Penrose-fest @ 95

In this talk, I revisit the problem of defining spacetime singularities in classical general relativity. In particular, I argue that singularities are best conceptualized as extrinsic, non-local, but localizable, properties of spacetime regions (of any size), and that there is no unique, best definition of a singular region of spacetime. There is, however, a schema that any adequate definition instantiates. Moreover, the question of what kind of incomplete curves witness singular structure is intimately connected to the question of what kind of curves represent possible trajectories of observers in physically reasonable motion. Finally, I discuss a sense in which singular regions can be “small” and present a result which proves the existence of such small singular regions in any singular spacetime based on the work of B.G. Schmidt (1971).

The creation of black hole thermodynamics (BHT) started in 1969 with the Penrose process of energy extraction from a rotating black hole and ended in 1974 with Hawking’s discovery of black hole radiation with a black body spectrum. We explain what happened in between, highlighting both Penrose’s profound influence on the entire process and Hawking’s motivation for his discovery, which despite also his major role in BHT - in competition with Wheeler’s students Christodoulou and Bekenstein at Princeton - had almost nothing to do with that and instead had everything to do with his work on primordial black holes, partly in collaboration with his PhD students Bernard Carr and Gary Gibbons, which crossed Zeldovich’s work in Moscow on superradiance of rotating black holes. (Joint work with Jeroen van Dongen).

The close similarities of the three laws of black hole mechanics, discovered by Bardeen, Carter and Hawking, with the laws of thermodynamics led to the identification of a multiple of the area of the event horizon with entropy. However, developments over the past two decades have shown that this paradigm is not viable for dynamical black holes, especially because of the teleological nature of event horizons. After a brief review of these limitations, I will show that they can be overcome by replacing event horizons with quasi-local horizons. The new first and second laws hold for black holes arbitrarily far from equilibrium and lead one to identify entropy with marginally trapped surfaces in these horizons. This generalization of black hole thermodynamics encompasses fully dynamical black holes that form due to gravitational collapse and undergo mergers in classical general relativity, as well as those that evaporate due to quantum effects. It is now being used to address open issues and puzzles in all these dynamical processes.

This talk will give a survey of the twistor programme and twistor theory. The first half will be devoted to the seminal series of papers by Roger Penrose through the late 60'2 and 70s, aiming to be non-technical and pictorial. These propose that in order to quantize gravity, space-time events themselves should emerge from the more fundamental geometry of the space of spinning massless particles, now known as twistor space. This embodies something of the spirit of relational or Machian principles and potentially allows events themselves to be quantized. The second half of the talk will explain how the programme has evolved from this period. Firstly it became a mathematical tool with surprisingly powerful and varied applications. But more recently it has been developed again as a fundamental arena for physics via twistor strings, ambitwistor strings and most recently, celestial holography. I hope to be able to give at least an impressionistic flavour of these developments that ave been contributed to by many groups over the years.

The mathematical objects deployed to represent structures and dynamics 'at infinity' have come to play deep explanatory roles in gravitational physics. After recapitulating how spacetime events infinitely far away can bear on understanding local phenomena, I describe the technical obstructions that arise in de-idealising asymptotically flat spacetimes to (more cosmologically relevant) asymptotically de Sitter ones. I refer to the search for boundary structures capable of appropriately hosting both gravitational radiation and accelerated expansion as the 'Problem of de Sitter Asymptotia'. I argue that, as opposed to a single-parameter limit, asymptotic flatness is best understood as a concord of multiple geometrical and dynamical conditions that only contingently cooperate. In the presence of a positive cosmological constant, the concord shatters and, depending on which aspects of physics facilitated by asymptotic flatness one pursues, substantially distinct de-idealising routes become available. I organise the landscape of positive proposals on the basis of their methodological commitments, identify conceptual continuities and irreconcilable incompatibilities, and insert myself in this implicit dialectic with historico-philosophical remarks. Finally, I describe how gravitational wave memory (a potential observable for the Laser Interferometer Space Antenna) provides an added impetus to address the problem of de Sitter Asymptotia, as well as a guiding constraint to evaluate candidate proposals.

The Giant Ring is a ring-like ultra-large-scale structure (uLSS) that appears to extend from the previously-reported Giant Arc (Lopez et al. 2022). It is an almost contiguous, overdense filament of MgII absorbers which appears as a Giant Ring, approximately 1Gpc across, from our line of sight. Previously, the Giant Arc (GA) and the Big Ring (BR; Lopez et al. 2024) were reported in the literature as uLSS discoveries that are very interesting for cosmology due to their huge sizes, their close cosmological proximity to each other, and their curious ring-like morphologies. Following this, there were hints that the GA could extend into a GR (Lopez et al. 2025), which was investigated further.

The method of discovery is mapping intervening MgII absorption systems in the spectra of background quasars to trace galaxies and galaxy clusters. This method was novel compared with standard observational techniques: it allows for the detection of faint matter in the intermediate-redshift Universe which might otherwise be difficult to detect; and this method provides very precise spectroscopic redshifts of the intervening matter.

There is now substantial evidence to support the reality of a GR: different observational methods affirm the presence of an overdense filament encompassed by underdense void regions, and multiple statistical tests confirm >4 sigma detection of a GR. Nested rings (such as the BR and GR) seem unlikely to occur in a FLRW homogeneous universe, so perhaps the explanation for these structures lies beyond standard cosmology. We now begin to consider Penrose’s Conformal Cyclic Cosmology as an explanation to the existence of ring-like ultra-large-scale structures in the Universe.

[FILL: Abstract text.]