  Matter interacting classically with gravity in 3+1 dimensions usually gives
rise to a continuum of degrees of freedom, so that, in any attempt to quantize
the theory, ultraviolet divergences are nearly inevitable. Here, we investigate
matter of a form that only displays a finite number of degrees of freedom in
compact sections of space-time. In finite domains, one has only exact, analytic
solutions. This is achieved by limiting ourselves to straight pieces of string,
surrounded by locally flat sections of space-time. Globally, however, the model
is not finite, because solutions tend to generate infinite fractals. The model
is not (yet) quantized, but could serve as an interesting setting for
analytical approaches to classical general relativity, as well as a possible
stepping stone for quantum models. Details of its properties are explained, but
some problems remain unsolved, such as a complete description of the most
violent interactions, which can become quite complex.
