Anıl Zenginoğlu

GRG article collection" Hyperboloidal foliations in the era of gravitational-wave astronomy"

On the occasion of #GR24Amaldi16, all articles in the collection "Hyperboloidal foliations in the era of gravitational-wave astronomy" are free-to-read from 10 July to 10 August 2025! link.springer.com/collections/... — Don't miss today's related talks by Anna Sancassani and Benjamin Leather!

Solution of a scattering problem using finite element methods with hyperboloidal compactification.

I finally got it!!!

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!

Bridging time across null horizons - General Relativity and Gravitation General relativity, as a diffeomorphism-invariant theory, allows the description of physical phenomena in a wide variety of coordinate systems. In the presence of boundaries, such as event horizons an...

Achievement unlocked 🥂 🧪: Published a technical physics paper with a philosophical opening: "What is time?"

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 full letter is here: chronicle.brightspotcdn.com/4c/5e/044424...

This is the language used for DEI in a letter from the Office for Civil Rights: "a shameful echo of a darker period in this country's history."

Times are changing.

Physics models reality.

If our experience of reality includes the decay of energy due to radiation, the coordinate system we use should respect that.

A prominent example is energy.

Energy at spatial infinity is conserved in time, but energy evolving along null infinity decays.

This is a physical observable evaluated at the asymptotic limit in different coordinate systems. But the coordinates are related by singular transformations.

In general relativity, general covariance applies only to coordinate systems related to each other by smooth transformations.

In the presence of boundaries, general covariance is explicitly broken. Gauge-fixing must consider the boundary structure.

The same is true for cosmological horizons and infinity.

Moments of time must be horizon-penetrating if the horizons are at a finite proper distance and hyperboloidal (asymptotically hyperbolic) if they are at infinity.

This also breaks time-reflection symmetry and provides a direction of time.

After Schwarzschild discovered the first black-hole solution of the Einstein equations in 1915, it took about 50 years to recognize that time must be redefined in the presence of horizons.

The Schwarzschild "singularity" is due to the wrong definition of time, which assumes synchronization.

Time must be defined differently when there are horizons in space.

Our usual definition of time across space implicitly assumes synchronization via two-way communication.

Horizons only allow one-way communication, so time must be adapted to one-way communication.

So, horizons exist even in flat spacetime where there's no gravity or expansion of space.

If we're interested in large-scale phenomena (propagation of waves across large distances, for example), we should consider horizons. We didn't notice them before because they are far away.

But there are other horizons.

Because of the expansion of space, there is a limiting surface beyond which we can never see. That's the cosmological horizon.

Infinity is another one. You can send radiation to infinity but can never receive it.

A horizon is a limiting surface of no return. It's the boundary beyond which interaction is impossible. We can send signals beyond the horizon but can never receive signals back.

Famously, black holes were the first relativistic horizons we discovered. The event horizon is a surface of no return. 🧪

Buying quantum computing stocks is all fun and games until you remember that Gutenberg was practically bankrupt because of his printing press.

New paper the cites the BHPToolkit: "Gravitational self-force with hyperboloidal slicing and spectral methods" by Benjamin Leather, arxiv.org/abs/2411.14976

Thanks

Anıl Zenginoğlu ‪University of Maryland‬ - ‪‪Cited by 2,783‬‬ - ‪Wave Equations‬ - ‪Gravitational Waves‬ - ‪Kalman Filters‬ - ‪Fluid Dynamics‬

👋 scholar.google.com/citations?us...

Thanks!

Anıl Zenginoğlu ‪University of Maryland‬ - ‪‪Cited by 2,783‬‬ - ‪Wave Equations‬ - ‪Gravitational Waves‬ - ‪Kalman Filters‬ - ‪Fluid Dynamics‬

Hi! I'm a physicist working in general relativity with occasional math. Please add me to the feed. Thanks!

scholar.google.com/citations?us...

It’s a two-way street. I believe there is work to be done at the classical level before we can understand the quantum.

What is time across space?

How do you construct a natural surface of simultaneity as a distant observer?

Does understanding time give us a hint about the quantum nature of gravity?

We live in hyperbolic times. So here's a paper about hyperbolic times, fresh off the press, published just yesterday.
https://buff.ly/3OjsJi3

Magritte's image of a pipe that's not a pipe.

Story by Borges "On Exactitude in Science"

I use these two images in my lecture on Qubits.

Even experts sometimes confuse the map with the territory.

I'm most excited about the connection of hyperboloidal surfaces to holography. There are a few calculations to be made on that front, so stay tuned.

Penrose time slices are hyperboloids with varying curvature.

It is often not appreciated that Penrose coordinates are hyperboloidal. I show that Penrose diagrams are hyperboloidal, which suggests that horizon-penetrating coordinates are also hyperboloidal.

Timekeepers connected at a fixed proper time make a hyperboloid in flat spacetime.

The paper has some other neat ideas. You can get the hyperboloidal time slices by sending out "timekeepers" in different directions. When their clock reads a specific value, the surface that connects them is a hyperboloid.

Standard time slices are not hyperbolic, so the meaning of holography in physics is unclear.

I argue that natural time slices for asymptotic observers are also hyperbolic. The stacked Escher drawings are exactly how Minkowski spacetime looks like to asymptotic observers.

Time as a stack of surfaces with hyperbolic geometry. By J.F. PODEVIN. https://www.podevin.com/post/2019/01/24/einsteins-dream-of-a-grand-unified-theory

The paper argues that a natural notion of time involves spatial surfaces with hyperbolic geometry.

You might have heard about holography and the AdS/CFT correspondence, which relies heavily on the hyperbolic geometry of AdS time slices.

The driving question of the paper is this: What is time across space?

In other words, How do you construct a natural surface of simultaneity as a distant observer? And also, does understanding time give us a hint about the quantum nature of gravity?

Time is a mystery worth thinking about.