# Another Kerr interior solution

## TL;DR

This paper presents a novel rotating anisotropic interior solution matching the Kerr exterior, satisfying all energy conditions and free of singularities, extending the class of physically realistic rotating compact objects.

## Contribution

It introduces the first known Kerr interior solution with an anisotropic source that meets all energy conditions and smoothly matches the Kerr exterior.

## Key findings

- Energy conditions are satisfied for a wide parameter range.
- Solution reduces to a regular Schwarzschild interior when rotation vanishes.
- Energy-momentum components are singularity free and physically consistent.

## Abstract

A stationary axially symmetric solution describing a rotating anisotropic source for Einstein Field Equations(EFE) is proposed which matches to the exterior Kerr metric. The anisotropic source satisfies all energy conditions - weak, strong, and dominant energy condition - for a wide range of metric's free parameters values. The resultant energy-momentum tensor components, and consequently energy density and pressure profiles, redshift function and angular velocity are singularity free and behave as expected. As rotation parameter goes to zero a spherical source consisting of normal and exotic matter is retrieved for the exterior Schwarzschild solution; the corresponding redshift function, however, is well-behaved and positive definite. This is the first solution of its kind.