Historical research guide · 0970 · 2025
Breaking spacetime
Pablo G Tello · Imogen Strong
In one minute
Pablo G Tello and Imogen Strong take a teaching idea and run it as far as it will go. Treat the fabric of spacetime as if it really were a fabric — an isotropic, brittle material — and apply Griffith’s fracture criterion, the century-old rule that tells an engineer when a crack in glass will run. Working inside a Planck-sized region, and asking when the energy a violently collapsing star can radiate exceeds the elastic energy stored there, they recover the maximum force that general relativity is hypothesised to allow, and they get it without string theory, cosmological arguments or black holes. The same step hands them a bonding energy for spacetime of about 10⁷⁸ joules per square metre, and a frequency at which spacetime’s stiffness would match it — the Planck frequency, and therefore out of reach. They close by asking whether a ball of light could collapse into a black hole, and conclude that vacuum polarisation, the Schwinger effect, would drain it first.
Connection
Chapter 4 treats the metric as something you can engineer, which means treating spacetime as a medium with properties — and this short paper puts numbers on two of them, a stiffness and a bond energy, using nothing more exotic than materials engineering. For chapter 3 it is the same instinct from the other direction: the vacuum answers back, here through the Schwinger effect, which the authors find is enough to stop a ball of light from ever closing into a horizon. And for chapter 1 it is a clean example of a stated speculation, offered as a pedagogical exercise with its own limits written on the front.
From the source
Treating the fabric of spacetime at face value as an isotropic, brittle material and applying Griffith’s fracture criterion inside a Planck volume — requiring that the maximum energy a violent astrophysical object can radiate in a Planck time exceed the elastic energy of that region — produces a relation whose right-hand side is the postulated maximum force allowed by general relativity, obtained without any of the string-theoretic, cosmological or black-hole arguments previously used to justify it.Section 3, An analogy for spacetime fracture, Equations 3 to 7 and the first of the three observations
The same relation yields a hypothetical bonding energy between spacetime’s fundamental building blocks of about 10⁷⁸ joules per square metre; below that value, the authors argue, a hypothetical spacetime break could occur from the elastic energy released by a speculated extremely dynamic astrophysical system.Section 3, second observation; Abstract
Using the frequency-dependent Young’s modulus of spacetime given by Rainer Weiss — about 10²⁰ times that of steel at 100 hertz, in answer to a question at Kip Thorne’s 2018 Hamilton Lecture at Princeton — the authors define an axial spacetime stiffness and find that for that stiffness to exceed the bond energy the required frequency would be of order 10⁴³ hertz, the same order as the Planck frequency, and therefore beyond what is possible.Section 1, Introduction; Section 3, third observation, Equations 8 and 9
Because the bond energy follows straight from the maximum luminosity, it can be read as the minimum spacetime bond-breaking energy — and it is not attainable in practice, since the maximum luminosity is itself a limit reached only when a highly dynamical object is exactly at its gravitational radius, at which point not even gravitational waves escape and no energy is radiated. The conclusion the authors draw is that in situations close to these extremes spacetime would remain unbroken.Section 3, closing paragraph
Following Álvarez-Domínguez and colleagues, who find that the dissipative effects of the Schwinger mechanism prevent a kugelblitz from forming over length scales from 10⁻²⁹ to 10⁸ metres, the authors apply the same bounds at the Planck radius: with a bond energy of 10⁷⁸ joules per square metre and a flux of order 10¹¹⁸ watts per square metre, the formation time works out at about 10⁻⁴⁰ seconds against a dissipation time equal to the Planck time of about 10⁻⁴⁴ seconds, so no kugelblitz can form even at Planck scales.Section 4, A kugelblitz?, Equations 10 to 14
The authors present the work as pedagogical and speculative, without full mathematical rigour, and offer it as a possible motivation for gravitational-wave research, on the grounds that gravitational waves are a consequence of spacetime vibration and are expected across frequencies from 10⁻¹⁷ hertz for ripples in the cosmological background upward.Section 1, Introduction; Section 5, Conclusions
The way in
https://doi.org/10.1088/1361-6404/ae04b4How to cite it
Pablo G Tello, Imogen Strong (2025) Breaking spacetime doi:10.1088/1361-6404/ae04b4