Averaged energy inequalities for the nonminimally coupled classical scalar field

The stress-energy tensor for the classical nonminimally coupled scalar field is known not to satisfy the pointwise energy conditions of general relativity. In this paper we show, however, that local averages of the classical stress-energy tensor satisfy certain inequalities. We give bounds for averages along causal geodesics and show, e.g., that in Ricci-flat background spacetimes, ANEC and AWEC are satisfied. Furthermore we use our result to show that in the classical situation we have an analogue to the phenomenon of quantum interest. These results lay the foundations for analogous energy inequalities for the quantized nonminimally coupled fields, which will be discussed elsewhere.