It represents a light so basically, it has similar features same as light and not more than the light can travel at 3x10^8 m/s. And also, particle must have mass enough to produce a certain amount of attracting force as it travels way beyond the speed of light. An object increases its mass as it travels a huge amount of speed say for example greater than light. Thus if it increases its mass then the force of attraction between anybody and that certain body increases.
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The flaw here is that gravity does not involve only mass but also energy. In this way, photons are sensitive to gravity as well.