Elastic rigid rod in an expanding universe
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866911081463545856 |
|---|---|
| author | Correia, Simão Natário, José Silva, Jorge Drumond |
| author_facet | Correia, Simão Natário, José Silva, Jorge Drumond |
| contents | We study the motion of a rigid elastic rod, initially set in its relaxed state along a spacelike geodesic, in an expanding Friedmann-Lemaître-Robertson-Walker universe. This leads to an initial boundary value problem (IBVP) for a nonlinear wave equation whose nonlinearity depends on a parameter $κ\geq 0$, related to the ratio between the rod's length and the cosmological scale. We show that if $κ$ is small enough then the solution to the IBVP is global in time and bounded, meaning that the rod's length oscillates around its initial value. For greater values of $κ$, however, the solution to the IBVP blows up in finite coordinate time, indicating that the rod is infinitely stretched by the cosmological expansion. This supports the widely held belief that sufficiently small bound systems do not follow the Hubble flow, whereas larger systems may do so. Similar conclusions apply to the tethered galaxy version of this problem, where the rod is used to connect two point masses (which results in nonlinear boundary conditions for the IBVP). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_21227 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Elastic rigid rod in an expanding universe Correia, Simão Natário, José Silva, Jorge Drumond General Relativity and Quantum Cosmology Mathematical Physics Analysis of PDEs 35L05, 74K05, 83C10, 83C55 We study the motion of a rigid elastic rod, initially set in its relaxed state along a spacelike geodesic, in an expanding Friedmann-Lemaître-Robertson-Walker universe. This leads to an initial boundary value problem (IBVP) for a nonlinear wave equation whose nonlinearity depends on a parameter $κ\geq 0$, related to the ratio between the rod's length and the cosmological scale. We show that if $κ$ is small enough then the solution to the IBVP is global in time and bounded, meaning that the rod's length oscillates around its initial value. For greater values of $κ$, however, the solution to the IBVP blows up in finite coordinate time, indicating that the rod is infinitely stretched by the cosmological expansion. This supports the widely held belief that sufficiently small bound systems do not follow the Hubble flow, whereas larger systems may do so. Similar conclusions apply to the tethered galaxy version of this problem, where the rod is used to connect two point masses (which results in nonlinear boundary conditions for the IBVP). |
| title | Elastic rigid rod in an expanding universe |
| topic | General Relativity and Quantum Cosmology Mathematical Physics Analysis of PDEs 35L05, 74K05, 83C10, 83C55 |
| url | https://arxiv.org/abs/2507.21227 |