## Lagrangian of General Relativity Over Three Dimensional Subspace

**Authors:** Malik Al Matwi

We restrict the Einstein-Hamiltonian Lagrangian to $3D$ surface $S^3(\sigma _1, \sigma _2, \sigma _3)$, we let this surface be immersed in arbitrary $4D$ spacetime manifold $M$ at constant time $x^0$. The gauge theory of general relativity asserts that the Einstein-Hamiltonian Lagrangian is invariant under infinitesimal variation of that surface, this determines the surface. By that we get continuity equation in arbitrary $4D$ spacetime, then we search for Lagrangian and equation of motion that give same continuity equation according to canonical field theory.

**Comments:** 9 Pages.

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### Submission history

[v1] 2019-03-20 03:15:28

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