arXiv subjects

Tapobrata Sarkar

Publications and source records attributed to Tapobrata Sarkar.

At least 55 records · Page 3Linked to original sources

arXiv2020

Complexity and information geometry in spin chains

We study Nielsen complexity and Fubini-Study complexity for a class of exactly solvable one dimensional spin systems. Our examples include the transverse XY spin chain and its natural extensions, the quantum compass model with and without an external magnetic field. We obtain the scaling behaviour of both complexities near quantum phase transitions in the thermodynamic limit, as a function of the system parameters. We provide analytical proofs of these, in an information geometric framework, which verify our numerical analysis. The scaling of the Nielsen complexity with the system size is also established, close to criticality. We also obtain analytic expressions for the Fubini-Study complexity in some special cases for all the models, while a numerical analysis in more generic situations is carried out. Our study clearly demonstrates the differences in the two notions of complexity in quasi-free fermionic systems.

cond-mat.stat-mech↗

arXiv2020

Modified gravity in the interior of population II stars

We study the effects of a beyond-Horndeski theory of modified gravity in the interior of a population II star. We consider a simple phenomenological model of a $1.1M_{\odot}$ star that has left the main sequence, has a thin Hydrogen burning shell with a partially degenerate isothermal core, surrounded by a radiative envelope having two regions of distinct opacities. Using suitable matching conditions at the two internal boundaries, a numerical analysis of the resulting stellar equations in modified gravity is carried out. While overall, gravity may be weakened, resulting in a decrease of the luminosity and an increase of the radius of the star, these effects are reversed near the core. It is suggested how the model, within its limitations, can yield a bound on the modified gravity parameter.

gr-qc↗

arXiv2020

Constraining modified gravity from tidal phenomena in binary stars

In beyond-Horndeski theories of gravity, the Vainshtein screening mechanism might only be partially effective inside stellar objects. This results in a modification of the pressure balance equation inside stars, often characterized by a single parameter ($Υ$) in isotropic systems. We show how to constrain such theories of modified gravity, using tidal effects. We study such effects in cataclysmic variable star binaries and numerically obtain limits on the critical masses of the donor stars, below which they are tidally disrupted, by modeling them in beyond-Horndeski theories. This is contrasted with values of the donor masses, obtained using existing observational data, by a Monte Carlo error progression method. A best fit scenario of the two yields a parametric constraint in the theories that we consider, within the approximations used. Here, we obtain the allowed range $ 0 \le Υ\le 0.47 $.

astro-ph.SR↗

arXiv2020

New class of naked singularities and their observational signatures

By imposing suitable junction conditions on a space-like hyper-surface, we obtain a two-parameter family of possible static configurations from gravitational collapse. These exemplify a new class of naked singularities. We show that these admit a consistent description via a two-fluid model, one of which might be dust. We then study lensing and accretion disk properties of our solution and point out possible differences with black hole scenarios. The distinctive features of our solution, compared to the existing naked singularity solutions in the literature are discussed.

gr-qc↗

arXiv2019

The geometry of RN-AdS fluids

We establish the parameter space geometry of a fluid system characterized by two constants, whose equation of state mimics that of the RN-AdS black hole. We call this the RN-AdS fluid. We study the scalar curvature on the parameter space of this system, and show its equivalence with the RN-AdS black hole, in the limit of vanishing specific heat at constant volume. Further, an analytical construction of the Widom line is established. We also numerically study the behavior of geodesics on the parameter space of the fluid, and find a geometric scaling relation near its second order critical point.

hep-th↗

arXiv2019

Tidal disruption near black holes and their mimickers

Black holes and wormholes are solutions of Einstein's field equations, both of which, from afar, look like a central mass. We show here that although at large distances both behave like Newtonian objects, close to the event horizon or to the throat, black holes and wormholes have different tidal effects on stars, due to their respective geometries. We quantify this difference by a numerical procedure in the Schwarzschild black hole and the exponential wormhole backgrounds, and compare the peak fallback rates of tidal debris in these geometries. The tidal disruption rates in these backgrounds are also computed. It is shown that these quantities are a few times higher for wormholes, compared to the black hole cases.

astro-ph.HE↗

arXiv2019

Observational signatures of wormholes with thin accretion disks

We numerically construct images of thin accretion disks in rotating wormhole backgrounds, for the Kerr-like and the Teo class of wormholes. Our construction is illustrated by two methods, a semi-analytic scheme where separated null geodesic equations obtained by analytically integrating the second order equations once are used, as well as by a numerical ray-tracing method utilizing a fourth order Runge-Kutta algorithm. Our result shows dramatic differences between accretion disk images in wormhole backgrounds, compared to black hole ones, specifically because a wormhole can in principle have accretion disks on both sides of its throat. We establish the nature of the images if the observer and the disk are on two opposite sides of the throat, and show that these can provide conclusive observational evidence of wormhole geometries.

gr-qc↗

arXiv2019

Collapse in $f(R)$ gravity and the method of $R$ matching

Collapsing solutions in $f(R)$ gravity are restricted due to junction conditions that demand continuity of the Ricci scalar and its normal derivative across the time-like collapsing hypersurface. These are obtained via the method of $R$-matching, which is ubiquitous in $f(R)$ collapse scenarios. In this paper, we study spherically symmetric collapse with the modification term $αR^2$, and use $R$-matching to exemplify a class of new solutions. After discussing some mathematical preliminaries by which we obtain an algebraic relation between the shear and the anisotropy in these theories, we consider two metric ansatzes. In the first, the collapsing metric is considered to be a separable function of the co-moving radius and time, and the collapse is shear-free, and in the second, a non-separable interior solution is considered, that represents gravitational collapse with non-zero shear viscosity. We arrive at novel solutions that indicate the formation of black holes or locally naked singularities, while obeying all the necessary energy conditions. The separable case allows for a simple analytic expression of the energy-momentum tensor, that indicates the positivity of the pressures throughout collapse, and is further used to study the heat flux evolution of the collapsing matter, whose analytic solutions are presented under certain approximations. These clearly highlight the role of modified gravity in the examples that we consider.

gr-qc↗

arXiv2019

Analytical approach to strong gravitational lensing from ultracompact objects

Strong gravitational lensing from black holes results in the formation of relativistic images, in particular, relativistic Einstein rings. For objects with event horizons, the radius of the unstable light ring (photon sphere) is the lowest radius at which a relativistic image might be formed. For horizonless ultracompact objects, additional relativistic images and rings can form inside this radius. In this paper, we provide an analytical approach to deal with strong gravitational lensing from such ultracompact objects, which is substantially different from the black hole cases, first reported by Bozza. Here, our analysis indicates that the angular separations and magnifications of relativistic images inside the unstable light ring (photon sphere) might be several orders of magnitude higher compared to the ones outside it. This indicates fundamental differences in the nature of strong gravitational lensing from black holes and ultracompact objects.

gr-qc↗

arXiv2019

Tidal effects away from the equatorial plane in Kerr backgrounds

We study tidal effects on self-gravitating Newtonian stars rotating around a Kerr black hole in stable circular orbits away from the equatorial plane. Such cases are exemplified by a non-vanishing Carter's constant. Here, we calculate the tidal disruption limit (Roche limit) of the star numerically, in Fermi normal coordinates. The Roche limit is found to depend strongly on the choice of the orbit, and differs significantly from the equatorial plane result as one approaches nearly polar orbits. As expected, this difference is large when the star is close to the black hole (near to the innermost stable circular orbit) and becomes smaller when the star is far from it. We also discuss the dependence of the Roche limit on the equation of state of the star, taking two specific parameter values as examples.

gr-qc↗

arXiv2018

A novel gravitational lensing feature by wormholes

Horizonless compact objects with light rings (or photon spheres) are becoming increasingly popular in recent years for several reasons. In this paper, we show that a horizonless object such as a wormhole of Morris-Thorne type can have two photon spheres. In particular, we show that, in addition to the one present outside a wormhole throat, the throat can itself act as an effective photon sphere. Such wormholes exhibit two sets of relativistic Einstein ring systems formed due to strong gravitational lensing. We consider a previously obtained wormhole solution as a specific example. If such type of wormhole casts a shadow at all, then the inner set of the relativistic Einstein rings will form the outer bright edge of the shadow. Such a novel lensing feature might serve as a distinguishing feature between wormholes and other celestial objects as far as gravitational lensing is concerned.

gr-qc↗

arXiv2018

Small Anisotropy in Stellar Objects in Modified Theories of Gravity

Interior structures of stellar objects might have small pressure anisotropy due to several reasons, including rotation and the presence of magnetic fields. Here, retaining the approximation of spherical symmetry, we study the possible role of small anisotropy in stellar interiors in theories of modified gravity, that are known to alter the hydrostatic equilibrium condition inside stars. We show how anisotropy may put lower and upper bounds on the modified gravity parameter depending on the polytropic equation of state, and determine them numerically. We also study the mass of stellar objects in these theories, assuming such equations of state, and find that the Chandrasekhar mass limit in white dwarf stars gets substantially modified compared to the isotropic case, even without assuming the presence of extreme magnetic fields. Effects of small pressure anisotropy on the Hydrogen burning limit in low mass stars are also briefly commented upon. It is shown that here the isotropic case can predict a theoretical lower bound on the scalar tensor parameter, in addition to a known upper bound.

astro-ph.SR↗

arXiv2018

On Strong Gravitational Lensing in Rotating Galactic Space-times

We study strong gravitational lensing in rotating space-times which can be thought of as realistic galactic models in General Relativity. To this end, using the Newman-Janis algorithm, we first obtain a rotating version of a static galactic metric advanced by Bharadwaj and Kar. This is matched with a generic external Kerr solution without a slowly-rotating approximation. Next, we construct a rotating version of Perlick's Bertrand space-times and establish this as a new rotating solution of Einstein's equations where each spatial radius admits a stable circular orbit. A rotating generalization of a strong lensing formalism due to Perlick is then applied to the rotating Bharadwaj-Kar metric and the differences with lensing in the purely Kerr background (for a Kerr black hole at the galactic center) is pointed out. Then, arguing that a rotating Bertrand space-time might be a realistic galactic model away from the galactic center, strong lensing is studied in this situation where the central singularity is naked. Possible observational signatures are elaborated upon, which might be useful in distinguishing black holes from naked singularities.

gr-qc↗

arXiv2017

Massless fermions in null Fermi coordinates and an application to analog gravity in $\text{He}^3$-A

Bogoliubov quasiparticles moving in the background of superfluid $\text{He}^3$-A see an apparently curved space-time metric when the background superfluid vacuum is in motion. We study how this curvature couples with the spins of the effectively massless quasiparticles. First, we set up the problem in null Fermi coordinates for radial as well as circular geodesics and then use it in the context of the analog metric seen by the quasiparticles. We obtain an effective magnetic interaction due to curvature coupling, and provide numerical estimates. Some possible implications of these results are then pointed out.

gr-qc↗

arXiv2017

On subregion holographic complexity and renormalization group flows

We investigate subregion holographic complexity in the context of renormalization group flow geometries. We use both the Poincaŕe slicing and the Janus ansatz as holographic duals to renormalization group flows in the boundary conformal field theory. In the former metric, subregion complexity is computed for a disc and a strip shaped entangling region. For the disc shaped region, consistent emergence of length scales for flow to the deep infra-red is established. For strip shaped regions, we find that complexity cannot locate holographic phase transitions in a sharp domain wall scenario. For smooth domain walls, we find that the complexity might be an indicator of such phase transitions, and give numerical evidence that its derivative changes sign across a transition. Finally, the complexity is computed numerically using the Janus ansatz.

hep-th↗

arXiv2017

Distinguishing between Kerr and rotating JNW space-times via frame dragging and tidal effects

In this paper, we first investigate some aspects of frame dragging in strong gravity. The computations are carried out for the Kerr black hole and for the rotating Janis-Newman-Winicour solution, that is known to have a naked singularity on a surface at a finite radius. For the Kerr metric, a few interesting possibilities of gyroscope precession frequency, as measured by a Copernican observer outside the ergoregion, are pointed out. It is shown that for certain angular velocities of a stationary observer, this frequency might vanish exactly, close to the ergoregion. Similar computations are repeated for static observers in the naked singularity background, and strong enhancement of the Lense-Thirring precession frequency compared to the black hole case is established. Then, we study the nature of tidal forces in the rotating naked singularity background, in Fermi normal coordinates. Here, physical quantities characterizing tidal disruptions of celestial objects in equatorial circular orbits are computed numerically. Our results here indicate that there might be significant deviations from corresponding Kerr black hole calculations, up to the level of approximation that we consider.

gr-qc↗

arXiv2017

Self-gravitating fluid systems and galactic dark matter

We study gravitational collapse with anisotropic pressures, whose end stage can mimic space-times that are seeded by galactic dark matter. To this end, we identify a class of space-times (with conical defects) that can arise out of such a collapse process, and admit stable circular orbits at all radial distances. These have a naked singularity at the origin. An example of such a space-time is seen to be the Bertrand space-time discovered by Perlick, that admits closed, stable orbits at all radii. Using relativistic two- fluid models, we show that our galactic space-times might indicate exotic matter, i.e one of the component fluids may have negative pressure for a certain asymptotic fall off of the associated mass density, in the Newtonian limit. We complement this analysis by studying some simple examples of Newtonian two-fluid systems, and compare this with the Newtonian limit of the relativistic systems considered.

astro-ph.GA↗

arXiv2017

On Holographic Rényi Entropy in Some Modified Theories of Gravity

We perform a detailed analysis of holographic entanglement Rényi entropy in some modified theories of gravity with four dimensional conformal field theory duals. First, we construct perturbative black hole solutions in a recently proposed model of Einsteinian cubic gravity in five dimensions, and compute the Rényi entropy as well as the scaling dimension of the twist operators in the dual field theory. Consistency of these results are verified from the AdS/CFT correspondence, via a corresponding computation of the Weyl anomaly on the gravity side. Similar analyses are then carried out for three other examples of modified gravity in five dimensions that include a chemical potential, namely Born-Infeld gravity, charged quasi-topological gravity and a class of Weyl corrected gravity theories with a gauge field, with the last example being treated perturbatively. Some interesting bounds in the dual conformal field theory parameters in quasi-topological gravity are pointed out. We also provide arguments on the validity of our perturbative analysis, whenever applicable.

hep-th↗