Yes, according to the theory of general relativity, regions of spacetime can have curvature without the presence of masses or objects like stars and galaxies. In general relativity, the curvature of spacetime is related to the distribution of energy and matter, as described by Einstein's field equations.
However, it's important to note that mass is not the only source of curvature in general relativity. Energy and momentum, including various forms of energy like radiation or dark energy, can also contribute to the curvature of spacetime. The presence of any form of energy or stress in a region can affect the geometry of spacetime, leading to curvature.
In fact, even in the absence of any matter or energy, spacetime can still possess intrinsic curvature. This is known as "vacuum curvature" or "curvature of empty space." According to quantum field theory, the vacuum of space is not completely empty but instead filled with quantum fluctuations and virtual particle-antiparticle pairs. These fluctuations can contribute to the curvature of spacetime on very small scales, giving rise to what is known as "quantum foam."
Additionally, gravitational waves, which are ripples in spacetime itself, can propagate through regions without any mass present. These waves can cause temporary curvature in spacetime as they pass through a region, even though they do not carry any mass themselves.
So, while the presence of mass and energy is a significant source of spacetime curvature, there are other factors and phenomena that can contribute to the curvature of spacetime, even in the absence of massive objects.