Searcharxiv⌕ Search

arXiv subjects

Madhukrishna Chakraborty

Publications and source records attributed to Madhukrishna Chakraborty.

17 recordsLinked to original sources
arXiv2026

Raychaudhuri Equation and Weyl-Driven Shear: A Weak-Field Approach to Lensing and Gravitational Waves

The letter studies phenomena like gravitational wave propagation and gravitational lensing using the celebrated Raychaudhuri equation (RE) in the weak field limit. Newtonian analogue of Relativistic RE has been explored. In doing so, role of shear has been found to be extremely important in explaining these phenomena. Consequently, the RE for shear has been used in course of the study and importance of Weyl curvature tensor in lensing and gravity wave propagation has been explicitly shown using a damped harmonic oscillator approach.

gr-qc↗
arXiv2025

Quasinormal modes and Grey body factors of Wormholes: From General prescription to Einstein Gauss Bonnet realizations

Traversable wormholes are one of the most exciting predictions of General Relativity that offer short-cuts through space-time. However, their feasibility requires the violation of the null energy condition and makes their detection a bit difficult. This paper aims to show the new avenues delving deep into the observational prospects of TWHs via quasinormal modes (QNMs) and gray body factors GBFs. These are the two elementary aspects of wave dynamics. Given their distinct spectral imprints, these features provide a potential means to distinguish wormholes from black holes in gravitational wave observations. The role of QNMs in characterizing the ringdown phase of perturbations and the GBFs in determining transmission probabilities through wormhole barriers have been explored by a general description and then fed to Einstein Gauss Bonnet WH solutions in isotropic as well as anisotropic cases. Finally, a correspondence of the QNM frequencies with radius of the WH shadows has been made and the effect of Gauss Bonnet parameter on the QNM spectra has been discussed.

gr-qc↗
arXiv2025

Wormholes: Myth or Reality? Prospects for Future Observations

Traversable wormholes (TWHs) remain one of the most intriguing predictions of General Relativity (GR), offering passage through space-time. However, their existence requires the violation of the null energy condition, making their detection a bit challenging. The essay aims at showing the new avenues probing the observational prospects of TWHs via quasinormal modes and grey body factors, the two fundamental aspects in wave dynamics. The role of QNMs in characterizing the ringdown phase of perturbations and the grey body factors in determining transmission probabilities through wormhole barriers has been investigated. Given their distinct spectral imprints, these features provide a potential means to distinguish wormholes from black holes in gravity wave observations. Advances in high-precision interferometry and multi-messenger astronomy may soon offer crucial insights into the existence of these exotic structures. Essay received Honorable Mention at the Gravity Research Foundation 2025 Awards for Essays on Gravitation

gr-qc↗
arXiv2025

Exploring Traversable Wormholes in $f(Q)$ gravity: Shadows and Quasinormal modes

The present work deals with some WH solutions in $f(Q)$ gravity theory for non-constant red-shift function subject to a power law model of $f(Q)$, $Q$ being the non-metricity scalar. Important properties of a WH configuration like the asymptotic flatness, traversability, flairing out condition and energy conditions have been checked for the obtained solutions. Shadows for these WHs have been determined and effect of non-metricity has been discussed. Finally, the paper gives an essence of Quasinormal modes and grey body factors for traversable WHs in general and $f(Q)$ wormholes in particular indicating a distinct signature of non-metricity influencing these observational tools.

gr-qc↗
arXiv2024

A study of Raychaudhuri equation and geodesic focusing in Fractal Universe

The paper deals with the modified Raychaudhuri equation (RE) within the framework of homogeneous and isotropic Fractal Universe. Focusing of a congruence of time-like geodesics has been examined for three generic choices of the fractal function. Finally, comments on the existence and possible avoidance of the initial big-bang singularity have been made by examining the sign of convergence scalar in the fractal models under consideration.

gr-qc↗
arXiv2024

Curvature form of Raychaudhuri equation and its consequences: A geometric approach

The paper aims at deriving a curvature form of the famous Raychaudhuri equation (RE) and the associated criteria for focusing of a hyper-surface orthogonal congruence of time-like geodesic. Moreover, the paper identifies a transformation of variable related to the metric scalar of the hyper-surface which converts the first order RE into a second order differential equation that resembles an equation of a Harmonic oscillator and also gives a first integral that yields the analytic solution of the RE and Lagrangian of the dynamical system representing the congruence.

gr-qc↗
arXiv2024

Classical and quantum analysis of gravitational singularity from Raychaudhuri equation

The present work deals with the Raychaudhuri equation (RE) to examine the space-time singularity both from classical and quantum point of view. The RE has been looked upon in terms of a classical linear Harmonic oscillator and Focusing theorem has been studied. Also, the Raychaudhuri scalar has been shown to affect the convergence and singularity formation in Black-holes and cosmology. Finally, resolution of initial big-bang singularity has been attempted quantum mechanically in two ways namely by canonical quantization and by formulation of Bohmian trajectories.

gr-qc↗
arXiv2024

A study on existence of Wormhole in Lemaitre-Tolman-Bondi model

An investigation has been done for possible existence of evolving wormhole (WH) solution in the background of inhomogeneous Lemaitre-Tolman-Bondi (LTB) space-time geometry. Using separable product form of the geometric (or area) radius, the shape function can be evaluated in terms of the functional part of the radial coordinate in the area radius. The conditions for a viable WH configuration have been examined.

gr-qc↗
arXiv2024

Cosmological Wormhole: An analytical description

An attempt has been made to have an analytical description for possible traversable wormhole in non-static spherically symmetric space-time supported by anisotropic fluid. Both trivial and non-trivial choices of the red-shift function result in identical WH configuration and it is possible to have emergent scenario for evolution of the background space-time in both the cases.

gr-qc↗
arXiv2024

Black Hole singularity and its possible mitigations: Reformulation of Penrose Singularity theorem using null Raychaudhuri matrix

In this paper, we introduce a notion of null Raychaudhuri matrix motivated by the matrix representation of tensor fields. The evolution of this matrix gives the matrix form of null Raychaudhuri equation. Using this distinct geometric approach, we have reformulated the original Penrose singularity theorem on Black-Hole and have commented on the characteristic of the Raychaudhuri matrix at the singularity. The paper also suggests two possible mitigations for the physical singularity of Schwarzschild black hole via the Wheeler-DeWitt formalism and Bohemian formalism.

gr-qc↗
arXiv2024

Raychaudhuri equation and the dynamics of cosmic evolution

The paper deals with the Raychaudhuri equation (RE) which is a non-linear ordinary differential equation in $Θ$, the expansion scalar corresponding to a geodesic flow. Focusing theorem which follows as a consequence of the RE has been restated in terms of the cosmic parameter $q$ (deceleration parameter) both for Einstein gravity and for modified gravity theories. Measurable quantities namely the luminosity distance and density parameter are shown to have an upper bound using the Raychaudhuri scalar. An analogy between geometric and cosmological RE has been made. Subsequently, to find the solution of the non-linear RE a transformation of variable related to the metric scalar of the hyper-surface has been identified which converts the former to a second order differential equation. Finally, the first integral of this second order differential equation gives the entire picture of the dynamics of cosmic evolution.

gr-qc↗
arXiv2023

On the consequences of Raychaudhuri equation in Kantowski-Sachs space-time

The paper aims to study the geometry and physics of the Raychaudhuri equation (RE) in the background of a homogeneous and anisotropic space-time described by Kantowski-Sachs (KS) metric. Role of anisotropy/shear in the context of convergence and possible avoidance of singularity has been analyzed subject to a physically motivated constraint. Moreover, using a suitable transformation the first order RE has been converted to a second order differential equation analogous to a Harmonic Oscillator and criterion for convergence has been shown to be associated with the time varying frequency of the Oscillator. Finally, the paper points out a geometric and physical notion of anisotropy along with their corresponding behavior towards convergence.

gr-qc↗
arXiv2023

Raychaudhuri equation and Bouncing cosmology

The present work deals with an exhaustive study of bouncing cosmology in the background of homogeneous and isotropic Friedmann-Lemaitre-Robertson-Walker space-time. The geometry of the bouncing point has been studied extensively and used as a tool to classify the models from the point of view of cosmology. Raychaudhuri equation (RE) has been furnished in these models to classify the bouncing point as regular point or singular point. Behavior of time-like geodesic congruence in the neighbourhood of the bouncing point has been discussed using the Focusing Theorem which follows as a consequence of the RE. An analogy of the RE with the evolution equation for a linear harmonic oscillator has been made and an oscillatory bouncing model has been discussed in this context.

gr-qc↗
arXiv2023

Raychaudhuri Equation from Lagrangian and Hamiltonian formulation : A Quantum Aspect

The paper deals with a suitable transformation related to the metric scalar of the hyper-surface so that the Raychaudhuri Equation (RE) can be written as a second order nonlinear differential equation. A first integral of this second order differential equation gives a possible analytic solution of the RE. Also, it is shown that construction of a Lagrangian (and hence a Hamiltonian) is possible, from which the RE can be derived. Wheeler-Dewitt equation has been formulated in canonical quantization scheme and norm of it's solution (wave function of the universe) is shown to affect the singularity analysis in the quantum regime for any spatially homogeneous and isotropic cosmology. Finally Bohmian trajectories are formulated with causal interpretation and these quantum trajectories unlike classical geodesics obliterate the initial big-bang singularity when the quantum potential is included.

gr-qc↗
arXiv2023

The classical and quantum implications of the Raychaudhuri Equation in f(T)-gravity

The present work deals with the classical and quantum aspects of the Raychaudhuri equation in the framework of f(T)-gravity theory. In the background of homogeneous and isotropic Friedmann Lemaitre Robertson Walker space time, the Raychaudhuri equation has been formulated and used to examine the focusing theorem and convergence condition for different choices of f(T). Finally in quantum cosmology, the wave function of the universe has been shown to be the energy eigen function of the time independent Schrodinger equation of a particle. Also probability measure on the mini-super space has been examined at zero volume for singularity analysis in the quantum regime. Lastly the Bohmian trajectory for the present quantum system has been explicitly determined for some particular choices.

gr-qc↗
arXiv2023

The Raychaudhuri Equation in inhomogeneous FLRW space-time : A $f(R)$-gravity model

In general description of the Raychaudhuri equation it is found that this first order non-linear differential equation can be written as a second order linear differential equation in the form of Harmonic Oscillator with varying frequency. Further, the integrability of the Raychaudhuri equation has been studied and also the expansion scalar is obtained in an explicit form. Subsequently, $f(R)$ gravity theory has been studied in the background of inhomogeneous FLRW spacetime with an aim to formulate the Raychaudhuri Equation. A congruence of time-like geodesics has been investigated using the Raychaudhuri Equation to examine whether the geodesics converge or not and some possible conditions are determined to avoid singularity. Finally, a brief quantum description has been presented.

gr-qc↗