General Relativity: Four Interior Friedmann–Lemaître–Robertson–Walker Metric Solutions...

June 25Jun 25

In Einstein's theory of general relativity, the interior metric or interior fluid solution, is an exact solution to the Einstein field equations and Einstein-Maxwell equations that describes the gravitational field and the space-time geometry in the interior of a non-rotating or rotating neutral or charged spherically symmetric body of mass M, which consists of an incompressible fluid and constant density throughout the body and has zero pressure at the surface and that the electric charge and angular momentum of the mass may be zero or non-zero, and the universal cosmological constant is zero. For a non-zero charged mass, the metric takes into account the Einstein-Maxwell field energy of an electromagnetic field within the space-time geometry. The space-time geometry is in Boyer-Lindquist coordinates.

Is the universe homogeneous and isotropic at large enough scales, as claimed by the cosmological principle and assumed by all models that use the Friedmann–Lemaître–Robertson–Walker metric, including the current version Lambda-CDM model, or is the universe inhomogeneous or anisotropic?

Is the Cosmic Microwave Background radiation dipole purely kinematic, or does it signal a possible breakdown of the Friedmann–Lemaître–Robertson–Walker metric?

Is the current standard model of cosmology Lambda-CDM model based upon the Friedmann–Lemaître–Robertson–Walker metric valid in the late universe?

Any discussions and/or peer reviews about this specific topic thread?

"You will do well to expand your horizons." - Fortune Cookie

Reference:

Wikipedia - Four-gradient As a Jacobian matrix for the SR Minkowski metric tensor: (ref. 1)

https://en.wikipedia.org/wiki/Four-gradient#As_a_Jacobian_matrix_for_the_SR_Minkowski_metric_tensor

Wikipedia - Minkowski space: (ref. 2)

https://en.wikipedia.org/wiki/Minkowski_space

Wikipedia - Friedmann–Lemaître–Robertson–Walker metric: (ref. 3)

https://en.wikipedia.org/wiki/Friedmann-Lemaître-Robertson-Walker_metric#Concept

Wikipedia - Exterior Reissner-Nordstrom metric: (ref. 4)

https://en.wikipedia.org/wiki/Reissner–Nordström_metric#Metric