Abstract: There is an interesting relation between the black hole theory under general relativity and thermodynamics.Considering a spherically static black hole,Einstein equation near the horizon of a Schwarzschild or Reissner-Nordstrom black hole can be deduced into the first law of thermodynamics.This can show the relation between Einstein equation and the black hole thermodynamics.It also reflects the consistence of the two theories.

Key words: spherically symmetric black hole, energy-momentum tensor, Einstein equation, the first law of thermodynamics, black hole thermodynamics