arXiv subjects

Soumya Bhattacharya

Publications and source records attributed to Soumya Bhattacharya.

At least 19 recordsLinked to original sources

arXiv2026

Gravitational wave memory and geodesic congruence response in generalised Ellis-Bronnikov wormholes

We investigate gravitational wave memory in generalised Ellis-Bronnikov wormhole spacetimes by studying the response of neighbouring timelike geodesics and geodesic congruences to a localized test gravitational wave pulse. Using proper time as the evolution parameter, we identify pulse-induced displacement and velocity memory after subtracting the background geodesic evolution. We further investigate the response of timelike congruences through the expansion and shear using the Raychaudhuri equations. We find that the memory response depends systematically on the wormhole throat radius, the steepness parameter and the location of the pulse relative to the throat. In particular, a pulse at the throat produces zero net integrated expansion but a finite shear response, while a pulse away from the throat generates an asymmetric congruence response. These results show that wormhole geometry can imprint characteristic signatures on both detector-based and congruence-based memory observables.

gr-qc↗

arXiv2026

Primordial Black Holes: A Review of Formation and Evolution

Primordial Black Holes (PBHs) have emerged as a leading non-particulate candidate for dark matter and a unique cosmological probe, a paradigm shift accelerated by the detection of anomalous binary mergers by the LIGO-Virgo-KAGRA (LVK) collaboration. While the literature is rich with phenomenological constraints, the fundamental quantum and relativistic underpinnings governing PBH genesis and evolution often receive comparatively less emphasis. This review aims to bridge that gap by systematically detailing the physics of PBH formation and their subsequent evolutionary trajectory. We critically examine the hydrodynamic complexity of the early universe, establishing the relativistic thresholds for collapse, the non-linear \emph{race against sound} in the primordial plasma, and the rigorous mathematical utility of the compaction function. Furthermore, by incorporating the dynamic nature of FLRW backgrounds, higher curvature corrections, and quantum backreaction via the memory burden effect, we challenge the standard hawking evaporation and show that extreme-curvature environments halt evaporation entirely, leaving Planck-scale relics that evade current extragalactic bounds. Finally, we map the multimessenger observational landscape, highlighting how the imminent search for sub-solar mass inspirals by next-generation gravitational wave observatories such as the Einstein Telescope and Cosmic Explorer could yield smoking-gun evidence for the PBH paradigm, ultimately transforming these primordial relics into unparalleled laboratories for high-energy physics.

gr-qc↗

arXiv2025

Effect of dark matter halo environment on GW memory signal

In this paper, we study the gravitational wave (GW) memory effect for a black hole embedded in a dark matter halo described by a Hernquist-type density profile, both with and without a spike. We first solve the geodesic equations in this spacetime under the influence of a GW pulse to examine how the combined effects of the dark matter halo and the GW pulse modify the geodesic deviation equation and particle trajectories. We then investigate how the memory effect manifests in the waveform in the presence of the dark matter halo. To do that, we analyze the memory contribution at asymptotic null infinity using the Bondi-Sachs formalism and, in particular, the Bondi-Metzner-Sachs (BMS) flux balance laws associated with BMS symmetries. This framework allows us to quantify the GW memory contribution to the waveform, incorporate it into the ringdown waveform templates, and thereby provide a possible avenue for extracting information about the dark matter halo parameters.

gr-qc↗

arXiv2025

Primes and polygonal numbers

A linear combination $aT_r(m)+bT_s(n)$ of an \mbox{$r$-gonal} number $T_r(m)$ and an $s$-gonal number $T_s(n)$ with mutually coprime positive integer coefficients $a$ and $b$ produces infinitely many primes as $m$ and~$n$ varies over the natural numbers, whereas the sum of the reciprocals of such primes converges unless $T_r(m)=m^2$ and $T_s(n)=n^2$. For each pair of coprime positive integers $a$ and $b$, there are arbitrary long arithmetic progressions among the primes of the form $am^2+bn^2$.

math.NT↗

arXiv2025

A White Paper on The Multi-Messenger Science Landscape in India

The multi-messenger science using different observational windows to the Universe such as Gravitational Waves (GWs), Electromagnetic Waves (EMs), Cosmic Rays (CRs), and Neutrinos offer an opportunity to study from the scale of a neutron star to cosmological scales over a large cosmic time. At the smallest scales, we can explore the structure of the neutron star and the different energetics involved in the transition of a pre-merger neutron star to a post-merger neutron star. This will open up a window to study the properties of matter in extreme conditions and a guaranteed discovery space. On the other hand, at the largest cosmological scales, multi-messenger observations allow us to study the long-standing problems in physical cosmology related to the Hubble constant, dark matter, and dark energy by mapping the expansion history of the Universe using GW sources. Moreover, the multi-messenger studies of astrophysical systems such as white dwarfs, neutron stars, and black holes of different masses, all the way up to a high redshift Universe, will bring insightful understanding into the physical processes associated with them that are inaccessible otherwise. This white paper discusses the key cases in the domain of multi-messenger astronomy and the role of observatories in India which can explore uncharted territories and open discovery spaces in different branches of physics ranging from nuclear physics to astrophysics.

astro-ph.HE↗

arXiv2025

Probing Chaos in Schwarzschild-de Sitter Spacetime: The Role of Black Hole and Cosmological Horizons

In this paper, we study the motion of a massless, chargeless particle in Schwarzschild-de Sitter spacetime, revealing exponential radial growth and potential chaos in an integrable system. Poincaré sections show regular Kolmogorov-Arnold-Moser (KAM) tori when black hole and cosmological horizons are distant, but distortions and chaos emerge as they converge. As the horizons coincide, the Poincaré sections fully contract and vanish, marking the system's transition to Nariai spacetime. \textit{Our analysis also suggests that, within the parameter range explored, the event horizon exerts a comparatively more substantial chaotic influence on the system, primarily due to its consistent proximity.} Additionally, we analyze the Lyapunov exponents to quantify the degree of chaos in the system. Our findings indicate that as the closeness of the two horizons increases, the most prominent Lyapunov exponent also increases, signifying a rise in chaotic behavior. By examining the long-term saturation values of the Lyapunov exponents, we confirm that they consistently comply with the Maldacena-Shenker-Stanford (MSS) bound.

gr-qc↗

arXiv2024

Gravitational memory signal from neutrino self-interactions in supernova

Neutrinos with large self-interactions, arising from exchange of light scalars or vectors with mass $M_ϕ\simeq 10{\rm MeV}$, can play a useful role in cosmology for structure formation and solving the Hubble tension. It has been proposed that large self-interactions of neutrinos may change the observed properties of supernova like the neutrino luminosity or the duration of the neutrino burst. In this paper, we study the gravitational wave memory signal arising from supernova neutrinos. Our results reveal that memory signal for self-interacting neutrinos are weaker than free-streaming neutrinos in the high frequency range. Implications for detecting and differentiating between such signals for planned space-borne detectors, DECIGO and BBO, are also discussed.

gr-qc↗

arXiv2024

Cosmic Acceleration and the notion of Alternative Vacuum in Nash Theory

We argue that Nash theory, a quadratic theory of Gravity, can describe a late-time cosmic acceleration without any exotic matter or cosmological constant. The observational viability of an exact cosmological solution of Nash theory is adjudged using a Markov chain Monte Carlo simulation and JLA+OHD+BAO data sets. Departures from standard ΛCDM cosmology are noted and analyzed. We prove that the Nash vacuum dynamics is equivalent to the dynamics of an Einstein vacuum plus a self-interacting Higgs scalar field, only if a mild evolution of the Higgs Vacuum Expectation Value is allowed. This leads to variations in the mass scales of fundamental particles and the fine structure constant. The variations are found to fit nicely with the analysis of molecular absorption spectra from a series of Quasars.

gr-qc↗

arXiv2024

Sengupta Transformations and Carrollian Relativistic Theory

A detailed and systematic formulation of Carrollian relativity is provided. Based on the transformations, first provided by Sengupta [19], we construct a mapping between Lorentz relativistic and Carrollian relativistic vectors. Using this map the Carroll theory is built from the standard Maxwell action. We show that we get self-consistent equations of motion from the action, both in electric and magnetic limits. We introduce Carroll electric and magnetic fields. A new set of maps is derived that connects Carroll electric and magnetic fields with the usual Maxwell ones and yields Carroll equations in terms of fields. Consistency of results with the potential formulation is shown. Carroll version of symmetries like duality, gauge, shift, Noether and boost are treated in details and their implications elaborated. Especially, boost symmetry provides a link to the various maps used in this paper.

hep-th↗

arXiv2024

Formulation of Galilean relativistic Born-Infeld theory

In this paper, we formulate, for the first time, in a systematic manner, Galilean relativistic Born-Infeld action in detail. Exploiting maps connecting Lorentz relativistic and Galilean relativistic vectors, we construct the two limits (electric and magnetic) of Galilean relativistic Born-Infeld action from usual relativistic Born-Infeld theory. An action formalism is thereby derived. From this action, equations of motion are obtained either in the potential or field formulation. Galilean version of duality transformations involving the electric and magnetic fields are defined. They map the electric limit relations to the magnetic ones and vice-versa, exactly as happens for Galilean relativistic Maxwell theory. We also explicitly show the Galilean boost and gauge invariances of the theory in both limits.

hep-th↗

arXiv2023

Action principle of Galilean relativistic Proca theory

In this paper, we discuss Galilean relativistic Proca theory in detail. We first provide a set of mapping relations, derived systematically, that connect the covariant and contravariant vectors in the Lorentz relativistic and Galilean relativistic formulations. Exploiting this map, we construct the two limits of Galilean relativistic Proca theory from usual Proca theory in the potential formalism for both contravariant and covariant vectors which are now distinct entities. An action formalism is thereby derived from which the field equations are obtained and their internal consistency is shown. Next we construct Noether currents and show their on-shell conservation. We introduce analogues of Maxwell's electric and magnetic fields and recast the entire analysis in terms of these fields. Explicit invariance under Galilean transformations is shown for both electric/magnetic limits. We then move to discuss Stuckelberg embedded Proca model in the Galilean framework.

hep-th↗

arXiv2023

Gravitational wave memory for a class of static and spherically symmetric spacetimes

This article aims at comparing gravitational wave memory effect in a Schwarzschild spacetime with that of other compact objects with static and spherically symmetric spacetime, with the purpose of proposing a procedure for differentiating between various compact object geometries. We do this by considering the relative evolution of two nearby test geodesics with in different backgrounds in the presence and absence of a gravitational wave pulse and comparing them. Memory effect due to a gravitational wave would ensure that there is a permanent effect on each spacetime and the corresponding geodesic evolution, being metric dependent, would display distinct results in each case. For a complete picture, we have considered both displacement and velocity memory effect in each geometry.

gr-qc↗

arXiv2023

New formulation of Galilean relativistic Maxwell theory

In this paper, we discuss Galilean relativistic Maxwell theory in detail. We first provide a set of mapping relations, derived systematically, that connect the covariant and contravariant vectors in the Lorentz relativistic and Galilean relativistic formulations. Exploiting this map, we construct the two limits of Galilean relativistic Maxwell theory from usual Maxwell's theory in the potential formalism for both contravariant and covariant vectors which are now distinct entities. Field equations are derived and their internal consistency is shown. The entire analysis is then performed in terms of electric and magnetic fields for both covariant and contravariant components. Duality transformations and their connection with boost symmetry are discussed which reveal a rich structure. The notion of twisted duality is introduced. Next we consider gauge symmetry, construct Noether currents and show their on-shell conservation. We also discuss shift symmetry under which the Lagrangian is invariant, where the corresponding currents are now on-shell conserved. At the end we analyse the theory by including sources for both contravariant and covariant sectors. We show that sources are now off-shell conserved

hep-th↗

arXiv2022

Gravitational wave memory in wormhole spacetimes

Gravitational wave memory is studied in the context of a certain class of braneworld wormholes. Unlike other wormhole geometries, this novel class of wormholes do not require any exotic matter fields for its traversability. First, we study geodesics in this wormhole spacetime, in the presence of a gravitational wave pulse. The resulting evolution of the geodesic separation shows the presence of displacement and velocity memory effects. Motivated by the same, we study the memory effects at null infinity using the Bondi-Sachs formalism, adapted for braneworld wormhole. Our analysis provides a non-trivial change of the Bondi mass after the passage of a burst of gravitational radiation and hence manifests the memory effect at null infinity. In both of these exercises, the presence of extra dimension and the wormhole nature of the spacetime geometry gets imprinted in the memory effect. Since future gravitational wave detectors will be able to probe the memory effect, the present work provides another avenue to search for compact objects other than black holes.

gr-qc↗

arXiv2021

Perturbations of giant magnons and single spikes in $\mathbb R \times S^2$

Perturbations of giant magnons and single spikes in a $2+1$ dimensional $\mathbb R \times S^2$ background spacetime are analysed. Using the form of the giant magnon solution in the Jevicki-Jin gauge,the well-known Jacobi equation for small normal deformations of an embedded time-like surface are written down. Surprisingly, this equation reduces to a simple wave equation in a Minkowski background. The finiteness of perturbations and the ensuing stability of such giant magnons under small deformations are then discussed. It turns out that only the zero mode has finite deformations and is stable. Thereafter, we move on to explore the single spike solution in the Jevicki-Jin gauge. We obtain and solve the perturbation equation numerically and address stability issues.

hep-th↗

arXiv2019

Irreducibility of a holomorphic eta quotient is determinable

We show that a holomorphic eta quotient has only finitely many factors. We also provide an algorithm for checking irreducibility of holomorphic eta quotients by constructing an upper bound for the minimum of the levels of the proper factors of a reducible holomorphic eta quotient.

math.NT↗

arXiv2018

Perturbations of spiky strings in AdS3

Perturbations of a class of semiclassical spiky strings in three dimensional Anti-de Sitter (AdS) spacetime, are investigated using the well-known Jacobi equations for small, normal deformations of an embedded timelike surface. We show that the equation for the perturbation scalar which governs the behaviour of such small deformations, is a special case of the well-known Darboux-Treibich-Verdier (DTV) equation. The eigenvalues and eigensolutions of the DTV equation for our case are obtained by solving certain continued fractions numerically. These solutions are thereafter utilised to further demonstrate that there do exist finite perturbations of the AdS spiky strings. Our results therefore establish that the spiky string configurations in AdS3 are indeed stable against small fluctuations. Comments on future possibilities of work are included in conclusion.

hep-th↗

arXiv2017

Finiteness of irreducible holomorphic eta quotients of a given level

We show that for any positive integer $N$, there are only finitely many holomorphic eta quotients of level $N$, none of which is a product of two holomorphic eta quotients other than 1 and itself. This result is an analog of Zagier's conjecture/ Mersmann's theorem which states that: Of any given weight, there are only finitely many irreducible holomorphic eta quotients, none of which is an integral rescaling of another eta quotient. We construct such eta quotients for all cubefree levels. In particular, our construction demonstrates the existence of irreducible holomorphic eta quotients of arbitrarily large weights.

math.NT↗