Discussion Overview
The discussion revolves around the complexities of calculating mass in strong gravitational fields, particularly in the context of singularities and the use of integrals involving the stress-energy tensor. Participants explore the implications of using different integrals, such as the Komar mass, and the challenges posed by singularities in various spacetime geometries.
Discussion Character
- Debate/contested
- Technical explanation
- Mathematical reasoning
Main Points Raised
- Some participants question the validity of using certain integrals for mass calculation in strong fields, suggesting that the integral of ##T_{00}## may not yield an invariant quantity due to its non-tensor nature.
- Others propose that the Komar mass may provide a more reliable measure, especially in cases where the stress-energy tensor is zero, such as in black holes.
- A participant illustrates the difference between the mass of an assembled planet and its dissassembled parts, emphasizing the role of gravitational binding energy, which is not captured by the integral of ##T^{00}##.
- Concerns are raised about the singularity at ##r=0## in Schwarzschild spacetime, with some arguing that it complicates mass calculations, while others assert that for static, spherically symmetric objects, there is no singularity at that point.
- There is a discussion about the necessity of using invariant quantities for mass calculations, with differing opinions on whether the time component of a 4-vector suffices.
- Some participants express uncertainty about the relationship between the Komar mass and the integral of ##T^{00}##, questioning whether they are fundamentally different or if they can yield similar results under certain conditions.
Areas of Agreement / Disagreement
Participants do not reach a consensus on the best approach to calculating mass in strong fields. Multiple competing views are presented regarding the use of different integrals and the implications of singularities.
Contextual Notes
Limitations include the dependence on specific coordinate choices and the unresolved nature of how gravitational binding energy can be localized within the framework of general relativity.