So you want to look for a "solid state contactor" or SSC, not an "SSR". SSRs are for little stuff, not motors. Most of the large motor control mfrs offer them.
SSCs will reject approx. 1.5W per running load amp per pole. You didn't post a current rating you are looking for, but if your load is 10A for example, the SSC will reject 30W of heat. It doesn't seem like much, but if the contactor is enclosed and not ventilated, it builds up. It also gets to the point where the heat sink for the SSC becomes somewhat large. In addition, SSCs are typically not able to handle operating temperatures greater than 40C (104F), so if this is going outdoors, that might be problematic too.
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