arXiv subjects

Sandip Chowdhury

Publications and source records attributed to Sandip Chowdhury.

5 recordsLinked to original sources

arXiv2022

Non-linear density-velocity dynamics in $f(R)$ gravity from spherical collapse

We investigate the joint density-velocity evolution in $f(R)$ gravity using smooth, compensated spherical top-hats as a proxy for the non-linear regime. Using the Hu-Sawicki model as a working example, we solve the coupled continuity, Euler and Einstein equations using an iterative hybrid Lagrangian-Eulerian scheme. The novel aspect of this scheme is that the metric potentials are solved for analytically in the Eulerian frame. The evolution is assumed to follow GR at very early epochs and switches to $f(R)$ at a pre-determined epoch. Choosing the `switching epoch' too early is computationally expensive because of high frequency oscillations; choosing it too late potentially destroys consistency with $Λ$CDM. To make an informed choice, we perform an eigenvalue analysis of the background model which gives a ballpark estimate of the magnitude of oscillations. There are two length scales in the problem: the comoving Compton wavelength of the associated scalar field and the width of the top-hat. The evolution is determined by their ratio. When the ratio is large, the evolution is scale-independent and the density-velocity divergence relation (DVDR) is unique. When the ratio is small, the evolution is very close to GR, except for the formation of a spike near the top-hat edge, a feature which has been noted in earlier literature. We are able to qualitatively explain this feature in terms of the analytic solution for the metric potentials, in the absence of the chameleon mechanism. In the intermediate regime, the evolution is profile-dependent and no unique DVDR exists.

astro-ph.CO↗

arXiv2021

Quantum potential in dust collapse with a negative cosmological constant

In the functional Schrodinger formalism, we obtain the wave function describing collapsing dust in an anti-de Sitter background, as seen by a co-moving observer, by mapping the resulting variable mass Schrodinger equation to that of the quantum isotonic oscillator. Using this wave function, we perform a causal de Broglie-Bohm analysis, and obtain the corresponding quantum potential. We construct a bouncing geometry via a disformal transformation, incorporating quantum effects. We derive the external solution that matches with this smoothly, and is also quantum corrected. Due to a pressure term originating from the quantum potential, an initially collapsing solution with a negative cosmological constant bounces back after reaching a minimum radius, and thereby avoids the classical singularity predicted by general relativity.

gr-qc↗

arXiv2021

Disformal transformations and the motion of a particle in semi-classical gravity

The approach to incorporate quantum effects in gravity by replacing free particle geodesics with Bohmian non-geodesic trajectories has an equivalent description in terms of a conformally related geometry, where the motion is force free, with the quantum effects inside the conformal factor, i.e., in the geometry itself. For more general disformal transformations relating gravitational and physical geometries, we show how to establish this equivalence by taking the quantum effects inside the disformal degrees of freedom. We also show how one can solve the usual problems associated with the conformal version, namely the wrong continuity equation, indefiniteness of the quantum mass, and wrong description of massless particles in the singularity resolution argument, by using appropriate disformal transformations.

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↗

arXiv2015

Zitterbewegung of a heavy hole in presence of spin-orbit interactions

We study the $zitterbewegung$ of a heavy hole in presence of both cubic Rashba and cubic Dresselhaus spin-orbit interactions. On contrary to the electronic case, $zitterbewegung$ does not vanish for equal strength of Rashba and Dresselhaus spin-orbit interaction. This non-vanishing of $zitterbewegung$ is associated with the Berry phase. Due to the presence of the spin-orbit coupling the spin associated with the heavy hole precesses about an effective magnetic field. This spin precession produces a transverse spin-orbit force which also generates an electric voltage associated with $zitterbewegung$. We have estimated the magnitude of this voltage for a possible experimental detection of $zitterbewegung$.

cond-mat.mes-hall↗