01
NOV
2021

Time boundaries, black holes and axions

Details of the arrangement of the fields. The blue lines are the electromagnetic flux lines, the red lines are the axion source and the light red discs are the axion current [Credit: J. Gratus, Adapted from Front cover Ann. Phys. 533, 6]

How modelling the next generation of electromagnetic materials for particle acceleration led to challenging a fundamental law of physics. A recently published paper co-authored by researchers from the Cockcroft Institute demonstrates how the laws of physics break down in a black hole or “singularity”.

The challenge of creating cheaper, compact, high-energy particle accelerators is driving many scientists to consider novel methods for particle acceleration.  These include using accelerating structures based on new materials, such as metamaterials and materials with a permittivity that varies rapidly in time.  These materials can be classified in terms of their electromagnetic constitutive relations, which include permittivity, permeability, magneto-electric effects as well as spatial and temporal dispersion.

Novel metamaterials are constructed from arrays of sub-wavelength structures, where at microwave frequencies these structures are millimetres in size. The continuing advances in manufacturing techniques implies that what can be achieved with metamaterials is, perhaps, only limited by our imagination.  In a previous publication, with contributions from these researchers at Cockcroft, it was reported what can be achieved by imagining materials with more exotic properties. A sudden change in permittivity (known as a temporal boundary) predicts exponential amplification of any signal trapped in the structure. Such a broadband amplifier would be exceedingly useful for manipulating particles.

However, it was shown previously that a detailed understanding of the constitutive relations is crucial when a material with loss is used, as conventional approaches in predicting behaviour leads to unphysical results, i.e. exponential signal growth with no external source of power. In contrast, the constitutive relation predicts a temporal boundary will create three, or more electromagnetic waves (Figure 1).

Pushing the imagination further, the researchers considered whether Maxwell’s equations can be modified, while being consistent with all experimental evidence. It turns out that the Maxwell macroscopic fields D and H cannot be measured directly. In experiments, one posits a model for the constitutive relations (e.g. the permittivity depends only on frequency) and measures the parameters of this model.  One questions whether the D and H fields are physical or just approximations, which can be used to categorise media.

Figure 1: A temporal boundary or transition [1].

As an example, it was found that a simple metamaterial made from wires and voltmeters, with a feedback system driving current through the wires, cannot be modelled if D and H exist. However it can be modelled if a new type of axionic medium is included.

Local electric charge conservation, i.e. the total charge in a small region, has been well confirmed by multiple experiments. It therefore is assumed that the global charge is also conserved i.e. the charge in a finite region of space only changes if charge enters or leave. However, this research shows that this need not be the case.

Scientists have recently detected the gravitational waves from astrophysical black holes and have even taken a photo of a supermassive black hole. Microscopic black holes have been predicted to form in particle collisions. Such microscopic black holes evaporate almost instantaneously. If such a black hole can be created and we could sink some of our axionic field in to it, together with some electric charge. This charge would then disappear into the black hole and out of the universe forever!

Cockcroft expert Dr Jonathan Gratus said: “Despite the fascinating diversions into fundamental physics, we see that the underlying physics and mathematics has direct application to particle acceleration. And who knows, perhaps a future generation of accelerator scientists will not only be creating black holes, but using them to accelerate their charged particles.”

Full paper available via:

J. Gratus, et al, Temporary Singularities and Axions: An Analytic Solution that Challenges Charge Conservation, Ann. Phys., 2021, 533, 6 – https://doi.org/10.1002/andp.202000565#

Further reading

[1] Temporal boundaries in electromagnetic materials, (2021) New Journal of Physics. 23 083032

[2] Electromagnetism, Axions, and Topology: a first-order operator approach to constitutive responses provides greater freedom, (2020) Physical Review A. 101, 4,

[3] Evaporating black-holes, wormholes, and vacuum polarisation: must they always conserve charge?, (2019) Foundations of Physics. 49, 4, p. 330-350.