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Gravitational waves in gauge theory gravity with a negative cosmological constant

In this paper, we discuss the gravitational waves in the context of gauge theory gravity with a negative cosmological constant. The gauge theory gravity is a gravity theory under gauge formulation in the language of geometric algebra. In contrast to general relativity, the background spacetime in gauge theory gravity is flat, the gauge freedom comes from the fact that equations in terms of physical quantities should be kept in a covariant form under spacetime displacement and rotation. Similar to the electromagnetism, the gauge formulation enables us to interpret the gravitational force as a gauge force on the background flat spacetime. The dynamical fields that describe the gravitational interactions are those position and rotation gauge fields introduced as the requirement of the gauge covariance. The gravitational field equations can be derived from the least action principle with the action as a gauge invariant quantity built from the covariant field strength. We discuss the gravitational wave solutions of the field equations with a negative cosmological constant, and show that these solutions are of Petrov type-N. We also discuss the velocity memory effect by calculating the velocity change of an initially free falling massive particle due to the presence of the gravitational waves.