Two alternative Arnowitt-Dresner-Misner($ADM$) formalisms using the conventions adopted by Misner-Thorne-Wheeler($MTW$) and Alcubierre applied to the Natario warp drive spacetime
Fernando Loup · HAL (Le Centre pour la Communication Scientifique Directe) · 2023
General Relativity describes the gravitational field using the geometrical line element of a given generic spacetime metric ds 2 = g µν dx µ dx ν where do not exists a clear difference between space and time.The 3 + 1 ADM formalism allows ourselves to separate from the generic equation ds 2 = g µν dx µ dx ν of a given spacetime the 3 dimensions of space(hypersurfaces) and the time dimension. We propose two new $ADM$ equations.We apply all these equations to the Natario warp drive spacetimefor both constant and variable velocities.