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Generally speaking, there is a negative kinetic energy term in the Lagrangianof the Einstein-Hilbert action of general relativity; On the other hand, thenegative kinetic energy term can be vanished by designating a specialcoordinate system. For general spherically symmetric metric, the question thatseeking special coordinate system that satisfies the positive kinetic energycoordinate condition is referred to solving a linear first-order partialdifferential equation. And then, we present a metric corresponding to theReissner-Nordstrom solution that satisfies the positive kinetic energycoordinate condition. Finally, we discuss simply the case of the Tolman metric.

On spherically symmetric metric satisfying the positive kinetic energy coordinate condition