Yes, according to general relativity, it is possible for regions of spacetime to have curvature without the presence of massive objects like stars and galaxies. In general relativity, the curvature of spacetime is not solely caused by the presence of mass; it can also arise due to other forms of energy and momentum, as described by the theory's field equations.
The concept of curvature in general relativity is intimately connected to the distribution of energy and momentum in the universe. Mass and energy, including those associated with stars and galaxies, contribute to the curvature of spacetime in their vicinity. This curvature affects the motion of objects and the propagation of light.
However, it's important to note that curvature in spacetime is not limited to regions with massive objects. Energy, including forms such as radiation or the presence of other types of fields, can also generate curvature. Even in empty space, quantum fields can exhibit fluctuations that contribute to the curvature of spacetime on small scales.
In cosmology, for example, the overall curvature of the universe can be influenced by the distribution of energy and matter on a large scale, including the presence of dark energy, which is a hypothetical form of energy associated with the accelerating expansion of the universe.
So, in summary, while the presence of mass and energy, including stars and galaxies, can cause significant curvature in the vicinity of those objects, regions of spacetime can exhibit curvature even in the absence of such massive structures due to the distribution of energy and other forms of matter or fields.