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View article: Bohr-Sommerfeld profile surgeries and Disk Potentials
Bohr-Sommerfeld profile surgeries and Disk Potentials Open
We construct a new surgery type operation by switching between two exact fillings of Legendrians which we call a BSP surgery. In certain cases, this surgery can preserve monotonicity of Lagrangians. We prove a wall-crossing type formula fo…
View article: Mechanics of geodesics in Information geometry and Black Hole Thermodynamics
Mechanics of geodesics in Information geometry and Black Hole Thermodynamics Open
In this article we shall discuss the theory of geodesics in information geometry, and an application in astrophysics. We will study how gradient flows in information geometry describe geodesics, explore the related mechanics by introducing…
View article: Optical properties of null geodesics emerging from dynamical systems
Optical properties of null geodesics emerging from dynamical systems Open
We study optical metrics via null geodesics as a central force system, deduce the related Binet equation and apply the analysis to certain solutions of Einstein’s equations with and without spherical symmetry. A general formula for the def…
View article: Fermat metric: Gravitational optics with Randers-Finsler geometry.
Fermat metric: Gravitational optics with Randers-Finsler geometry. Open
In this article I first introduce and cover preliminaries of point particle mechanics in a Randers-Finsler spacetime, and describe formulation of different equivalent spacetimes via Jacobi-Maupertuis and Eisenhart lift. Then I proceed to d…
View article: Mechanical equivalence of Rander-Finsler spacetimes via Jacobi metric and Eisenhart lift
Mechanical equivalence of Rander-Finsler spacetimes via Jacobi metric and Eisenhart lift Open
In this review article with some original work of my own, I first cover preliminaries of point particle mechanics, introduce the nature and role of the constraint of a mechanical system. Then, starting from a general Randers-Finsler spacet…
View article: Review of Mechanically equivalent Randers-Finsler spacetimes via Jacobi metric and Eisenhart lift
Review of Mechanically equivalent Randers-Finsler spacetimes via Jacobi metric and Eisenhart lift Open
In this review article with some original work of my own, I first cover preliminaries of point particle mechanics, introduce the nature and role of the constraint of a mechanical system. Then, starting from a general Randers-Finsler spacet…
View article: More on Jacobi metric: Randers-Finsler metrics, frame dragging and geometrisation techniques
More on Jacobi metric: Randers-Finsler metrics, frame dragging and geometrisation techniques Open
In this article, I demonstrate a new method to derive Jacobi metrics from Randers-Finsler metrics by introducing a more generalised approach to Hamiltonian mechanics for such spacetimes and discuss the related applications and properties. …
View article: Eisenhart lift and Randers-Finsler formulation for scalar field theory
Eisenhart lift and Randers-Finsler formulation for scalar field theory Open
We study scalar field theory as a generalization of point particle mechanics\nusing the Polyakov action, and demonstrate how to extend Lorentzian and\nRiemannian Eisenhart lifts to the theory in a similar manner. Then we explore\nextension…
View article: Jacobi-Maupertuis metric of Lienard type equations and Jacobi Last\n Multiplier
Jacobi-Maupertuis metric of Lienard type equations and Jacobi Last\n Multiplier Open
We present a construction of the Jacobi-Maupertuis (JM) principle for an\nequation of the Lienard type, viz \\ddot{x} + f(x)x^2 + g(x) = 0 using Jacobi's\nlast multiplier. The JM metric allows us to reformulate the Newtonian equation\nof m…
View article: Jacobi-Maupertuis metric of Lienard type equations and Jacobi Last Multiplier
Jacobi-Maupertuis metric of Lienard type equations and Jacobi Last Multiplier Open
We present a construction of the Jacobi-Maupertuis (JM) principle for an equation of the Lienard type, viz \ddot{x} + f(x)x^2 + g(x) = 0 using Jacobi's last multiplier. The JM metric allows us to reformulate the Newtonian equation of motio…
View article: Jacobi–Maupertuis metric and Kepler equation
Jacobi–Maupertuis metric and Kepler equation Open
This paper studies the application of the Jacobi–Eisenhart lift, Jacobi metric and Maupertuis transformation to the Kepler system. We start by reviewing fundamentals and the Jacobi metric. Then we study various ways to apply the lift to Ke…
View article: Dynamical systems of null geodesics and solutions of Tomimatsu-Sato 2
Dynamical systems of null geodesics and solutions of Tomimatsu-Sato 2 Open
We have studied optical metrics via null geodesics and optical-mechanical formulation of classical mechanics, and described the geometry and optics of mechanical systems with drag dependent quadratically on velocity. Then we studied null g…
View article: The Optical Mechanics of Gravity
The Optical Mechanics of Gravity Open
We have studied optical metrics via null geodesics, formulated classical mechanics in optical- mechanical terms, and described the geometry of mechanical systems with drag. Then, we apply the formulation to other solutions of Einstein's eq…
View article: Jacobi-Maupertuis-Eisenhart metric and geodesic flows
Jacobi-Maupertuis-Eisenhart metric and geodesic flows Open
The Jacobi metric derived from the line element by one of the authors is shown to reduce to the standard formulation in the non-relativistic approximation. We obtain the Jacobi metric for various stationary metrics. Finally, the Jacobi-Mau…
View article: Schwarzschild instanton in emergent gravity
Schwarzschild instanton in emergent gravity Open
In the bottom-up approach of emergent gravity, we attempt to find symplectic gauge fields emerging from Euclidean Schwarzschild instanton, which is studied as electromagnetism defined on the symplectic space [Formula: see text]. Geometrica…
View article: First integrals of Generalized Darboux-Halphen systems and Membrane Paradigm
First integrals of Generalized Darboux-Halphen systems and Membrane Paradigm Open
The Darboux-Halphen system of equations have common or individual additive terms depending on the matrices defining Yang-Mills gauge potential fields. Tod (Phys. Lett. A 190 (1994) 221-224), described a conserved quantity for the classical…
View article: Taub-NUT and Dynamical Systems : the geometric connection demystified
Taub-NUT and Dynamical Systems : the geometric connection demystified Open
A short analysis of the curvature of the Taub-NUT tells us if it truly is a gravitational instanton, followed up by a brief review of its other geometrical properties. We follow this up with a comparison to Bertrand spacetime and computati…