Bereshit 27:41– Esav creating an alibi to enable him to kill Yaakov

Bereshit 27:41 records that Esav said in his heart that he would only kill Yaakov after Yitzhak died. I understand that the phrase “speaking to the heart” means talking out loud to one’s self since otherwise how could Rivka have known that Esav wanted to kill Yaakov. Yet, why did Rivka send away Yaakov immediately, 27:43, if Esav only threatened to kill Yaakov after Yitzhak died? What was the great urgency?

Esav had a problem since he wanted both to kill Yaakov and to get the blessings. However, if he killed Yaakov when Yitzhak was alive then there was a good probability that Yitzhak would not be willing to bless him. But, he was not willing to wait for Yitzhak to die to take his revenge on Yaakov, and hence he decided to set up an alibi that would exonerate him from being a suspect if Yaakov had an "untimely" death. The alibi was that he started the rumor that he was only going to take revenge after Yitzhak died, and then he could kill Yaakov without being a suspect. Rivka realized that Esav really intended to kill Yaakov at his first chance without waiting for Yitzhak to die, and hence she immediately sent Yaakov away to her family to protect him from Esav.