arXiv subjects

Rajendra Prasad Bhatt

Publications and source records attributed to Rajendra Prasad Bhatt.

6 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

Response of a Kerr black hole to a generic tidal perturbation

We derive the response, the real part of which provides the tidal Love numbers, for non-extremal as well as extremal Kerr black holes under generic tidal perturbations. Our results suggest that the static as well as dynamical (linear-in-frequency) Love numbers vanish for both Schwarzschild and slowly rotating (linear-in-angular momentum) Kerr black holes, under generic perturbations. The vanishing of static and dynamical Love numbers also holds for axisymmetric tidal perturbations of non-extremal and extremal Kerr black holes. In fact, even under generic tidal perturbations, the static Love numbers of Kerr black holes vanish identically. The only case with non-zero Love numbers corresponds to the non-axisymmetric dynamical tidal perturbations of Kerr black holes (to arbitrary order of angular momentum). We also demonstrate that the non-zero dynamical Love numbers, for both non-extremal and extremal Kerr black holes, get modified under the change of the sign of the spin-weight, for electromagnetic and gravitational tidal perturbations.

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arXiv2025

Rotating black holes experience dynamical tides

We find the dynamical tidal response of a Kerr black hole (BH) and demonstrate its tidal Love numbers to be non-vanishing when present in a non-axisymmetric external tidal field. To leading order, they depend quadratically on the black hole spin and linearly on the mode frequency. This implies that Kerr BHs are deformable under certain external, time-dependent perturbations. Since non-vanishing tidal Love numbers have been used in compact binary coalescences observed by the LIGO-Virgo-KAGRA (LVK) Collaboration to infer their non-BH nature, our findings have important implications on such inferences from future gravitational wave observations.

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arXiv2024

Scalar tidal response of a rotating BTZ black hole

We study the response of a rotating BTZ black hole to the scalar tidal perturbation. We show that the real component of the tidal response function isn't zero, indicating that a rotating BTZ black hole possesses non-zero tidal Love numbers. Additionally, we observe scale-dependent behaviour, known as log-running, in the tidal response function. We also conduct a separate analysis on an extremal rotating BTZ black hole, finding qualitative similarities with its non-extremal counterpart. In addition, we present a procedure to calculate the tidal response function of a charged rotating BTZ black hole as well.

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arXiv2023

Addressing issues in defining the Love numbers for black holes

We present an analytic method for calculating the tidal response function of a nonrotating and a slowly rotating black hole from the Teukolsky equation in the small-frequency and near horizon limit. We point out that in the relativistic context, there can be two possible definitions of the tidal Love numbers and the dissipative part that arises from the tidal response function. Our results suggest that both of these definitions predict zero tidal Love numbers for a nonrotating black hole. On the other hand, for a slowly rotating black hole in a generic tidal environment, these two definitions of the tidal Love numbers do not coincide. While one procedure suggests zero tidal Love numbers, the other procedure gives purely imaginary tidal Love numbers. As expected, the dissipative terms differ as well. We emphasize that in our analysis, we keep all the terms linear in the frequency, unlike previous works in the literature. Following this, we propose a procedure to calculate the tidal response function -- and hence the Love numbers -- for an arbitrarily rotating black hole.

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arXiv2022

Analog Raychaudhuri equation in mechanics

Usually, in mechanics, we obtain the trajectory of a particle in a given force field by solving Newton's second law with chosen initial conditions. In contrast, through our work here, we first demonstrate how one may analyse the behaviour of a suitably defined family of trajectories of a given mechanical system. Such an approach leads us to develop a mechanics analog following the well-known Raychaudhuri equation largely studied in Riemannian geometry and general relativity. The idea of geodesic focusing, which is more familiar to a relativist, appears to be analogous to the meeting of trajectories of a mechanical system within a finite time. Applying our general results to the case of simple pendula, we obtain relevant quantitative consequences. Thereafter, we set up and perform a straightforward experiment based on a system with two pendula. The experimental results on this system are found to tally well with our proposed theoretical model. In summary, the simple theory, as well as the related experiment, provides us with a way to understand the essence of a fairly involved concept in advanced physics from an elementary standpoint.

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