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Everything about Isotropic coordinates
Coordinate system used to represent certain spacetimes
In the theory of Lorentzian manifolds, spherically symmetric spacetimes admit a family of nested round spheres. There are several different types of coordinate chart which are adapted to this family of nested spheres; the best known is the Schwarzschild chart, but the isotropic chart is also often useful. The defining characteristic of an isotropic chart is that its radial coordinate is defined so that light cones appear round. This means that, the angular isotropic coordinates do not faithfully represent distances within the nested spheres, nor does the radial coordinate faithfully represent radial distances. On the other hand, angles in the constant time hyperslices are represented without distortion, hence the name of the chart. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Isotropic coordinatesA 5-minute orientation
- Skim a recent paper: The isotropic relaxed micromorphic model in polar coordinates and its application to an elastostatic axisymmetric extension problemInfluential work since 2022
- Pick up a classic book: Stochastic Structural DynamicsThe most-reprinted book on the subject
- Read the landmark paper: New algorithms to obtain analytical solutions of Einstein’s equations in isotropic coordinatesCited 58 times
- Go sideways: Gaussian polar coordinatesA closely related topic
- Go sideways: Spherically symmetric spacetimeA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
New algorithms to obtain analytical solutions of Einstein’s equations in isotropic coordinates
Anisotropic static spheres with linear equation of state in isotropic coordinates
Compact stars with linear equation of state in isotropic coordinates
Oppenheimer-Snyder collapse with maximal time slicing and isotropic coordinates
Schwarzschild black hole as moving puncture in isotropic coordinates
A class of relativistic anisotropic charged stellar models in isotropic coordinates
Modal analysis of asymmetric rotor system with isotropic stator using modulated coordinates
General solution technique for transient thermoelasticity of transversely isotropic solids in cylindrical coordinates
🆕 Influential since 2022
The isotropic relaxed micromorphic model in polar coordinates and its application to an elastostatic axisymmetric extension problem
On the problem of solvability of nonlinear boundary value problems for shallow isotropic shells of Timoshenko type in isometric coordinates
On the Problem of Solvability of Nonlinear Boundary Value Problems for Shallow Isotropic Shells of Timoshenko Type in Isometric Coordinates
On the existence of solutions to nonlinear boundary value problems for non-flat isotropic shells of Timoshenko type in arbitrary curvilinear coordinates
Anisotropic stellar objects cast in isotropic coordinates
📚 Books worth reading
- 📕Stochastic Structural DynamicsCho W. S. To · 2013
Cardiovascular Solid MechanicsJay D. Humphrey · 2002- 📕Reflection and Transmission of Electromagnetic Plane Waves on and Through Isotropic and Anisotropic Uniaxial PlatesIbrahim Ibrahim · 2018
The geometry of Walker manifoldsMiguel Brozos-Vázquez · 2009- 📕The equations of an isotropic elastic solid in polar and cylindrical coordinates, their solutions and applications · 1889
- 📕Reflection and Transmission of Electromagnetic Plane Waves on and Through Isotropic and Anisotropic Uniaxial PlatesIbrahim Ibrahim Msc · 2018
- 📕Behandeling van de koppelkromme met behulp van isotrope coördinatenJakob Tjakko Groenman · 1950
- 📕De l'emploi des droites isotropes comme axes de coordonnéesAndré Haarbleicher · 1931
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
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