Exact results in a punctured neighborhood of a strong curvature singularity
arXiv:2407.07010 · doi:10.1103/PhysRevD.111.024063
Abstract
By constructing a model of spacetime having a strong curvature singularity in which causal geodesics are complete, but more generic causal curves are not, we explicitly show that some electrostatic field configurations on that background are bounded on every open punctured neighborhood of the curvature singularity. Our calculations are performed using the analog gravity description provided by Plebanski and Tamm, according to which the characterization of the electromagnetic field on a generic curved background is equivalent to solving Maxwell's equations in flat space with a matter content verifying certain nontrivial constitutive relations. The regularity of the electric field as it approaches what could be considered the worst conceivable physical condition, opens the door to further investigation into the possibility of propagating signals capable of crossing a spacetime singularity.
arXiv comment9 pages, 4 figures. This version incorporates some changes in the exposition, including a new title and some extended passages. Main results and conclusions remain intact. Accepted in Phys. Rev. D
References in corpus (19)
- Analogue Gravity
- Sudden Future Singularities
- Singularity Theorems and Their Consequences
- Geodesic behavior of sudden future singularities
- Electromagnetic fields in curved spacetimes
- Towards a metamaterial simulation of a spinning cosmic string
- A Completely Covariant Approach to Transformation Optics
- Anisotropic metamaterial as an analogue of a black hole
- How Information Crosses Schwarzschild's Central Singularity
- Generalized Transformation Optics of Linear Materials
- Covariant electrodynamics in linear media: Optical metric
- The regular black hole in four dimensional Born-Infeld gravity
- Electrodynamics and spacetime geometry I: Foundations
- Ray trajectories for a spinning cosmic string and a manifestation of self-cloaking
- Chronology Protection Implementation in Analogue Gravity
- BTZ gems inside regular Born-Infeld black holes
- Repulsive gravity near naked singularities and point massive particles
- Stress and Geometry for Isotropic Singularities
- Exact results on analogue gravity in optical Plebanski-Tamm media