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In the middle of the picture is a 1kg weight, accelerating to the right. Around it in white are shown the gravito-geodesics. These are more bunched-up at the left (and more spread-out at the right). Since these geodesics only propagate at the speed of light, they lag behind the motion of the 1kg weight. This results in a gravito-inductive force which pulls back on the weight, F=ma (where m is the 1kg mass and a is its acceleration). This explains why there is a manifestation of inertia.