Macbook Pro 2010 Screen goes blank

First step in Troubleshooting to do is to start in Safe mode. (Hold Shift during start up)

That will eliminate 99% of foreign applications causing the problem.

That will also show if it is a hardware problem. Sometimes it is enough to start in Safe mode to fix small problems.

If problem continues, run the Apple Hardware test, that might show problems with hardware. (hold "D" during start up).

For more clearer picture of your system, I recommend to run the EterSoft analytical tool. EtreCheck is a simple little app to display the important details of your system configuration.

I recently had the same frequent reboot problem on a newer macbook pro running the latest El Capitan. The screen would just go black then a white apple logo would appear. Log back into the system and a kernel panic message would be presented.

It turns out that the Spotlight index database had been corrupted. Not certain as to how the database got corrupted, perhaps software installs with large file and directory numbers.

The corruption was corrected by using System Preferences > Spotlight > Privacy to remove the existing spotlight database. When you get into the Spotlight Privacy window no existing directory or drive will be present.

1. Create one by adding the Macintosh HD by selecting the "+" and then reboot the system.
2. Once the system is up, open System Preferences > Spotlight > Privacy again and remove the added Macintosh HD.
3. Reboot the system once again

This should solve the corrupted Spotlight database and the reboot/kernel panic should not occur.