as we know , both mass and energy can bend space-time , and we know that accelerate mass can radiate gravitational-wave , but my question is that : bent space-time by energy can also radiate gravitational-wave?
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General relativity makes no distinction between "mass" and "energy". Mass is just one form of energy, a form that happens to be intrinsic to certain particles.
For example, a kugelblitz is a theoretical black-hole formed entirely of photons. It would be indistinguishable from a regular black-hole. If the process that formed the kugelblitz had a quadrupole moment (if, for example, the light that was being concentrated to form the black hole was coming from one direction) then the formation of the black hole would produce gravitational waves, without any matter being accelerated
In the inspiral of two black holes, much of the "mass" is actually in the form of kinetic and gravitational potential energy. It is this energy that powers the production of gravitational waves that can be detected from halfway across the observable universe.
