JOEL - In 3 Nephi chapters 8 and 9 we read of several catastrophic events that accompanied the death of Jesus. There was a great storm; terrible thunder and lightening; tornados; earthquakes; cities being buried or burned or flooded; others sinking into the ocean; and a thick darkness covering the land for three days. Matthew and Luke of the Bible tell of a darkness over the earth; the temple veil being rent; and the earth quaking.
There is little additional historical evidence about these events at the death of Christ besides what we read in the scriptures. There have been references made to a historian named Phlegon who lived in the first century, who mentioned the darkness and earthquakes at the time of Jesus' death in his books called Chronicles(80 AD). He said:
"Now, in the fourth year of the 202nd Olympiad [AD 32-33], a great eclipse of the sun occurred at the sixth hour [noon] that excelled every other before it, turning the day into such darkness of night that the stars could be seen in heaven, and the earth moved in Bithynia, toppling many buildings in the city of Nicaea."
There was also a man named Thallus, a Greek writer from around 50 AD, who talked of the Crucifixion, and mentions the darkness and earthquakes which followed it. See the following web page:
http://www.christianstudycenter.com/refs/jesus.htm#dark
Besides these references a possible explanation to the lack of historical evidence might be attributed to the possibility that all of these manifestations of the crucifixion may not have been a worldwide occurrence. They may have only been localized to the places where the people lived who recorded it in the Bible and Book of Mormon. Quite often when someone in the scriptures mentions that something happened to the "whole earth", they mean that it happened in the whole area of the earth where they are living; not necessarily the entire planet.
"And the locusts went up over all the land of Egypt, and rested in all the coasts of Egypt. . . . For they covered the face of the whole earth, . . . and there remained not any green thing . . . through all the land of Egypt." (Exodus 10:14-15)
Here the phrase whole earth is equated only with the land of Egypt and not the entire planet earth.
This could account in part for the lack of secular historical writings about the event. No one else who would have written about it was in the immediate area to see or experience it. Or we have simply not yet found their records.
Other than these possibilities I have mentioned, we must have faith that the Bible and Book of Mormon are themselves historically accurate.