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This work aims to derive the isotropic metric and explore its significance in general relativity.

April 7, 2026AxiomsOpen Access

Spacetime Metrics with Spherical Symmetry: A Short Review on the Riemann Tensors and Kretschmann Scalars

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This work aims to derive the isotropic metric and explore its significance in general relativity.
Derived the isotropic metric using vacuum field equations in Cartesian coordinates.
Calculated the Ricci tensor in spherical coordinates to verify consistency.
Analytically computed the Riemann tensor in Cartesian coordinates.
Evaluated the Kretschmann scalar from the Riemann tensor.
Confirmed the isotropic metric's validity for modeling static neutron stars and regular black holes.
Showed that the Kretschmann scalar is free from metric singularities, unlike the standard Schwarzschild metric.

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This review analyzes spherical spacetime metrics, focusing on isotropic forms and their implications for theoretical models.

Hector Eduardo Roman (2026) studied this question.

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