Spacetime in Semiclassical Gravity

This article will summarize selected aspects of the semiclassical theory of gravity, which involves a classical gravitational field coupled to quantum matter fields. Among the issues which will be discussed are the role of quantum effects in black hole physics and in cosmology, the effects of quantum violations of the classical energy conditions, and inequalities which constrain the extent of such violations. We will also examine the first steps beyond semiclassical gravity, when the effects of spacetime geometry fluctuations start to appear.