latentcorpse said:yes but what about the t=0 big bang singularity. is this a singularity because we can only extrapolate geodesics as far back as to a time just after t=0 but we can't extend them to the t=0 region of spacetime itself and so the geodesics are incomplete?
Geodesic incompleteness is a phenomenon in general relativity (GR) where a geodesic (the path followed by an object under the influence of gravity) cannot be extended indefinitely, leading to a singularity. In simpler terms, it is a point in space-time where our current understanding of GR breaks down and we are unable to make any meaningful predictions.
Singularities in GR are caused by extreme conditions, such as infinite density or curvature, which result in a breakdown of the equations that govern the behavior of space-time. These conditions typically occur within black holes or during the Big Bang, where the gravitational force is incredibly strong.
Geodesic incompleteness is the result of singularities in GR. When a singularity occurs, it creates a point in space-time where geodesics cannot be extended, leading to geodesic incompleteness. In other words, singularities are the cause and geodesic incompleteness is the effect.
The existence of singularities in GR has been a subject of debate and research for many years. While they do pose challenges for our current understanding of the universe, they also provide insight into the nature of space-time and the laws of physics. Many scientists believe that a more complete theory, such as quantum gravity, may help resolve the issue of singularities in GR.
Singularities cannot be directly observed or studied, as they are hidden behind an event horizon in the case of black holes or occurred in the past during the Big Bang. However, scientists can study their effects on the surrounding space-time and make predictions based on our current understanding of GR. Advanced technologies, such as gravitational wave detectors, may also provide indirect evidence of singularities.