Does Momentum Contribute to Gravitational Fields Beyond Mass and Kinetic Energy?

General relativity (GR) is often discussed in terms of its fundamental principles, such as the influence of mass and kinetic energy on gravity. However, the role of momentum in gravitational fields is a complex and often overlooked aspect. According to GR, gravitational fields are not only influenced by mass and energy but also by momentum, at least within the context of the 4-momentum from special relativity (SR).

The Role of Momentum in General Relativity

In GR, gravity is described by the curvature of spacetime, which is influenced by the stress-energy tensor. The stress-energy tensor encapsulates the energy, momentum, and stress associated with matter and fields within a given volume. Unlike in special relativity (SR), where momentum and energy are treated more separately, in GR, the stress-energy tensor provides a more comprehensive description, emphasizing the interconnection between these quantities.

The key insight is that every component of the stress-energy tensor is related to the flux of momentum. To understand this better, it is essential to delve into the stress-energy tensor and its components. The energy density component, often referred to as the "energy content," is actually the flux of the time component of momentum across a surface of constant time. Similarly, the other components of the stress-energy tensor represent the flux of spatial momentum components across surfaces orthogonal to the time component.

Interpreting the Stress-Energy Tensor

For a deeper understanding of the stress-energy tensor, consider the relationship between energy, momentum, and stress. As TR Live explains in his answer, 'What exactly is the stress energy momentum tensor in Einstein’s field equations?', the stress-energy tensor is a fundamental object that determines the gravitational field. This tensor is built from the energy-momentum content of the system, and it includes not only mass but also kinetic energy and momentum.

The mass of protons and neutrons, which make up most matter, is often thought of as mass alone. However, this mass is not just inert mass; it is the result of the kinetic energy of quarks and gluons. These particles are bound together, forming the protons and neutrons, and the energy of their interactions is a significant component of the overall mass.

Particles and Momentum

Particles with energy carry momentum, and this is crucial for understanding the full picture of gravity in GR. Within the framework of GR, the momentum of particles is as important as their mass and kinetic energy. The stress-energy tensor effectively captures the momentum flux, making it a comprehensive descriptor of the gravitational field's source.

This means that the stress-energy tensor, rather than simply being dominated by mass and energy, includes the flux of momentum. This flux of momentum is a significant component of the gravity, indicating that momentum indeed plays a role in the creation of gravitational fields beyond the simple consideration of mass and kinetic energy.

Conclusion

The role of momentum in gravitational fields, as described by general relativity, is not secondary or insignificant. Instead, it is an integral part of the stress-energy tensor, providing a more complete picture of the gravitational field's source. Understanding the interplay between mass, energy, and momentum is crucial for a comprehensive grasp of gravity in the context of modern physics.

By recognizing the significance of momentum in the stress-energy tensor, we can better comprehend the intricate nature of gravitational phenomena. This understanding not only enriches our theoretical framework but also has practical implications for various fields, including cosmology, astrophysics, and gravitational astronomy.