, our analysis reveals that PBH masses can increase by an order of magnitude before evaporation, leading to substantial modifications of their lifetime and cosmological imprints. We quantify the resulting shifts in the minimum PBH mass constrained by Big Bang Nucleosynthesis (BBN), the revised lower bound for PBHs surviving today, and the dark matter parameter space allowed by PBH evaporation. Furthermore, we show that the enhanced accretion alters the high-frequency gravitational wave spectrum from PBH evaporation, potentially within the reach of future detectors. Our results provide a comprehensive, relativistically consistent framework to delineate the role of PBHs in early-universe cosmology and dark matter phenomenology.

astro-ph.CO↗

arXiv2025

Extreme mass ratio inspirals in the cold vector dark matter environment

With regard to the observed dark matter density profile in galaxies and clusters, the scalar dark matter scenario has been previously studied for potential detectability through gravitational wave observations at measurable signal-to-noise ratios. In the present study, we consider the case of dark matter described by a massive vector field, also referred to as the Proca field. The density profile in the vicinity of the black hole is explicitly constructed for a broad range of dark matter mass, $μ\sim 10^{-10}-10^{-15}{\mathrm eV}$, which allows it to exhibit both particle and wave-like characteristics. While in the particle regime, the computation of the DM density distribution is analytically tractable, we find it convenient to compute the same numerically in the wave regime. Nevertheless, in the outer region, the surrounding dark matter is assumed to follow a broken power-law distribution, represented by a Navarro-Frenk-White (NFW) profile with a central spike. For the purpose of investigating the detectability of the vector dark matter in the gravitational wave spectrum, we have modelled a stellar-mass black hole ($1M_{\odot}$) inspiralling into a Schwarzschild black hole of mass $10^4M_{\odot}$ within such a vector dark matter environment. With this setup, we analyzed the dephasing in the gravitational wave strain induced by vector dark matter and performed a Fisher forecast for upcoming LISA observations, with particular emphasis on the distinctive features in both the particle and wave regimes of the dark matter. Additionally, most of the important results have been compared with the scalar dark matter case.

gr-qc↗

arXiv2025

The Bottom-Up Approach for Powerful Testing with FWER Control

We seek to design novel multiple testing procedures, which take into account a relevant notion of ''power'' or true discovery on the one hand, and allow computationally efficient test design and application on the other. Towards this end we characterize the optimal procedures that strongly control the family-wise error rate, for a range of power objectives measuring the success of multiple testing procedures in making true individual discoveries, and under a reasonable set of assumptions. While we cannot generally find these optimal solutions in practice, we propose the bottom-up approach, which constructs consonant closed testing procedures, while taking into account the overall power objective in designing the tests on every level of the closed testing hierarchy. This leads to a general recipe, yielding novel procedures which are computationally practical and demonstrate substantially improved power in both simulations and a real data study, compared to existing procedures.

stat.ME↗

arXiv2025

Superradiant scattering of electromagnetic fields from ringing black holes

Detection of gravitational waves (GWs) paves the beginning of a new era of gravitational wave astronomy. Black holes (BHs) in their ringdown phase provide the cleanest signal of emitted GWs that imprint the fundamental nature of BHs under low energy perturbation. Apart from GWs, any complementary signature of ringing BHs can be of paramount importance. Motivated by this we analyzed the scattering of electromagnetic waves in such a background and demonstrated that the absorption cross section of a ringing Schwarzschild BH can be superradiant. Moreover, we have found out that such superradiant phenomena are transient in nature with a characteristic time scale equal to the GW oscillation time scale. We further point out that the existing ground-based Low Frequency Array (LOFAR), radio telescopes, may be able to detect such transient signals from BHs of mass range $M\sim 10^{-1} - 10^{-2} M_{\odot}$, which should necessarily be of primordial origin. Our present result opens up an intriguing possibility of observing the black hole merging phenomena through electromagnetic waves.

gr-qc↗

arXiv2025

Axion-Photon Conversion in FLRW with Primordial Magnetic Fields: Explaining the Radio Excess

We explore the possibility of axion-photon conversion as a common origin of two low-frequency anomalies: the isotropic radio excess (ARCADE2) and the deep global 21-cm absorption trough (EDGES). From the axion-photon action in an FLRW background with primordial magnetic fields (PMFs), we derive the scale-dependent conversion probability including plasma effects. Resonant conversion, arising when the axion mass matches the plasma-induced photon mass, produces soft photons in the MHz-GHz range. By modeling stochastic PMFs with amplitude $B_0$ and spectral index $n_{\rm B}$, we show that axion-like particles with mass $\sim 10^{-14}$-$10^{-12}\,\mathrm{eV}$ and nanogauss-level nearly scale invariant PMFs can explain both ARCADE2 and EDGES. Heating from PMF dissipation via ambipolar diffusion and turbulent decay reduces the 21-cm trough, shifting the viable parameter space. Our results stem from a consistent theoretical framework developed from first principles and a combined analysis of the radio excess and global 21-cm signal, while remaining consistent with CMB bounds on PMFs and $ΔN_{\rm eff}$. We conclude that global 21-cm observations may offer potential sensitivity to axions, primordial magnetism, and dark-sector physics.

astro-ph.CO↗

arXiv2025

Superradiant scattering of massive scalar field due to magnetically charged rotating black hole

Rotating black holes are well known to amplify the perturbing bosonic fields in certain parameter spaces. This phenomenon is popularly known as superradiance. In addition to rotation in the spacetime, charge plays a crucial role in the amplification process. In the present study, we have considered the spacetime of a magnetically charged rotating black hole emerging from the coupling of nonlinear electromagnetic field configuration to gravity. Due to this black hole spacetime, we have studied the scattering states of a massive scalar field and investigated the superradiant amplification process. We find that the magnetic charge of the spacetime affects the magnitude of the amplification and also significantly enlarges the allowed frequency ranges for which superradiance happens. In comparison, our analysis reveals that some of the behaviours are quite similar to what has been found in the case of the Kerr-Newmann black hole. Moreover, in specific parameter spaces, we observe exact similarities, which could imply a probable correspondence between the magnetically charged black hole and the Kerr-Newman black hole in certain scenarios. In addition to this, we have investigated the superradiant instability regime due to the massive potential barrier and also compared our results with that of the Kerr-Newmann black hole.

gr-qc↗

arXiv2024

Sonoluminescence: Photon production in time dependent analog system

Sonoluminescence is a well known laboratory phenomenon where an oscillating gas bubble in the appropriate environment periodically emits a flash of light in the visible frequency range. In this submission, we study the system in the framework of analog gravity. We model the oscillating bubble in terms of analog geometry and propose a non-minimal coupling prescription of the electromagnetic field with the geometry. The geometry behaves as an analogous oscillating time dependent background in which repeated flux of photons are produced in a wide frequency range through parametric resonance from quantum vacuum. Due to our numerical limitation, we could reach the frequency up to $\sim 10^5 ~\mbox{m}^{-1}$. However, we numerically fit the spectrum in a polynomial form including the observed frequency range around $\sim 10^7 ~\mbox{m}^{-1}$. Our current analysis seems to suggest that parametric resonance in analog background may play a fundamental role in explaining such phenomena in the quantum field theory framework.

hep-th↗

arXiv2024

Sonofermionescence: Fermions from Ringing Bubble of Sonoluminescence

Time-dependent gravitational background is well known as a theoretical laboratory for quantum mechanical particle production. In the present analysis, we explore such production in a time-dependent analog system. This is the follow-up of our earlier study on the Sonoluminescence phenomenon, which is modelled in terms of analog geometry coupled with the electromagnetic field exhibiting the quantum production of photons. In the same analog geometry, we studied fermion production. Although fermions have not been observed yet in the sonoluminescence experiment, we have shown here that such a system can produce a repeated flux of fermions via the parametric resonance from a quantum vacuum. Our analysis seems to suggest that in the laboratory setup, time-dependent analog systems could be an interesting playground where phenomena of quantum mechanical particle production can be observed.

hep-th↗

arXiv2024

A comparative study of the absorption cross section of static regular black holes for electromagnetic field

In this article, we report our study on the absorption cross section for the electromagnetic field due to static spherically symmetric regular black holes of two distinct categories: the Fan-Wang generic class and the Simpson-Visser class. Existing studies on these two categories have relied on the WKB method, which applies to the low-frequency regime. In our analysis, we have numerically evaluated the absorption cross section for the electromagnetic field across all frequency ranges. To compute the absorption cross section, we followed a gauge-invariant approach, which avoids the need for gauge fixing for the electromagnetic field, thereby simplifying the methodology further. To emphasize the usefulness of this gauge invariant approach we have performed the same analysis for Simpson-Visser class black holes, which is more general in terms of the structure of the metric. For both types of regular black holes, the influence of regularity parameters on the absorption cross section reveals fundamental properties of their spacetime and their interactions with the surrounding astrophysical environment. Moreover, certain similarities observed between the Reissner-Nordström black hole and regular black holes of the Fan-Wang generic class indicate potential scenarios of correspondence between linear and nonlinear electrodynamics when coupled with gravity.

gr-qc↗

arXiv2022

Inference with approximate local false discovery rates

Efron's two-group model is widely used in large scale multiple testing. This model assumes that test statistics are mutually independent, however in realistic settings they are typically dependent, and taking the dependence into account can boost power. The general two-group model takes the dependence between the test statistics into account. Optimal policies in the general two-group model require calculation, for each hypothesis, of the probability that it is a true null given all test statistics, denoted local false discovery rate (locFDR). Unfortunately, calculating locFDRs under realistic dependence structures can be computationally prohibitive. We propose calculating approximate locFDRs based on a properly defined N-neighborhood for each hypothesis. We prove that by thresholding the approximate locFDRs with a fixed threshold, the marginal false discovery rate is controlled for any dependence structure. Furthermore, we prove that this is the optimal procedure in a restricted class of decision rules, where decision for each hypothesis is only guided by its N-neighborhood. We show through extensive simulations that our proposed method achieves substantial power gains compared to alternative practical approaches, while maintaining conceptual simplicity and computational feasibility. We demonstrate the utility of our method on a genome wide association study of height.

stat.ME↗

arXiv2022

Ringing Black Hole is Superradiant: Ultra-light Scalar Field

Superradiance has been studied quite extensively in the context of static (charged) and rotating black hole spacetime. In this paper, we report for the first time that for a minimally coupled scalar field, the absorption cross-section of a Schwarzschild black hole in its ring down phase can be superradiant. Our present result opens up an intriguing possibility of observing the black hole merging phenomena through other fundamental fields.

gr-qc↗

arXiv2021

Effect of transcription reinitiation in stochastic gene expression

Gene expression (GE) is an inherently random or stochastic or noisy process. The randomness in different steps of GE, e.g., transcription, translation, degradation, etc., leading to cell-to-cell variations in mRNA and protein levels. This variation appears in organisms ranging from microbes to metazoans. Stochastic gene expression has important consequences for cellular function. The random fluctuations in protein levels produce variability in cellular behavior. It is beneficial in some contexts and harmful to others. These situations include stress response, metabolism, development, cell cycle, circadian rhythms, and aging. Different model studies e.g., constitutive, two-state, etc., reveal that the fluctuations in mRNA and protein levels arise from different steps of gene expression among which the steps in transcription have the maximum effect. The pulsatile mRNA production through RNAP-II based reinitiation of transcription is an important part of gene transcription. Though, the effect of that process on mRNA and protein levels is very little known. The addition of any biochemical step in the constitutive or two-state process generally decreases the mean and increases the Fano factor. In this study, we have shown that the RNAP-II based reinitiation process in gene transcription can have different effects on both mean and Fano factor at mRNA levels in different model systems. It decreases the mean and Fano factor both at the mRNA levels in the constitutive network whereas in other networks it can simultaneously increase or decrease both quantities or it can have mixed-effect at mRNA levels. We propose that a constitutive network with reinitiation behaves like a product independent negative feedback circuit whereas other networks behave as either product independent positive or negative or mixed feedback circuit.

q-bio.MN↗

arXiv2020

Control of noise in gene expression by transcriptional reinitiation

Gene expression is a random or noisy process. The process consists of several random events among which the reinitiation of transcription by RNAP is an important one. The RNAP molecules can bind the gene only after the promoter gets activated by transcription factors. Several transcription factors bind the promoter to put the gene in the active state. The gene turns into inactive state as the bound transcription factors leave the promoter. During the active period of the gene, many RNAP molecules transcribe the gene to synthesize the mRNAs. The binding event of RNAP to the active state of the gene is a probabilistic process and therefore, introduces noise or fluctuations in the mRNA and protein levels. In this paper, we analytically calculate the Fano factor in mRNA and protein levels and also the probability distribution of mRNA numbers exactly with the binding event of RNAPs in gene transcription process. The analytically calculated expression of Fano factor of proteins shows excellent agreement with an experimental result. Then we show that the Fano factor in mRNA levels can be sub-Poissonian due to the reinitiation of transcription by RNAP and the mean mRNA level can be increased without increasing the Fano factor. Our study show that the Fano factor can also be reduced keeping mRNA levels fixed. We find that the reinitiation of transcription can behave as a fine-tuned control process to regulate the mRNA/protein level in the cell.

q-bio.MN↗