Partial Derivatives on Causal Sets
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913353797992448 |
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| author | Shuman, Samuel |
| author_facet | Shuman, Samuel |
| contents | We will discuss two approaches to estimating partial derivatives and the metric components; one utilizing past work describing a causal set $\Box$ operator, and one using a construction from linear algebra called the Moore-Penrose inverse. After running numerical tests on a causal diamond in $\mathbb{M}^2$, we find that the approach using the Moore-Penrose inverse is significantly more accurate. Despite the large variances in the method using the $\Box$ operator, there is reason to believe both approaches should become more accurate at higher densities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_10574 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Partial Derivatives on Causal Sets Shuman, Samuel General Relativity and Quantum Cosmology We will discuss two approaches to estimating partial derivatives and the metric components; one utilizing past work describing a causal set $\Box$ operator, and one using a construction from linear algebra called the Moore-Penrose inverse. After running numerical tests on a causal diamond in $\mathbb{M}^2$, we find that the approach using the Moore-Penrose inverse is significantly more accurate. Despite the large variances in the method using the $\Box$ operator, there is reason to believe both approaches should become more accurate at higher densities. |
| title | Partial Derivatives on Causal Sets |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2405.10574 |