  We derive the Einstein field equations and black hole entropy from the first
law of thermodynamics on a holographic time-like screen. Because of the
universality of gravity, the stress tensor on the screen must be independent of
the details of matter fields, so it should be a pure geometric quantity. For
simplicity, we assume that the stress tensor on the screen depends on surface
Ricci curvature and extrinsic curvature linearly. Then we prove that the
surface stress tensor is just the Brown-York stress tensor plus terms which do
not affect the field equations of gravitation and the entropy of the system. By
assuming a generalized "Fine first law of thermodynamics" or the usual
universal first law of thermodynamics on the screen, we can derive the matter
field equations as well.
