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==== Field Equations ==== The field equations govern the behavior of electromagnetic and gravitational fields in spacetime. In the context of electrogravitics, these equations describe how electromagnetic fields interact with gravitational fields and spacetime curvature. The field equations include: <math>\nabla_\mu F^{\mu\nu} = \mu_0 J^\nu</math> * <math>\nabla_\mu</math>: Covariant derivative operator. * <math>J^\nu</math>: Four-current density representing the distribution of electric charge and current. <math>G_{\mu\nu} = \frac{8\pi G}{c^4} T_{\mu\nu}</math> * <math>G_{\mu\nu}</math>: Einstein tensor representing the curvature of spacetime due to gravity. * <math>G</math>: Gravitational constant. * <math>c</math>: Speed of light in vacuum. * <math>T_{\mu\nu}</math>: Stress-energy tensor representing the energy-momentum distribution in spacetime. <math>\nabla_\mu G^{\mu\nu} = 0</math> * <math>\nabla_\mu</math>: Covariant derivative operator. * <math>G^{\mu\nu}</math>: Components of the Einstein tensor.
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