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Results tagged with general-relativity
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user 156492
For questions about mathematical problems arising from general relativity, the branch of physics which provides and studies the currently accepted geometric description of gravity.
6
votes
Proving an identity used in general relativity
This is the differential form of the Reilly formula. It holds for a function on any pseudo-Riemannian manifold. (Robert C. Reilly. Applications of the Hessian operator in a Riemannian manifold, Indian …
- 2,247
3
votes
0
answers
71
views
Lorentzian cobordism through the dominant energy condition
Is the answer to the following problem, or some close variant thereof, known? Briefly:
Given two initial data sets $I_1=(M,g_1,k_1)$ and $I_2=(M,g_2,k_2)$, is there a time-oriented spacetime satisfyi …
- 2,247
20
votes
0
answers
2k
views
Schoen and Yau's proof of the higher dimensional positive mass theorem
In April 2017 Schoen and Yau posted on the arxiv their solution of the time-symmetric positive mass theorem in all dimensions, which has been a significant conjecture since the 70s. As of now, July 20 …
- 2,247
9
votes
Accepted
Is Witten's proof of the positive mass theorem rigorous?
The positive mass theorem is more or less to do with the geometry of a type of positive scalar curvature condition.
Witten's work considers harmonic spinors, which are solutions to a certain linear el …
- 2,247
4
votes
Usage/Application of Raychaudhuri equation in Riemann geometry or pure maths
For any 1-form $\omega$ on a pseudo-Riemannian manifold, the product rule and commutation identity say that
$$\omega^p\nabla_p\nabla_q\omega^q-\nabla^q(\omega^p\nabla_p\omega_q)=-\omega^p\omega^qR_{pq …
- 2,247