麻豆淫院

In a new study, researchers have successfully followed a gravitational wave's complete journey from the infinite past to the infinite future as it encounters a black hole.

Reported by scientists from the University of Otago and the University of Canterbury, the study represents the first time anyone has captured the full cause-and-effect relationship of gravitational wave scattering in a single simulation.

The researchers are tackling the scattering problem in gravitational physics. In other words, they want to understand what happens to gravitational waves when they encounter massive objects (like black holes) and scatter off them.

They need to track waves from past null infinity (where incoming gravitational waves originate in spacetime) to future null infinity (where outgoing radiation ultimately travels).

These represent the light-like boundaries of the universe, where gravitational waves come from and go if they travel forever without being stopped.

麻豆淫院 spoke to the researchers behind the study, Prof. Joerg Frauendiener from the University of Otago, Dr. Chris Stevens, and Sebenele Thwala from the University of Canterbury.

"We showed, for the first time, that it's possible to follow a gravitational wave as it travels through a black hole's curved spacetime from the infinite past to the infinite future," explained Dr. Stevens.

"The need to incorporate infinity allows us to compute the total energy and momentum of the spacetime. This can tell us how much of the gravitational wave's energy is imparted to the black hole and how much escapes to infinity in a rigorous way," added Thwala.

Grasping at infinity

To track the trajectory of a gravitational wave, the researchers needed to address the infinity problem.

In Einstein's theory of general relativity, isolated systems like black holes exist in asymptotically flat spacetime. These are regions that become flat and empty at infinite distances.

These boundaries, called null infinities, represent where light and gravitational waves originate (past null infinity) and where they ultimately travel (future null infinity).

Traditional simulations can only capture finite regions of spacetime, missing the complete picture of how waves travel from their origins to their ultimate destinations. In essence, they don't tell the full story.

"Our work resolves the gravitational wave on past null infinity, evolves the fully nonlinear Einstein equations through the black hole spacetime, and naturally extracts the gravitational waveform at future null infinity," explained Prof. Frauendiener.

This comprehensive approach provides what the researchers call the true cause-and-effect relationship between the incoming and outgoing radiation.

A mathematical tour de force

The researchers used the Friedrich's Generalized Conformal Field Equations (GCFE), a mathematical framework that rescales spacetime to bring infinite distance into a finite computational domain. This makes the infinite accessible.

To solve the evolution equations, the researchers built a custom software package known as COnFormal Field Equation Evolver (COFFEE). Using COFFEE, the researchers simulated gravitational wave pulses of varying strengths encountering a Schwarzschild black hole.

The researchers tested a range of wave amplitudes, tracking how much of their energy was absorbed versus scattered when encountering the black hole.

Their simulations revealed that spacetime is exceptionally stiff.

For incoming waves having weak amplitudes, only about 8.5% of the energy scattered back to infinity, with the rest being absorbed by the black hole. Even for waves with strong amplitudes, only about 20% of the energy escaped.

Measuring energy at infinity

To understand how much energy flows in and out during the scattering process, the researchers calculated two quantities: Bondi energy and Bondi news at both infinities.

"The Bondi news is simply a quantity that 'brings news' that there is gravitational radiation. "Namely, if it is non-zero, there is gravitational radiation, and zero otherwise," explained Thwala.

On the other hand, Bondi energy is the total energy on a light cone from any point in spacetime. It is one of the few rigorous ways to define energy in general relativity.

These measurements allowed the researchers to verify energy conservation with remarkable precision throughout their simulations, providing crucial validation of their numerical methods.

They also observed fascinating nonlinear effects. Despite injecting simple wave patterns, the complex dynamics of curved spacetime generated additional wave modes through backreaction. This is essentially when waves create new waves as they propagate.

Most intriguingly, when outgoing radiation reached future null infinity, it exhibited characteristic oscillations known as quasinormal ringing, which is the black hole's natural vibration frequency.

The researchers found that this frequency remained unchanged regardless of the incoming wave's properties, suggesting it depends solely on the black hole itself.

Implications and refining the model

Dr. Stevens emphasized the importance of their work, saying, "Having data at both infinities allows one to make rigorous statements about what is going in to what is going out for the first time.

"This can begin to answer questions about how black holes scatter gravitational waves, and how much energy is absorbed by the black hole, and how much is radiated away."

This holds particular importance in modern astronomy, where experiments like LIGO detect gravitational waves emerging from black holes or neutron stars.

Despite showing promise, the researchers identify a challenge that remains to be addressed.

"The main problem with the current method is that the initial wave is not set directly on past null infinity," said Prof. Frauendiener. "Being able to set the ingoing wave directly, then evolving it to future null infinity, would be ideal."

For now, the researchers plan to focus on uncovering global properties of the scattering problem instead of extending their method to more complex scenarios.

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