  We provide a novel model of gravity by using adjoint frame fields in four
dimensions. It has a natural interpretation as a gravitational theory of a
complex metric field, which describes interactions between two real metrics.
The classical solutions establish three appealing features. The spherical
symmetric black hole solution has an additional hair, which includes the
Schwarzschild solution as a special case. The de Sitter solution is realized
without introducing a cosmological constant. The constant flat background
breaks the Lorentz invariance spontaneously, although the Lorentz breaking
effect can be localized to the second metric while the first metric still
respects the Lorentz invariance.
