arXiv subjects

Anish Agashe

Publications and source records attributed to Anish Agashe.

9 recordsLinked to original sources

arXiv2025

Static Charged Polytropic Spheres with a Cosmological Constant: Physical Acceptability and Trapped Orbits

We consider static charged fluid spheres with a cosmological constant. We assume a polytropic equation of state, $p \propto \rho^\Gamma$, and a power law charge distribution, $q\propto r^n$. Using this, we convert the generalised Tolman-Oppenheimer-Volkoff equation into a differential equation for the mass profile. By solving this equation numerically, we analyse both physical and geometric properties of charged polytropic fluid spheres for different values of $n$ and $\Gamma$. By imposing subluminal sound speeds and energy conditions, we restrict ourselves to configurations that are physically acceptable. Then, within these physical models, we study internal trapping of circular geodesics and find the trapping regions in the $n$-$\Gamma$ parameter space. Going beyond the traditionally studied case of null geodesics, we consider orbits of charged and/or massive particles as well. We show that for neutral null particles (and only for them), the possibility of internal trapping is determined purely through geometry. In the other three cases, properties such as the particle's own charge and/or energy also play a role. In general, we find that trapping of all types of particles is allowed for a broad range of $n$ and $\Gamma$.

gr-qc↗

arXiv2025

The Tolman VII Space-time in the Presence of a Charge and a Cosmological Constant

The Tolman VII space-time is one of the few physically acceptable exact solutions in general relativity. In this paper, we derive a generalised Tolman VII solution which includes a charge and a cosmological constant. We analyse the spatial geometry of the solution and present conditions for zero and non-zero spatial curvature. We show that for a particular value of the boundary, the Tolman VII space-time can be matched to the charged Nariai space-time. This represents a new class of interior Nariai solutions. Matching with the Reissner-Nordström-de Sitter space-time, we derive analytic expressions for the metric functions and the pressure. Using this, we show that the solution allows for trapped null geodesics for a broad range of values for the total charge, central density, and the cosmological constant. We investigate the physical properties and derive an equation of state for the fluid. We show that the fluid can be considered a polytrope with, $Γ\sim 2.5$. Finally, we analyse the sound speed and energy conditions to conclude that only a subclass of the solution follows all the basic physical acceptability criteria.

gr-qc↗

arXiv2024

Schrödinger Connections: From Mathematical Foundations Towards Yano-Schrödinger Cosmology

Schrödinger connections are a special class of affine connections, which despite being metric incompatible, preserve length of vectors under autoparallel transport. In the present paper, we introduce a novel coordinate-free formulation of Schrödinger connections. After recasting their basic properties in the language of differential geometry, we show that Schrödinger connections can be realized through torsion, non-metricity, or both. We then calculate the curvature tensors of Yano-Schrödinger geometry and present the first explicit example of a non-static Einstein manifold with torsion. We generalize the Raychaudhuri and Sachs equations to the Schrödinger geometry. The length-preserving property of these connections enables us to construct a Lagrangian formulation of the Sachs equation. We also obtain an equation for cosmological distances. After this geometric analysis, we build gravitational theories based on Yano-Schrödinger geometry, using both a metric and a metric-affine approach. For the latter, we introduce a novel cosmological hyperfluid that will source the Schrödinger geometry. Finally, we construct simple cosmological models within these theories and compare our results with observational data as well as the $Λ$CDM model.

gr-qc↗

arXiv2024

On the Effects of Non-metricity in an Averaged Universe

In the covariant averaging scheme of macroscopic gravity, the process of averaging breaks the metricity of geometry. We reinterpret the back-reaction within macroscopic gravity in terms of the non-metricity of averaged geometry. This interpretation extends the effect of back-reaction beyond mere dynamics to kinematics of geodesic bundles. With a 1+3 decomposition of the spacetime, we analyse how geometric flows are modified by deriving the Raychaudhuri and Sachs equations. We also present the modified forms of Gauss and Codazzi equations. Finally, we derive an expression for the angular diameter distance in Friedmann Lemaître Robertson Walker universe and show that non-metricity modifies it only through the Hubble parameter. Thus, we caution against overestimating the influence of back-reaction on the distances.

gr-qc↗

arXiv2023

Lagrangian Formulation of the Raychaudhuri Equation in Non-Riemannian Geometry

The Raychaudhuri equation for a congruence of curves in a general non-Riemannian geometry is derived. A formal connection is established between the expansion scalar and the cross-sectional volume of the congruence. It is found that the expansion scalar is equal to the fractional rate of change of volume, weighted by a scalar factor that depends on the non-Riemannian features of the geometry. Treating the congruence of curves as a dynamical system, an appropriate Lagrangian is derived such that the corresponding Euler-Lagrange equation is the Raychaudhuri equation. A Hamiltonian formulation and Poisson brackets are also presented.

gr-qc↗

arXiv2023

Spherical and Plane Symmetric Solutions in Macroscopic Gravity

The theory of macroscopic gravity provides a formalism to average the Einstein field equations from small scales to largest scales in space-time. It is well known that averaging is an operation that does not commute with calculating the Einstein tensor and this leads to a correction term in the field equations known as back-reaction. In this work, we derive exact solutions to the macroscopic gravity field equations assuming that the averaged geometry is plane or spherically symmetric, and the source is taken as vacuum, dust, or perfect fluid. We then focus on the specific cases of spherical symmetry and derive solutions that are analogous to the Schwarzschild, Tolman VII, and Lema\^ıtre-Tolman-Bondi solutions. The geodesic equations and curvature structure are contrasted with the general relativistic counterparts for the Schwarzschild and Lema\^ıtre-Tolman-Bondi solutions.

gr-qc↗

arXiv2023

Kinematics in Metric-Affine Geometry

In a given geometry, the kinematics of a congruence of curves is described by a set of three quantities called expansion, rotation, and shear. The equations governing the evolution of these quantities are referred to as kinematic equations. In this paper, the kinematics of congruence of curves in a metric-affine geometry are analysed. Without assuming an underlying theory of gravity, we derive a generalised form of the evolution equations for expansion, namely, Raychaudhuri equation (timelike congruences) and Sachs optical equation (null congruences). The evolution equations for rotation and shear of both timelike and null congruences are also derived. Generalising the deviation equation, we find that torsion and non-metricity contribute to a relative acceleration between neighbouring curves. We briefly discuss the interpretation of the expansion scalars and derive an equation governing angular diameter distances. The effects of torsion and non-metricity on the distances are found to be dependent on which curves are chosen as photon trajectories. We also show that the rotation of a hypersurface orthogonal congruence (timelike or null) is a purely non-Riemannian feature.

gr-qc↗

arXiv2022

An Almost-FLRW Universe as the Averaged Geometry in Macroscopic Gravity

It is well-known that spacetime averaging is an operation that does not commute with building the Einstein tensor. In the framework of Macroscopic gravity (MG), a covariant averaging procedure, this non-commutativity gives averaged field equations with an additional correction term known as back-reaction. It is important to explore whether such a term, even if known to be small, may or may not cause any systematic effect for precision cosmology. In this work, we explore the application of the MG formalism to an almost Friedmann-Lemaître-Robertson-Walker (FLRW) model. Namely, we find solutions to the field equations of MG taking the averaged universe to be almost-FLRW modelled using a linearly perturbed FLRW metric. We study several solutions with different functional forms of the metric perturbations including plane waves ansatzes. We find that back-reaction terms are present not only at the background level but also at perturbed level, reflecting the non-linear nature of the averaging process. Thus, the averaging effect can extend to both the expansion and the growth of structure in the universe.

gr-qc↗

arXiv2020

Separating the Intrinsic Alignment Signal and the Lensing Signal using Self-Calibration in Photo-z Surveys with KiDS450 and KV450 Data

To reach the full potential for the next generation of weak lensing surveys, it is necessary to mitigate the contamination of intrinsic alignments (IA) of galaxies in the observed cosmic shear signal. The self calibration (SC) of intrinsic alignments provides an independent method to measure the IA signal from the survey data and the photometric redshift information. It operates differently from the marginalization method based on IA modeling. In this work, we present the first application of SC to the KiDS450 data and the KV450 data, to split directly the intrinsic shape - galaxy density (Ig) correlation signal and the gravitational shear - galaxy density (Gg) correlation signal, using the information from photometric redshift (photo-z). We achieved a clear separation of the two signals and performed several validation tests. Our measured signals are found to be in general agreement with the KiDS450 cosmic shear best-fit cosmology, for both lensing and IA measurements. For KV450, we use partial (high-z) data, and our lensing measurements are also in good agreement with KV450 cosmic shear best-fit, however, our IA signal suggests a larger IA amplitude. We discussed the impact of photo-z quality on IA detection and several other potential systematic biases. Finally, we discuss the potential application of the information extracted for both the lensing signal and the IA signal in future surveys.

astro-ph.CO↗