Lie symmetries in higher dimensional charged radiating stars

Area of Science:

• Gravitational physics
• Theoretical astrophysics
• Differential geometry

Background:

• Gravitational collapse of radiating stars is a key phenomenon in astrophysics.
• Higher-dimensional spacetimes offer new perspectives on fundamental physics.
• Lie symmetry analysis is a powerful tool for solving differential equations.

Purpose of the Study:

• To investigate Lie symmetry properties of spherically symmetric radiating stars in higher dimensions.
• To analyze the influence of matter variables and kinematic quantities on Lie symmetries.
• To reveal the explicit dependence of charge and spacetime dimension on Lie symmetry generators.

Main Methods:

• Application of Lie symmetry analysis to the field equations of radiating stars.
• Examination of variations in functions and dependent variables.
• Derivation of group invariant solutions using obtained Lie symmetries.

Main Results:

• Explicit dependence of charge and spacetime dimension on Lie symmetry generators identified for the first time.
• Influence of various kinematical features (shear, geodesic, etc.) and matter variables on Lie symmetries demonstrated.
• Appearance of a linear equation of state observed.
• Recovery of known four-dimensional models from the higher-dimensional framework.

Conclusions:

• Lie symmetry analysis provides a systematic way to study complex astrophysical phenomena.
• Higher dimensions and specific matter/kinematic properties significantly impact the symmetry structure of collapsing stars.
• The study offers a generalized framework applicable to various models of gravitational collapse.