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## Main Question or Discussion Point

Hello,

Can anyone explain to me the next settence, found here in section 1.4:

"The causal structure of the Green’s functions is richer in curved spacetime: While in flat spacetime the retarded Green’s function has support only on the future light cone of [itex]x'[/itex], in curved spacetime its support extends inside the light cone as well;[itex]G^{\alpha}_{+\beta '}[/itex] is therefore nonzero when [itex]x\in I^{+}(x')[/itex], which denotes the chronological future of [itex]x'[/itex]. This property reflects the fact that in curved spacetime, electromagnetic waves propagate not just at the speed of light, but at all speeds smaller than or equal to the speed of light; the delay is caused by an interaction between the radiation and the spacetime curvature. A direct implication of this property is that the retarded potential at [itex]x[/itex] is now generated by the point charge during its entire history prior to the retarded time [itex]u[/itex] associated with [itex]x[/itex]: the potential depends on the particle’s state of motion for all times [itex]\tau \leq u[/itex]."

I do understand the implications of such but why is there a tail term in the Green function?why do "electromagnetic waves propagate not just at the speed of light, but at all speeds smaller than or equal to the speed of light; the delay is caused by an interaction between the radiation and the spacetime curvature."

Thank you

Can anyone explain to me the next settence, found here in section 1.4:

"The causal structure of the Green’s functions is richer in curved spacetime: While in flat spacetime the retarded Green’s function has support only on the future light cone of [itex]x'[/itex], in curved spacetime its support extends inside the light cone as well;[itex]G^{\alpha}_{+\beta '}[/itex] is therefore nonzero when [itex]x\in I^{+}(x')[/itex], which denotes the chronological future of [itex]x'[/itex]. This property reflects the fact that in curved spacetime, electromagnetic waves propagate not just at the speed of light, but at all speeds smaller than or equal to the speed of light; the delay is caused by an interaction between the radiation and the spacetime curvature. A direct implication of this property is that the retarded potential at [itex]x[/itex] is now generated by the point charge during its entire history prior to the retarded time [itex]u[/itex] associated with [itex]x[/itex]: the potential depends on the particle’s state of motion for all times [itex]\tau \leq u[/itex]."

I do understand the implications of such but why is there a tail term in the Green function?why do "electromagnetic waves propagate not just at the speed of light, but at all speeds smaller than or equal to the speed of light; the delay is caused by an interaction between the radiation and the spacetime curvature."

Thank you