The theory of special relativity does not include acceleration nor does it include gravity. The theory of general relativity includes both acceleration and gravity. Constant acceleration is completely equivalent to a uniform gravitational field. A beam of light bends under acceleration, so it should bend under gravity. This was shown to be correct during a solar eclipse.
Clocks run slower in gravitational field.
Energy is lost by means of increasing the wavelength, known as gravitational redshift . Einstein suggested a test. Starlight grazing near the surface of the Sun should bend. This phenomenon can only be observed during a solar eclipse. The deflection was measured and it agreed perfectly with the predicted value.