In this colloquium, I discuss conservation laws in a presence of gravity including general relativity. After an introduction, contents of my colloquium are
I. Energy non-conservation in general relativity
I-1. Why is energy conserved?
I-2. Energy non-conservation in general relativity: Expanding Universe
I-3. Cases for energy conservation in a curved spacetime
II. Gravitational fields carry energy? Noether’s 2nd theorem and general relativity
II-1. Energy of gravitational field?
II-2. Noether’s 2nd theorem
II-3. Noether’s 2nd theorem in general relativity
III. Conserved charge in curved spacetime (including GR)
III-1. Proposal for a conserved charge
III-2. Perfect fluid and Stefan-Boltzmann law
III-3. A simple model of expanding Universe (scalar+radiation)
IV. Summary
Questions and comments during my presentation are very welcome.