This is a finite element solution of a scattering problem using hyperboloidal compactification.
A method developed in an unknown niche corner of mathematical relativity and conformal geometry is now ready for real-world problems!
This is a finite element solution of a scattering problem using hyperboloidal compactification.
A method developed in an unknown niche corner of mathematical relativity and conformal geometry is now ready for real-world problems!
The paper addresses an aspect of this timeless question in a rather technical sense: How should we construct time in GR with its black holes and observers?
link.springer.com/article/10.1...
The paper addresses an aspect of this timeless question in a rather technical sense: How should we construct time in GR with its black holes and observers?
link.springer.com/article/10.1...
Times are changing.
Times are changing.
In the presence of boundaries, general covariance is explicitly broken. Gauge-fixing must consider the boundary structure.
In the presence of boundaries, general covariance is explicitly broken. Gauge-fixing must consider the boundary structure.
Famously, black holes were the first relativistic horizons we discovered. The event horizon is a surface of no return. 🧪
Famously, black holes were the first relativistic horizons we discovered. The event horizon is a surface of no return. 🧪
https://buff.ly/3OjsJi3
https://buff.ly/3OjsJi3
Here's a paper about hyperbolic times, fresh off the press, published just yesterday.
pubs.aip.org/aapt/ajp/art...
Here's a paper about hyperbolic times, fresh off the press, published just yesterday.
pubs.aip.org/aapt/ajp/art...
Quantum physics is not only the physics at small scales. There are macroscopic quantum phenomena.
The spacetime metric is a Lorentzian signature tensor with precisely one negative eigenvalue
The Higgs field (see below) gives mass to fundamental particles, like the electron and the quarks in protons and neutrons. But most of the mass of protons and neutrons is due to the binding energy of the strong interaction. That thus applies to your body too.
Quantum physics is not only the physics at small scales. There are macroscopic quantum phenomena.
🧪⚛️ #🧮
🧪⚛️ #🧮
🧪 #🧮
🧪 #🧮
arxiv.org/abs/2411.04955
arxiv.org/abs/2411.04955
Quasinormal modes deliver small scale information to the observer, whereas the tail delivers large scale information.
The tail is a memory effect telling you what perturbed the spacetime long time ago
Quasinormal modes deliver small scale information to the observer, whereas the tail delivers large scale information.
The tail is a memory effect telling you what perturbed the spacetime long time ago
The idea is to map the unbounded domain to a bounded domain.
The trick is to combine spatial mapping with a transformation of time.
Code is included in Google Colab.
anilzen.github.io/post/2023/wa...
The idea is to map the unbounded domain to a bounded domain.
The trick is to combine spatial mapping with a transformation of time.
Code is included in Google Colab.
anilzen.github.io/post/2023/wa...
It's a hyperboloid.
Soap bubbles are minimal surfaces. They minimize area to enclose a given volume of air. Similarly, hyperboloids maximize volume to enclose a given spacetime volume.
anilzen.github.io/post/2023/sp...
It's a hyperboloid.
Soap bubbles are minimal surfaces. They minimize area to enclose a given volume of air. Similarly, hyperboloids maximize volume to enclose a given spacetime volume.
anilzen.github.io/post/2023/sp...