Binary stars orbiting a black hole, gravitational waves rippling outwards.

Unlocking the Cosmos: How New Theories of Gravity Could Rewrite Our Understanding of Black Holes and Binary Stars

Rhea Morgan in Science & Nature August 2025 • 5 min read.

"Dive into the groundbreaking Einstein-Æther theory and discover how it challenges general relativity, offering new insights into gravitational waves and the extreme behaviors of binary star systems."

The era of gravitational wave astronomy has dawned, thanks to the advanced Laser Interferometer Gravitational-Wave Observatory (aLIGO). These groundbreaking detections have not only confirmed the existence of gravitational radiation from coalescing compact binaries but have also opened a new window into the universe's most extreme gravitational environments. The subtle ripples in spacetime carry information about the orbital evolution of these binaries, making their observation a prime target for testing the limits of our current understanding of gravity.

Einstein-Æther theory (Æ-theory) emerges as a compelling framework for these tests. It dares to challenge one of general relativity's most fundamental principles: local Lorentz invariance. This challenge is mounted through the introduction of a unit timelike vector field, the 'æther field,' which interacts non-minimally with the metric tensor. This interaction sparks the activation and propagation of scalar, vectorial, and tensorial metric perturbations within compact binary systems, offering a richer, more complex gravitational landscape.

While recent gravitational wave observations have stringently constrained the speed at which tensor modes propagate, they remain silent on the other modes. These other modes are currently only weakly constrained by observations within our solar system and from binary pulsars. The key to unlocking further insights lies in constructing detailed gravitational wave models within Æ-theory, which necessitates a deeper understanding of coalescing binaries and their behavior. During their inspiral phase, these binaries trace trajectories that can be modeled as a series of oscillating Keplerian orbits, their paths gradually altered by the emission of gravitational waves. This process occurs within the post-Newtonian (PN) approximation, where changes in the semimajor axis and orbital eccentricity are governed by the rate at which the binary loses orbital energy and angular momentum. Æ-theory proposes modifications to these rates, attributing them to the activation of scalar and vectorial tensor perturbations that carry energy and angular momentum away from the binary. These subtle alterations can then influence the chirping rate of gravitational waves, imprinting a unique signature onto the GW phase. If this signature is absent from observational data, it could serve as a powerful tool to constrain the theory.

Angular Momentum Loss in Einstein-Æther Theory: A Deep Dive

Binary stars orbiting a black hole, gravitational waves rippling outwards.

A pivotal aspect of understanding binary systems within Æ-theory involves studying the rates at which these systems lose energy and angular momentum, particularly when they exhibit eccentricity. This is key to determining how the semimajor axis and orbital eccentricity decay due to gravitational wave emission. First, the gravitational wave stress-energy pseudotensor (SET) is calculated. This is done by expanding the field equations to the second order in perturbations around a flat background.

The SET is then used to calculate the energy and angular momentum flux, which are carried by all propagating modes. These fluxes are expressed in terms of derivatives of the fields. Using a multipolar expansion of the fields, these fluxes are calculated in terms of derivatives of multipole moments. The energy and angular momentum flux is presented as a function of the orbital parameters of the binary using a Keplerian parametrization. This method verifies previous energy flux calculations, extending them to include angular momentum flux for the first time.

Key steps in this process include:

Computing the gravitational wave stress-energy pseudotensor (SET).
Calculating energy and angular momentum flux.
Applying a multipolar expansion of the fields.
Using a Keplerian parametrization.

The generic finding is that, within Æ-theory, the decay rate of the semimajor axis and the orbital eccentricity is faster than predicted by general relativity when dipole emission is present. This is because the increased rate of decay will imprint on the chirping rate of emitted gravitational waves, potentially observable in future GW observations.

Implications and Future Directions

These results can be used in various ways, including constructing a leading-order GR deviation model for the GWs emitted during the inspiral of eccentric compact binaries. These findings pave the way for interesting constraints on Æ-theory using future GW observations from advanced LIGO, third-generation GW detectors, or space-based detectors. Another avenue for future work is to revisit strong-field sensitivity calculations and recompute binary pulsar constraints, considering recent tensor propagation speed constraints. The angular momentum flux calculations presented here can be extended to binary pulsars with varying eccentricities, enriching our understanding of gravitational interactions.

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This article was crafted using a human-AI hybrid and collaborative approach. AI assisted our team with initial drafting, research insights, identifying key questions, and image generation. Our human editors guided topic selection, defined the angle, structured the content, ensured factual accuracy and relevance, refined the tone, and conducted thorough editing to deliver helpful, high-quality information.See our About page for more information.

This article is based on research published under:

DOI-LINK: 10.1103/physrevd.98.124015, Alternate LINK

Title: Angular Momentum Loss For A Binary System In Einstein-Æther Theory

Journal: Physical Review D

Publisher: American Physical Society (APS)

Authors: Alexander Saffer, Nicolás Yunes

Published: 2018-12-14

Everything You Need To Know

How does Einstein-Æther theory challenge the fundamental principles of general relativity, and what are the implications for our understanding of gravity?

Einstein-Æther theory challenges general relativity by introducing a 'æther field,' a unit timelike vector field that interacts with the metric tensor. This interaction leads to scalar, vectorial, and tensorial metric perturbations within compact binary systems, resulting in a richer gravitational landscape than predicted by general relativity. This is in contrast to general relativity, where local Lorentz invariance is a fundamental principle. The Æ-theory suggests modifications to the rate at which binaries lose energy and angular momentum, which influences the chirping rate of gravitational waves and provides a method for constraining the theory based on observational data.

How has the detection of gravitational waves by the advanced Laser Interferometer Gravitational-Wave Observatory (aLIGO) contributed to testing our understanding of gravity in extreme environments?

The detection of gravitational waves by the advanced Laser Interferometer Gravitational-Wave Observatory (aLIGO) allows for the study of gravitational radiation from coalescing compact binaries. These observations provide data about the orbital evolution of these binaries, offering an opportunity to test the limits of our current understanding of gravity. The subtle ripples in spacetime carry information that can be analyzed to understand the behavior of gravity in extreme gravitational environments. These observations help confirm the existence of gravitational radiation and also provide a testing ground for theories like Einstein-Æther theory.

What is the significance of studying the rates at which binary systems lose energy and angular momentum within Einstein-Æther theory, and how does it differ from general relativity?

In Einstein-Æther theory, the rate at which binary systems lose energy and angular momentum is crucial for determining the decay of the semimajor axis and orbital eccentricity. This involves calculating the gravitational wave stress-energy pseudotensor (SET), and then using this pseudotensor to compute the energy and angular momentum flux, which are carried by all propagating modes. These fluxes are expressed in terms of derivatives of multipole moments and are parametrized using a Keplerian parametrization. The theory predicts a faster decay rate of the semimajor axis and orbital eccentricity compared to general relativity when dipole emission is present, influencing the chirping rate of gravitational waves.

How can future gravitational wave observations be used to further constrain Einstein-Æther theory and refine our understanding of gravitational interactions?

Future gravitational wave observations from advanced LIGO, third-generation GW detectors, and space-based detectors can be used to place constraints on Einstein-Æther theory. By constructing leading-order GR deviation models for the GWs emitted during the inspiral of eccentric compact binaries, scientists can compare theoretical predictions with observational data. Additionally, revisiting strong-field sensitivity calculations and recomputing binary pulsar constraints, while considering recent tensor propagation speed constraints, will further refine our understanding. The angular momentum flux calculations can be extended to binary pulsars with varying eccentricities.

What are the limitations of current gravitational wave observations in fully testing Einstein-Æther theory, particularly concerning scalar and vectorial modes, and what steps are needed to overcome these limitations?

While gravitational wave observations have stringently constrained the speed at which tensor modes propagate, scalar and vectorial modes remain weakly constrained. These other modes are only weakly constrained by observations within our solar system and from binary pulsars. Gaining further insights necessitates constructing detailed gravitational wave models within Einstein-Æther theory, requiring a deeper understanding of coalescing binaries and their behavior. These models, coupled with future observations, offer the potential to discover or constrain the properties of these additional modes.