arXiv subjects

Sumanta Chakraborty

Publications and source records attributed to Sumanta Chakraborty.

At least 109 records · Page 6Linked to original sources

arXiv2018

Inverting a normal harmonic oscillator: Physical interpretation and applications

A harmonic oscillator with time-dependent mass $m(t)$ and a time-dependent (squared) frequency $ω^2(t)$ occurs in the modelling of several physical systems. It is generally believed that systems, with $m(t)>0$ and $ω^2(t)>0$ (normal oscillator) are stable while systems with $m(t)>0$ and $ω^2(t)<0$ (inverted oscillator) are unstable. We show that it is possible to represent the \textit{same} physical system either as a normal oscillator or as an inverted oscillator by redefinition of dynamical variables. While we expect the physics to be invariant under such redefinitions, it is not obvious how this invariance actually comes about. We study the relation between these two, normal and inverted, representations of an oscillator in detail both in Heisenberg and Schrödinger pictures to clarify several conceptual and technical issues. The situation becomes more involved when the oscillator is coupled to another (semi)classical degree of freedom $C(t)$ and we want to study the back-reaction of the quantum system $q(t)$ on $C(t)$, in the semi-classical approximation. We provide a simple prescription for the back-reaction based on energy conservation and study that the dynamics of the full system in both normal and the inverted oscillator representation. The physics again remains invariant but there are some extra subtleties which we clarify. The implications of these results for quantum field theory in cosmological backgrounds are discussed briefly in an appendix.

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arXiv2018

Horndeski theories confront the Gravity Probe B experiment

In this work we have investigated various properties of a spinning gyroscope in the context of Horndeski theories. In particular, we have focused on two specific situations --- (a) when the gyroscope follows a geodesic trajectory and (b) when it is endowed with an acceleration. In both these cases, besides developing the basic formalism, we have also applied the same to understand the motion of a spinning gyroscope in various static and spherically symmetric spacetimes pertaining to Horndeski theories. Starting with the Schwarzschild de-Sitter spacetime as a warm up exercise, we have presented our results for two charged Galileon black holes as well as for a black hole in scalar coupled Einstein-Gauss-Bonnet gravity. In all these cases we have shown that the spinning gyroscope can be used to distinguish black holes from naked singularities. Moreover, using the numerical estimation of the geodetic precession from the Gravity Probe B experiment, we have constrained the gauge/scalar charge of the black holes in these Horndeski theories. Implications are also discussed.

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arXiv2018

Signatures of extra dimensions in gravitational waves from black hole quasi-normal modes

In this work we have derived the evolution equation for gravitational perturbation in four dimensional spacetime in presence of a spatial extra dimension. The evolution equation is derived by perturbing the \emph{effective} gravitational field equations on the four dimensional spacetime, which inherits non-trivial higher dimensional effects. Note that this is \emph{different} from the perturbation of the five dimensional gravitational field equations, existing in literature, and possess quantitatively new features. The gravitational perturbation has further been decomposed into a purely four dimensional part and another piece that depends on extra dimensions. The four dimensional gravitational perturbation now admits massive propagating degrees of freedom, owing to the existence of higher dimensions. We have also studied the influence of these massive propagating modes on the quasi-normal mode frequencies, signaling the higher dimensional nature of the spacetime, and have contrasted these massive modes with the massless modes in general relativity. Surprisingly, it turns out that the massive modes experience much smaller damping compared to the massless modes in general relativity and may even \emph{dominate} over and above the general relativity contribution if one observes the ringdown phase of a black hole merger event at sufficiently late times. Furthermore, the whole analytical framework has been supplemented by the fully numerical Cauchy evolution problem as well. In this context we have shown that except for minute details the overall features of the gravitational perturbations are captured in both the Cauchy evolution as well as in the analysis of quasi-normal modes. The implications on observations of black holes with LIGO and proposed space missions like LISA are also discussed.

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arXiv2018

Unruh effect for inertial observers through vacuum correlations

We study a dynamic version of the Unruh effect in a two dimensional collapse model forming a black hole. In this two-dimensional collapse model a scalar field coupled to the dilaton gravity, moving leftwards, collapses to form a black hole. There are two sets of asymptotic ($t\to\infty$) observers, around $x\to\infty$ and $x\to-\infty$. The observers at the right null infinity witness a thermal flux of radiation associated with time dependent geometry leading to a black hole formation and its subsequent Hawking evaporation, in an expected manner. We show that even the observers at left null infinity find themselves in thermal ambiance, without experiencing any change of spacetime geometry all along their trajectories. They remain as inertial observers in a \emph{flat} region of spacetime where curvature tensor identically vanishes in a portion of full spacetime. These observers find the state of the quantum field in a late time thermal configuration, with \emph{exactly the same} temperature as measured by the observers at right null infinity, {\it despite being inertial in flat spacetime region throughout their history}. This is very closely related to the standard Unruh effect in the flat spacetime, except for a key difference --- since they are inertial throughout and {\it have no causally connected source in the past light cone to account for what they see}. The result arises from quantum correlations which extend outside the past light cone and is conceptually similar to the EPR correlations.

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arXiv2018

Packing extra mass in compact stellar structures: An interplay between Kalb-Ramond field and extra dimensions

We have derived the Buchdahl's limit for a relativistic star in presence of the Kalb-Ramond field in four as well as in higher dimensions. It turns out that the Buchdahl's limit gets severely affected by the inclusion of the Kalb-Ramond field. In particular, the Kalb-Ramond field in four spacetime dimensions enables one to pack extra mass in any compact stellar structure of a given radius. On the other hand, a completely opposite picture emerges if the Kalb-Ramond field exists in higher dimensions, where the mass content of a compact star is smaller compared to that in general relativity. Implications are discussed.

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arXiv2018

Field equations for Lovelock gravity: An alternative route

We present an alternative derivation of the gravitational field equations for Lovelock gravity starting from the Newton's law, which is closer in spirit to the thermodynamic description of gravity. As a warm up exercise, we have explicitly demonstrated that projecting the Riemann curvature tensor appropriately and taking a cue from Poisson's equation, the Einstein's equations immediately follow. The above derivation naturally generalizes to Lovelock gravity theories where an appropriate curvature tensor satisfying the symmetries as well as the Bianchi derivative properties of the Riemann tensor has to be used. Interestingly, in the above derivation, the thermodynamic route to gravitational field equations, suited for null hypersurfaces, emerge quiet naturally.

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arXiv2018

1/r potential in higher dimensions

In Einstein gravity, gravitational potential goes as $1/r^{d-3}$ in $d$ non-compactified spacetime dimensions, which assumes the familiar $1/r$ form in four dimensions. On the other hand, it goes as $1/r^α$, with $α=(d-2m-1)/m$, in pure Lovelock gravity involving only one $m$th order term of the Lovelock polynomial in the gravitational action. The latter offers a novel possibility of having $1/r$ potential for the non-compactified dimension spectrum given by $d=3m+1$. Thus it turns out that in the two prototype gravitational settings of isolated objects, like black holes and the universe as a whole --- cosmological models, the Einstein gravity in four and $m$th order pure Lovelock gravity in $3m+1$ dimensions behave in a similar fashion as far as gravitational interactions are considered. However propagation of gravitational waves (or the number of degrees of freedom) does indeed serve as a discriminator because it has two polarizations only in four dimensions.

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arXiv2017

Excavating black hole continuum spectrum: Possible signatures of scalar hairs and of higher dimensions

Continuum spectrum from black hole accretion disc holds enormous information regarding the strong gravity regime around the black hole and hence about the nature of gravitational interaction in extreme situations. Since in such strong gravity regime the dynamics of gravity should be modified from the \EH one, its effect should be imprinted on the continuum spectrum originating from the black hole accretion. To explore the effects of these alternative theories on the black hole continuum spectrum in an explicit manner, we have discussed three alternative gravitational models having their origin in three distinct paradigms --- (a) higher dimensions, (b) higher curvature gravity and (c) Horndeski theories. All of them can have signatures sculptured on the black hole continuum spectrum, distinct from the standard general relativistic scenario. Interestingly all these models exhibit black hole solutions with tidal charge parameter which in these alternative gravity scenarios can become negative, in sharp contrast with the Reissner-Nordström black hole. Using the observational data of optical luminosity for eighty Palomer Green quasars we have illustrated that the difference between the theoretical estimates and the observational results gets minimized for negative values of the tidal charge parameter. As a quantitative estimate of this result we concentrate on several error estimators, including reduced $χ^{2}$, Nash-Sutcliffe efficiency, index of agreement etc. Remarkably, all of them indicates a negative value of the tidal charge parameter, signaling the possibility of higher dimensions as well as scalar charge at play in those high gravity regimes.

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arXiv2017

Entropy of a box of gas in an external gravitational field $-$ revisited

Earlier it was shown that the entropy of an ideal gas, contained in a box and moving in a gravitational field, develops an area dependence when it approaches the horizon of a static, spherically symmetric spacetime. Here we extend the above result in two directions; viz., to (a) the stationary axisymmteric spacetimes and (b) time dependent cosmological spacetimes evolving asymptotically to the de Sitter or the Schwarzschild de Sitter spacetimes. While our calculations are exact for the stationary axisymmetric spacetimes, for the cosmological case we present an analytical expression of the entropy when the spacetime is close to the de Sitter or the Schwarzschild de Sitter spacetime. Unlike the static spacetimes, there is no hypersurface orthogonal timelike Killing vector field in these cases. Nevertheless, the results hold and the entropy develops an area dependence in the appropriate limit.

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arXiv2017

Gravity stabilizes itself

We show that a possible resolution to the stabilization of an extra spatial dimension (radion) can be obtained solely in the context of gravitational dynamics itself without the necessity of introducing any external stabilizing field. In this scenario the stabilized value of the radion field gets determined in terms of the parameters appearing in the higher curvature gravitational action. Furthermore, the mass of the radion field and its coupling to the standard model fields are found to be in the weak scale implying possible signatures in the TeV scale colliders. Some resulting implications are also discussed.

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arXiv2017

A Novel Derivation of the Boundary Term for the Action in Lanczos-Lovelock Gravity

We present a novel derivation of the boundary term for the action in Lanczos-Lovelock gravity, starting from the boundary contribution in the variation of the Lanczos-Lovelock action. The derivation presented here is straightforward, i.e., one starts from the Lanczos-Lovelock action principle and the action itself dictates the boundary structure and hence the boundary term one needs to add to the action to make it well-posed. It also gives the full structure of the contribution at the boundary of the complete action, enabling us to read off the degrees of freedom to be fixed at the boundary, their corresponding conjugate momenta and the total derivative contribution on the boundary. We also provide a separate derivation of the Gauss-Bonnet case.

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arXiv2017

Cosmological implications of shift symmetric Galileon field

A ghost-free metric formulation of the recently proposed covariant Galileon model \cite{RPgal} which retains the internal shift symmetry has been constructed. This presents a new result because the covariant Galileon models introduced so far in the literature lacks the full Galileon symmetry. We demonstrate that the same general procedure is applicable to all the Galileon interaction terms and the resulting ghost-free Galileon action respecting internal shift symmetry cannot predict the late time acceleration of the universe. However, weakly breaking the shift symmetry in the covariant Galileon Lagrangian, allows us to include an appropriate potential term which can explain late time acceleration, in accordance with recent findings in the literature.

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arXiv2017

Black Holes: Eliminating Information or Illuminating New Physics?

Black holes, initially thought of as very interesting geometric constructions of nature, over time, have learnt to (often) come up with surprises and challenges. From the era of being described as merely some interesting and exotic solutions of \gr, they have, in modern times, really started to test our confidence in everything else, we thought we know about the nature. They have in this process, also earned a dreadsome reputation in some corners of theoretical physics. The most serious charge on the black holes is that they eat up information, never to release and subsequently erase it. This goes absolutely against the sacred principles of all other branches of fundamental sciences. This realization has shaken the very base of foundational concepts, both in quantum theory and gravity, which we always took for granted. Attempts to exorcise black holes of this charge, have led us to crossroads with concepts, hold dearly in quantum theory. The sphere of black hole's tussle with quantum theory has readily and steadily grown, from the advent of the Hawking radiation some four decades back, into domain of quantum information theory in modern times, most aptly, recently put in the form of the firewall puzzle. Do black holes really indicate something sinister about their existence or do they really take the lid off our comfort with ignoring the fundamental issues, our modern theories are seemingly plagued with? In this review, we focus on issues pertaining to black hole evaporation, the development of the information loss paradox, its recent formulation, the leading debates and promising directions in the community.

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arXiv2017

Strong gravitational lensing --- A probe for extra dimensions and Kalb-Ramond field

Strong field gravitational lensing in the context of both higher spacetime dimensions and in presence of Kalb-Ramond field have been studied. After developing proper analytical tools to analyze the problem we consider gravitational lensing in three distinct black hole spacetimes --- (a) four dimensional black hole in presence of Kalb-Ramond field, (b) brane world black holes with Kalb-Ramond field and finally (c) black hole solution in $f(T)$ gravity. In all the three situations we have depicted the behavior of three observables: the asymptotic position approached by the relativistic images, the angular separation and magnitude difference between the outermost images with others packed inner ones, both numerically and analytically. Difference between these scenarios have also been discussed along with possible observational signatures.

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arXiv2017

Buchdahl compactness limit for a pure Lovelock static fluid star

We obtain the Buchdahl compactness limit for a pure Lovelock static fluid star and verify that the limit following from the uniform density Schwarzschild's interior solution, which is universal irrespective of the gravitational theory (Einstein or Lovelock), is true in general. In terms of surface potential $Φ(r)$, it means at the surface of the star $r=r_{0}$, $Φ(r_{0}) < 2N(d-N-1)/(d-1)^2$ where $d$, $N$ respectively indicate spacetime dimensions and Lovelock order. For a given $N$, $Φ(r_{0})$ is maximum for $d=2N+2$ while it is always $4/9$, Buchdahl's limit, for $d=3N+1$. It is also remarkable that for $N=1$ Einstein gravity, or for pure Lovelock in $d=3N+1$, Buchdahl's limit is equivalent to the criteria that gravitational field energy exterior to the star is less than half its gravitational mass, having no reference to the interior at all.

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arXiv2017

Boundary terms of the Einstein-Hilbert action

The Einstein-Hilbert action for general relativity is not well posed in terms of the metric $g_{ab}$ as a dynamical variable. There have been many proposals to obtain an well posed action principle for general relativity, e.g., addition of the Gibbons-Hawking-York boundary term to the Einstein-Hilbert action. These boundary terms are dependent on what one fixes on the boundary and in particular on spacetime dimensions as well. Following recent works of Padmanabhan we will introduce two new variables to describe general relativity and the action principle with these new dynamical variables will turn out to be well posed. Then we will connect these dynamical variables and boundary term obtained thereof to existing literature and shall comment on a few properties of Einstein-Hilbert action which might have been unnoticed earlier in the literature. Before concluding with future prospects and discussions, we will perform a general analysis of the boundary term of Einstein-Hilbert action for null surfaces as well.

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arXiv2017

Constraining some Horndeski gravity theories

We discuss two spherically symmetric solutions admitted by the Horndeski (or scalar tensor) theory in the context of solar system and astrophysical scenarios. One of these solutions is derived for Einstein-Gauss-Bonnet gravity, while the other originates from the coupling of the Gauss-Bonnet invariant with a scalar field. Specifically, we discuss the perihelion precession and the bending angle of light for these two different spherically symmetric spacetimes derived in references \cite{Maeda:2006hj} and \cite{Sotiriou:2014pfa} respectively. The later in particular, applies only to the black hole spacetimes. We further delineate on the numerical bounds of relevant parameters of these theories from such computations.

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arXiv2016

Kinematics of Radion field: A possible source of dark matter

The discrepancy between observed virial and baryonic mass in galaxy clusters have lead to the missing mass problem. To resolve this, a new, non-baryonic matter field, known as dark matter has been invoked. However, till date no possible constituents of the dark matter components are known. This has led to various models, by modifying gravity at large distances to explain the missing mass problem. The modification to gravity appears very naturally when effective field theory on a lower dimensional manifold, embedded in a higher dimensional spacetime is considered. It has been shown that in a scenario with two lower dimensional manifolds separated by a finite distance is capable to address the missing mass problem, which in turn determines the kinematics of the brane separation. Consequences for galactic rotation curves are also described.

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