arXiv subjects

Rajes Ghosh

Publications and source records attributed to Rajes Ghosh.

At least 19 recordsLinked to original sources

arXiv2026

Universal Ladder Structure Across Scales: From Quantum to Black Hole Physics

Second-order ordinary linear differential equations appear ubiquitously across physics, describing the behavior of systems from the quantum world of atoms to the classical world of gravitating bodies. We present a unified symmetry-based framework that provides a ``litmus-test criterion'' to determine when such a system admits a hierarchical ladder structure, and, whenever it does, explicitly constructs the ladder. This approach uncovers a previously underappreciated connection to supersymmetric quantum mechanics and a deep commonality among diverse physical problems. Applications to the quantum harmonic oscillator and dynamical tidal response of Kerr black holes are presented to illustrate the framework.

gr-qc↗

arXiv2025

Strong-field Gravitational Wave Lensing in the Kerr Background

Gravitational-wave (GW) lensing can encode valuable information about the properties of the intervening lens, but most existing studies remain restricted to the small-deflection, weak-field regime. To bridge this crucial gap, this work presents the first systematic analysis of strong-field, wave-optical GW lensing by a Kerr black hole (BH), extending recent results for non-rotating lens to the astrophysically more relevant case of spinning-lens. Using the Mano-Suzuki-Takasugi formalism, we compute the strong-field scattering factor and show that the the spin produces characteristic modifications to the lensed waveform, and high-frequency incident radiation is not strongly absorbed by the BH lens, contrary to earlier claims. We further derive explicit expressions for the observed waveform for the general source-lens-observer configuration, showcasing the distortions produced by the scattering and quantifying their departure from the Schwarzschild case. Specializing to on-axis scattering, a mismatch analysis for a GW150914-like source lensed by a Kerr BH of mass $M=10^2~\mathrm{M}_\odot$ situated $100M$ away from the source reveals percent-level deviations from the unscattered wave at scattering angles near $30^\circ$, across a range of lens spin values. The mismatch generally decreases as the scattering angle increases, but this behavior can change substantially when polarization mixing induced by scattering becomes significant. In such cases, components that are absent/suppressed in the direct signal may become appreciable due to scattering effects. For a fixed scattering angle, however, the mismatch shows only a weak dependence on the BH spin in the case of on-axis scattering, which may improve for more general configurations. The framework developed here offers a unified treatment of strong-field GW scattering in Kerr spacetime for interpreting future high-precision GW observations.

gr-qc↗

arXiv2025

Generalized Perturbed Kepler Problem: Gravitational Wave Imprints from Eccentric Compact Binaries

Observations of astrophysical binaries may reveal departures from pure Keplerian orbits due to environmental influences, modifications to the underlying gravitational dynamics, or signatures of new physics. In this work, we develop a unified framework to systematically study such perturbations in the ambit of the perturbed Kepler problem and explore their impact on eccentric orbital dynamics and gravitational wave emission. Unlike traditional parametrized frameworks such as post-Newtonian and post-Einsteinian expansions, our approach offers a more source-specific modeling strategy, making it more natural to trace the physical origins of eccentric binary model parameters. Starting from a general perturbed potential, we derive the modified orbit and compute the associated gravitational fluxes and phase evolution, assessing their observational relevance for both current and future detectors. This framework thus offers a general and physically transparent toolkit for probing such subtle deviations from standard dynamics in gravitational wave data.

gr-qc↗

arXiv2025

Can Rotating Black Holes Have Short Hairs?

Despite the no-hair theorem, several notable hairy black hole (BH) solutions exist in both General Relativity and modified gravity theories. For such hairs to be detectable, they must extend sufficiently beyond the event horizon. This idea has been rigorously formalized by the no-short hair theorem, which dictates that all existing hairs of a static spherically symmetric BH must extend at least to the innermost light ring (LR). However, the theorem's applicability to the astrophysically relevant rotating BHs remains elusive as yet. To address this gap, we examine its validity for rotating BHs in the Konoplya-Rezzolla-Zhidenko-Stuchl\'ik and Johannsen classes. Interestingly, for Klein-Gordon separable BHs in these classes that are solutions of non-vacuum GR, the no-short hair property continues to hold. However, unlike in static cases, this result may not apply in a theory-agnostic fashion due to the rotation-induced repulsive effects. Consequently, we identify a minimal set of additional criteria on the metric and matter content needed for such a generalization in other theories. Our study marks an important first step toward establishing general results on the extent of rotating BH hairs, reinforcing their observational detections. Further extension of this novel result for rotating horizonless objects is also discussed.

gr-qc↗

arXiv2024

Probing Spacetime Symmetries Using Gravitational Wave Ringdown

The uniqueness and rigidity theorems assert that the asymptotically flat, vacuum, stationary rotating black hole solution in general relativity must be the Kerr solution, exhibiting novel symmetries such as axisymmetry and circularity. In our analysis of post-merger ringdown signal from coalescing black hole binary systems, we identify potential observational signatures for deviations from these Kerr symmetries. Utilizing ringdown data from the gravitational wave event GW150914, we place significant constraints on such deviations. Our analysis introduces a new and novel approach for testing spacetime symmetries through gravitational wave observations.

gr-qc↗

arXiv2024

Birkhoff's Theorem and Uniqueness: A Peek Beyond General Relativity

In General Relativity, Birkhoff's theorem asserts that any spherically symmetric vacuum solution must be static and asymptotically flat. In this paper, we study the validity of Birkhoff's theorem for a broad class of modified gravity theories in four spacetime dimensions, including quadratic and higher-order gravity models. We demonstrate that the Schwarzschild spacetime remains the unique Einstein branch solution outside any spherically symmetric configuration of these theories. Consequently, unlike black holes, the breakdown of junction conditions at the surface of the star further implies that the actual spacetime metric outside a horizonless star in these modified theories cannot simultaneously be spherically symmetric and remain within the Einstein branch. This insight offers a unique observational probe for theories beyond General Relativity.

gr-qc↗

arXiv2024

Restoring Causality in Higher Curvature Gravity

Incorporating higher curvature terms into gravity theories modifies the classical field equations, potentially leading to theoretical issues like Shapiro time advancements that violate the Camanho, Edelstein, Maldacena, and Zhiboedov (CEMZ) causality criterion. We explore this criterion within the context of Generalised Quadratic Gravity (GQG), a higher curvature theory with a distinct graviton three-point coupling from General Relativity (GR). By constructing an exact shock wave solution of GQG and calculating the Shapiro time shift for a massless probe graviton, we demonstrate that it can remain strictly positive within a classically allowed parameter space of couplings, ensuring the theory's adherence to the CEMZ criterion. This finding indicates that GQG can offer a causal extension beyond GR, paving the way for further exploration into the consistency of classical higher curvature gravity theories.

hep-th↗

arXiv2024

Theoretical and Observational Constraints on Theories Beyond General Relativity

This thesis embarks on a comprehensive investigation of modified gravity theories and their implications on the properties of compact objects. Our primary objective is to shed light on the fundamental nature of gravity by exploring potential departures from General Relativity (GR) through a combination of theoretical analyses and observational techniques. On the theoretical side, we consider black hole thermodynamics, stability of compact objects, presence of black hole hairs, and the issue of causality that may provide valuable input towards the ultimate quantum theory of gravity. Moreover, on the observational side, we employ gravitational wave observations and black hole perturbation theory to explore new aspects of gravity and put stringent bounds on the beyond-GR parameters. To provide a structured overview of the thesis, we have organized it into chapters that progressively delve deeper into these diverse aspects of modified gravity and compact objects. Each chapter is dedicated to a specific facet of our investigation, building a coherent narrative that spans both theoretical and observational explorations. We aspire to achieve nothing less than imparting valuable insights and novel perspectives that may significantly enhance our understanding of the fundamental nature of gravitation.

gr-qc↗

arXiv2024

Parameterized Non-circular Deviation from the Kerr Paradigm and Its Observational Signatures: Extreme Mass Ratio Inspirals and Lense-Thirring Effect

Recent gravitational wave observations and shadow imaging have demonstrated the astonishing consistency of the Kerr paradigm despite all the special symmetries assumed in deriving the Kerr metric. Hence, it is crucial to test the presence of these symmetries in astrophysical scenarios and constraint possible deviations from them, especially in strong field regimes. With this motivation, the present work aims to investigate the theoretical consequences and observational signatures of non-circularity in a unified theory-agnostic manner. For this purpose, we construct a general non-circular metric with a small parameterized deviation from Kerr. This metric preserves the other properties of Kerr, such as stationarity, axisymmetry, asymptotic flatness, and the equatorial reflection symmetry. Apart from the resulting mathematical simplifications, this assumption is crucial to disentangle the consequences of relaxing circularity from other properties. Then, after discussing various novel theoretical consequences, we perform a detailed analysis of extreme mass ratio inspirals and Lense-Thirring precession in the context of this newly constructed metric. Our study clearly shows the promising prospects of detecting and constraining even a slight non-circular deviation from the Kerr paradigm using the future gravitational wave observations by the Laser Interferometer Space Antenna.

gr-qc↗

arXiv2024

Exploring Ladder Symmetry and Love Numbers for Static and Rotating Black Holes

Black hole solutions of general relativity exhibit a symmetry for the static perturbations around these spacetimes, known as "ladder symmetry". This symmetry proves useful in constructing a tower of solutions for perturbations and elucidating their general properties. Specifically, the presence of this symmetry leads to vanishing of the tidal love number associated with black holes. In this work, we find the most general spherical symmetric and static black hole spacetime that accommodates this ladder symmetry for scalar perturbation. Furthermore, we extend our calculations beyond spherical symmetry to find the class of stationary Konoplya-Rezzolla-Zhidenko black holes, which also possess a similar ladder structure.

gr-qc↗

arXiv2023

Formation and Stability of Area Quantized Black Holes

We investigate the ergoregion instability of area-quantized rotating quantum black holes (QBH) under gravitational perturbation. We show that the instability can be avoided in binary systems that include QBHs if the separation between the inspiralling components at the onset of black hole formation is less than a critical value. We also analyze the formation history of such systems from stellar progenitors and demonstrate that a significant fraction of progenitor masses cannot lead to QBH formation, making it unlikely for LIGO-Virgo black hole binaries to comprise rotating QBHs.

gr-qc↗

arXiv2023

Hairy Black Holes: Non-existence of Short Hairs and Bound on Light Ring Size

Several hairy black hole solutions are known to violate the original version of the celebrated no-hair conjecture. This prompted the development of a new theorem that establishes a universal lower bound on the extension of hairs outside any $4$-dimensional black hole solutions of general relativity. Our work presents a novel generalization of this ``no-short hair'' theorem, which notably does not use gravitational field equations and is valid for arbitrary spacetime dimensions ($D \geq 4$). Consequently, irrespective of the underlying theory of gravity, the ``hairosphere'' must extend to the innermost light ring of the black hole spacetime. Various possible observational implications of this intriguing theorem are discussed, and other useful consequences are explored.

gr-qc↗

arXiv2023

Does the speed of gravitational waves depend on the source velocity?

The second postulate of special relativity states that the speed of light in vacuum is independent of the emitter's motion. The test of this postulate so far remains unexplored for gravitational radiation. We analyze data from the LIGO-Virgo detectors to test this postulate within the ambit of a model where the speed of the emitted GWs ($c'$) from a binary depends on a characteristic velocity $\tilde{v}$ proportional to that of the reduced one-body system as $c' = c + k\, \tilde{v}$, where $k$ is a constant. We have estimated the upper bound on the 90\% credible interval over $k$ to be ${k \leq 8.3 \times {10}^{-18}}$, which is several orders of magnitude more stringent compared to previous bounds obtained from electromagnetic observations. The Bayes' factor supports the second postulate with a strong evidence that the data is consistent with the null hypothesis $k = 0$, upholding the principle of relativity for gravitational interactions.

gr-qc↗

arXiv2023

Quasi-normal modes of non-separable perturbation equations: the scalar non-Kerr case

Scalar, vector and tensor perturbations on the Kerr spacetime are governed by equations that can be solved by separation of variables, but the same is not true in generic stationary and axisymmetric geometries. This complicates the calculation of black-hole quasi-normal mode frequencies in theories that extend/modify general relativity, because one generally has to calculate the eigenvalue spectrum of a two-dimensional partial differential equation (in the radial and angular variables) instead of an ordinary differential equation (in the radial variable). In this work, we show that if the background geometry is close to the Kerr one, the problem considerably simplifies. One can indeed compute the quasi-normal mode frequencies, at least at leading order in the deviation from Kerr, by solving an ordinary differential equation subject to suitable boundary conditions. Although our method is general, in this paper we apply it to scalar perturbations on top of a Kerr black hole with an anomalous quadrupole moment, or on top of a slowly rotating Kerr background.

gr-qc↗

arXiv2023

Regularized Stable Kerr Black Hole: Cosmic Censorships, Shadow and Quasi-Normal Modes

Black hole solutions in general relativity come with pathologies such as singularity and mass inflation instability, which are believed to be cured by a yet-to-be-found quantum theory of gravity. Without such consistent description, one may model theory-agnostic phenomenological black holes that bypass the aforesaid issues. These so-called regular black holes are extensively studied in the literature using parameterized modifications over the black hole solutions of general relativity. However, since there exist several ways to model such black holes, it is important to study the consistency and viability of these solutions from both theoretical and observational perspectives. In this work, we consider a recently proposed model of regularized stable rotating black holes having two extra parameters in addition to the mass and spin of a Kerr solution. We start by computing their quasi-normal modes under scalar perturbation and investigate the impact of those additional parameters on black hole stability. In the second part, we study the shadow structures of these regularized black holes and obtain stringent bounds on the parameter space requiring consistency with Event Horizon Telescope observations of $M87^*$ and $Sgr\, A^*$ shadows.

gr-qc↗

arXiv2022

Constraining the topological Gauss-Bonnet coupling from GW150914

Recent gravitational wave observation based on the data from GW150914 has confirmed Hawking's area theorem and estimated the increase in total horizon area during a merger process of two Kerr black holes. We use this result and the validity of the second law to obtain the first observational bound on the 4D topological Gauss-Bonnet coupling as $γ\lesssim 2.804^{+7.946}_{-1.169} \times 10^{9}\, m^2$ with $95 \%$ credibility.

gr-qc↗

arXiv2021

Signature of Non-uniform Area Quantization on Black Hole Echoes

A classical black hole is characterized by a horizon that absorbs radiation of all frequencies incident on it. Perturbation of these black holes is well-understood via exponentially damped sinusoids known as quasi-normal modes. Any departure from such classical behavior near the horizon may induce significant modifications in the late time evolution of the perturbation leading to so-called gravitational wave echoes. This work considers the effect of black hole area-quantization on the formation of gravitational wave echoes. We investigate how the resulting echo waveform may depend on various model parameters. Our study opens up a new window to distinguish different models of area quantization using future gravitational wave observations and provides a novel probe to study the near horizon physics.

gr-qc↗

arXiv2021

Signature of Non-uniform Area Quantization on Gravitational Waves

Quantum aspects of black holes may have observational imprints on their absorption and emission spectrum. In this work, we consider the possibility of non-uniform area quantization and its effects on the phasing of gravitational waveform from coalescing black hole inspirals. These observations may provide detectable effects distinct from that of a uniform area quantization and allow us to put bounds on various parameters of the underlying model. Our work can also be regarded as a novel test for the area-entropy proportionality of black hole solutions in general relativity.

gr-qc↗