The discussion centers on the relationship between the conservation of the energy-momentum tensor and the existence of solutions to Einstein's equations in general relativity. It is established that if the energy-momentum tensor is not conserved, then solutions to Einstein's equations do not exist. Conversely, the question arises whether the conservation of the energy-momentum tensor guarantees the existence of solutions. The challenge lies in proving this relationship, particularly since the metric tensor influences the covariant derivative that defines energy-momentum conservation.
PREREQUISITESThe discussion is beneficial for physicists, mathematicians, and students of general relativity who are exploring the foundational aspects of Einstein's equations and the conservation of energy-momentum in gravitational contexts.
atyy said:I wonder: how do we know the energy-momentum tensor is conserved until we have a solution, since the metric enters the covariant derivative which defines energy momentum conservation?