Symmetry and Asymmetry in Astrophysics and Gravitation

Dear Colleagues,

This Special Issue, “Symmetry and Asymmetry in Astrophysics and Gravitation”, will feature contributions from various disciplines in theoretical physics and astronomy in which symmetry and asymmetry play a role. The emphasis will be on symmetries from mathematics with applications in physics. Below, we provide a brief summary of some of the key ideas.

Details:

1. Quantum mechanics (QM) and general relativity (GRT) describe, with exceedingly accuracy, small-scale physics—i.e., the sub-atomic elementary particles—and the large-scale universe. The latter was Einstein’s great achievement. His GRT has been tested with extremely precision in many experiments and observations. QM has perhaps been tested even more accurately in laboratory settings. Together, these theories explain (almost) all known phenomena related to elementary particles. There is, however, a border region where indeterministic QM transitions into deterministic GRT. This region exists near the horizon of a black hole, where curvature (or energy density) becomes so large that quantum effects begin to influence GRT. An overarching theory is therefore required—namely, a theory of quantum gravity. There are two main approaches: either modify GRT or QM. The latter is considered blasphemous by many theorists. However, turning GRT into a quantum field theory appears doomed to fail. How can indeterminism be incorporated into gravitational theory? A new direction may lie in changes in the topology of space.
2. Physicists still do not fully understand what black holes actually are. Are they always formed by the collapse of a star or neutron star? Where is the mass of the hole located—at the centre with infinite density? That idea is untenable. One cannot hide behind the statement that this information remains concealed behind the horizon, because information does not remain hidden. What will a local observer record? The black hole will evaporate, and the information will eventually return. What will remain? Could primordial black holes have formed in the early universe? Theorists speak of instanton formation, a solution that also appears in the Standard Model (SM) of particle physics—namely in the Yang–Mills field (YM). This is interesting in the context of unification models, as the YM field plays a fundamental role in the SM, especially through self-(anti)dual solutions.
3. In both the SM and GRT, the search for symmetries is an essential guiding principle. One example is the charge–parity–time (CPT) invariance in GRT. The SM is fundamentally based on identifying the correct symmetries. Consider Dirac's construction of antiparticles (‘mathematical beauty = truth’). The SM is rich in symmetries, and the incorporation of the Yang–Mills field through SU(3) symmetry was one of its greatest achievements. The distinction between fermions and bosons remains an open issue. Numerous attempts have been made to unify the symmetries of GRT and the SM. We are all familiar with Penrose's monumental work, The Road to Reality.
4. There are, however, differing ideas on how to approach the immense problem of quantum gravity. Should we be more rigorous when proposing new theories? Are additional dimensions required? Should we explore new topological representations of spacetime? And what about reformulating QM itself? As Nobel laureate 't Hooft has argued, ‘There is something wrong with QM.’
5. Cosmology faces two major unresolved problems: the cosmological constant problem and dark matter. Einstein already struggled with the former. The enormous discrepancy between the values predicted by QM and GRT remains unresolved. Ideally, one would like to eliminate this constant altogether. Dark matter presents another propound challenge, particularly in explaining galactic rotation curves. Recent data from the DESI observatory impose strict constraints on the existence of this invisible form of matter. While many candidates have been proposed—WIMPs, axions, mini black holes—clear experimental evidence remains elusive.
6. What about extra dimensions? This is, of course, a controversial subject. Yet, it should be remembered that Kaluza and Klein, Einstein's contemporaries, proposed a five-dimensional universe in 1921 to unify GRT and electromagnetism. A more recent application is the five-dimensional Anti-de Sitter (AdS) cosmological model, a maximally symmetric solution of Einstein’s equations with a negative cosmological constant. Schrödinger provided an early application of this 5D model in his book Expanding Universe. The de Sitter model possesses the six-parameter Lorentz group together with the four-parameter translation group, and Schrödinger already applied the antipodal mapping known as the ‘elliptic’ interpretation.

The most famous application is the AdS₅/CFT correspondence, which is closely related to the holographic principle. Plato already suggested that ‘truth or reality is perhaps nothing more than a shadow of images’. The 5D AdS model can be equivalently described by a 4D conformal field theory—a hologram dual. The principle has been applied to a wide range of models, including the Randall–Sundrum warped 5D brane-world scenarios.

The symmetry properties of these models are particularly intriguing. Poincare’s theorem states that every 3D topological manifold with a trivial fundamental symmetry group is homotopic to the 3-sphere S³. The 3-sphere can be obtained through Hopf fibration from a 5D space. Moreover, complex coordinates can be introduced on S³, allowing the application of spinor mathematics, as fermions carry representation of SL(2,C). The rotation group SO(3) in 3D space is double-covered by the group of 3-spheres of quaternions in 4D space.

Dr. Reinoud Jan Slagter
Prof. Dr. Wenbin Lin
Guest Editors

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• general relativity
• symmetries
• astrophysics
• cosmology
• symmetry breaking
• quantum gravity
• black holes
• topology change
• extra-dimensions