arXiv subjects

Sayuri Singh

Publications and source records attributed to Sayuri Singh.

5 recordsLinked to original sources

arXiv2022

Gaussian curvature of spherical shells: A geometric measure of complexity

In this paper we consider a semitetrad covariant decomposition of spherically symmetric spacetimes and find a governing hyperbolic equation of the Gaussian curvature of two dimensional spherical shells, that emerges due to the decomposition. The restoration factor of this hyperbolic travelling wave equation allows us to construct a geometric measure of complexity. This measure depends critically on the Gaussian curvature, and we demonstrate this geometric connection to complexity for the first time. We illustrate the utility of this measure by classifying well known spherically symmetric metrics with different matter distributions. We also define an order structure on the set of all spherically symmetric spacetimes, according to their complexity and physical properties.

gr-qc↗

arXiv2018

Conformal Symmetries of Locally Rotationally Symmetric Spacetimes

In this paper we investigate conformal symmetries in Locally Rotationally Symmetric (LRS) spacetimes using a semitetrad covariant formalism. We demonstrate that a general LRS spacetime which rotates and spatially twists simultaneously has an inherent homothetic symmetry in the plane spanned by the fluid flow lines and the preferred spatial direction. We discuss the nature and consequence of this homothetic symmetry showing that a null Killing horizon arises when the heat flux has an extremal value. We also consider the special case of a perfect fluid and the restriction on the conformal geometry.

gr-qc↗

arXiv2017

Rotating and spatially twisting Locally Rotationally Symmetric Spacetimes in f(R)-Gravity: a No-Go theorem

Recently, in a series of papers, we established the existence and found a general solution for the simultaneously rotating and twisting locally rotationally symmetric spacetimes in general relativity, which can model inhomogeneous and dynamic astrophysical bodies. However, these spacetimes necessarily require imperfect fluids with entropy flux. Therefore, in this paper, we investigate the existence of these spacetimes in generic f(R)-gravity models, where the entropy flux is generated purely by higher order curvature effects, while the standard matter still remains a perfect fluid. However, we transparently demonstrate here, that the symmetries of these spacetimes force the theory to be general relativity. This is a novel study that shows how the geometrical properties of a spacetime can be used to restrict the theories of gravity.

gr-qc↗

arXiv2017

Rotating and twisting locally rotationally symmetric spacetimes: a general solution

In this paper we derive a general solution for the most general rotating and twisting locally rotationally symmetric spacetimes. This is achieved in three steps. First we decompose the manifold via 1+1+2 semi-tetrad formalism that yields a set of geometrical and thermodynamic scalars for the spacetime. We then recast the Einstein field equations in terms of evolution and propagation of these scalars. It is then shown that this class of spacetimes must possess self similarity and we use this property to solve for these scalars, thus obtaining a general solution. This solution has a number of very interesting cosmological or astrophysical consequences which we discuss in detail.

gr-qc↗

arXiv2016

New class of LRS spacetimes with simultaneous rotation and spatial twist

We establish the existence and find the necessary and sufficient conditions for a new class of solutions of Locally Rotationally Symmetric spacetimes that have non vanishing rotation and spatial twist simultaneously. We transparently show that the existence of such solutions demand non vanishing and bounded heat flux and these solutions are self similar. We provide a brief algorithm indicating how to solve the system of field equations with the given Cauchy data on an initial spacelike Cauchy surface. Finally we argue that these solutions can be used as a first approximation from spherical symmetry to study rotating, inhomogeneous, dynamic and radiating astrophysical stars.

gr-qc↗