CAUSALITY, SYMMETRY, GAUGE, AND VALIDITY OF LINEARIZED GRAVITY FOR WAVES

Based on causality, the validity of linearized gravity for waves is examined. To analyze the linearized equations, symmetry is elucidated in connection with the principle of causality. It is concluded that the gauge condition may not necessarily be compatible with causality and that for gravitational waves, linearized gravity may not be valid. To illustrate this, a gravitational plane wave is provided as an example. Concurrently, it is pointed out that the applicability of the ''gauge condition'' for weak gravity has actually never been generally established if the resulting coordinates are expected to be physically realizable. The example also shows that implications of linearized gravity on plane waves ate not generally valid.