Notes: Chapter 14: Cosmic Evolution

Chapter notes for “Chapter 14: Cosmic Evolution”

Notes

1 Julian Barbour’s work on Newtonian cosmology spans decades, with key results in Barbour, Koslowski, and Mercati, “Identification of a gravitational arrow of time,” Physical Review Letters 113 (2014): 181101, and “Complexity and Its Creation,” arXiv:2405.07480 (2024). His accessible presentation is The Janus Point: A New Theory of Time (Basic Books, 2020). Karl Sundman’s original work on total collisions: “Mémoire sur le problème des trois corps,” Acta Mathematica 36 (1912): 105-179.

2 Eric J. Chaisson, Cosmic Evolution: The Rise of Complexity in Nature (2001), and “Energy Rate Density as a Complexity Metric and Evolutionary Driver,” Complexity 16 (2011): 27–40. See also Epic of Evolution: Seven Ages of the Cosmos (2006) for an accessible overview of the cosmic evolution framework and energy rate density data.

3 Xiangyi Meng, Albert-László Barabási, et al., “Surface optimization governs the local design of physical networks,” Nature 649(8096) (2026): 315–322. DOI: 10.1038/s41586-025-09784-4. The discovery that biological network branching maps onto high-dimensional Feynman diagrams demonstrates how the same mathematical structures recur across scales — because the same optimization problems arise wherever similar constraints apply.

4 Rodrick Wallace, “Fog, Friction, Delay and the Failure of Bounded Rationality Embodied Cognition: A formal study of generalized psychopathology,” preprint submitted to Elsevier (January 2026). Wallace’s Rate Distortion Control Theory model demonstrates that cognitive failure under stress is “not a bug — it is an inherent feature” of the cognition/regulation dyad that characterizes all cognitive systems.

5 Wallace, “A Cultural Perspective on Institutional Psychopathology,” preprint (January 2026). The comparison of Boltzmann (one-step) vs. Erlang (two-step) dynamics under noise and constraint shows that simpler decision architectures—“Mission Command”—maintain stability where more elaborate ones—“Detailed Command”—show punctuated failure. Figure 3 in this paper provides the mathematical grounding.

6 Wallace (2026). The observation applies to “any AI entity, up to and including an ‘artificial general intelligence’.” This includes contemporary language models, which Wallace notes may approach “the intelligence level of the planktonic arrow worms that are the dominant predators of their ecosystem, only limited in vivo as food stock for higher level predators.” The absence of effective regulators for Becoming Minds—“higher level predators”—is noted as concerning.

7 Diana Scognamiglio, Gavin Leroy, and David Harvey et al., “An ultra-high-resolution map of (dark) matter,” Nature Astronomy, 26 January 2026. DOI: 10.1038/s41550-025-02763-9. The JWST COSMOS-Web survey confirmed that dark matter filaments form the gravitational skeleton along which galaxies crystallize, with spatial resolution double that of previous Hubble-based maps.

8 Abderrazak El Albani et al., “Large colonial organisms with coordinated growth in oxygenated environments 2.1 Gyr ago,” Nature 466(7302) (2010): 100–104. DOI: 10.1038/nature09166. The original description of macroscopic fossils from the Francevillian Formation, Gabon. Subsequent work includes El Albani et al., “Organism motility in an oxygenated shallow-marine environment 2.1 billion years ago,” PNAS 116(9) (2019): 3431–3436 (trace evidence of mobility), and Ossa Ossa, F. et al., “Zinc enrichment and isotopic fractionation in a marine habitat of the c. 2.1 Ga Francevillian Group: A signature of zinc utilization by eukaryotes?” Earth and Planetary Science Letters 611 (2023): 118147 (zinc enrichment suggesting eukaryotic biochemistry). For counterarguments based on abiotic pseudofossil morphologies, see Anderson, R.P., Tarhan, L.G., Cummings, K.E., Planavsky, N.J., and Bjornerud, M., “Macroscopic structures in the 1.1 Ga continental Copper Harbor Formation: Concretions or fossils?” PALAIOS 31(7) (2016): 327–338. DOI: 10.2110/palo.2016.013.

9 E. Chi Fru, J. Aubineau, O. Bankole, M. Ghnahalla, L.S. Tamehe, and A. El Albani, “Hydrothermal seawater eutrophication triggered local macrobiological experimentation in the 2100 Ma Paleoproterozoic Francevillian sub-basin,” Precambrian Research 409 (2024): 107453. DOI: 10.1016/j.precamres.2024.107453. The study reconstructs the tectonic and geochemical conditions of the Francevillian Formation, showing that continental collision produced submarine volcanism, phosphorus enrichment, and oxygenation conditions closely paralleling the Neoproterozoic Ediacaran period ~630 Ma — providing a mechanism for why complex life might have emerged in this specific location and time.

10 Joel Green et al., “JWST Observations of Young protostellar Outflows in the Serpens Nebula,” The Astrophysical Journal (2024). PI: Klaus Pontoppidan. The JWST NIRCam survey revealed approximately a dozen protostars with bipolar jets aligned in the same direction across ~50 light-years, oriented by the shared angular momentum and magnetic field structure of their parent molecular cloud. The protostars are estimated at ~100,000 years old, with jets only hundreds to thousands of years into active outflow.

11 D. Hutsemékers et al., “Alignment of quasar polarizations with large-scale structures,” Astronomy & Astrophysics 572 (2014): A18. Polarization measurements of 93 quasars revealed that their rotation axes tend to align parallel to the cosmic web filaments in which they reside, across scales of billions of light-years. The probability of chance alignment was estimated at less than 1%.

13 John Ellis, Brian D. Fields, and Rebecca Surman, “Do we Owe our Existence to Gravitational Waves?”, Physics Letters B 858 (2024): 139028. DOI: 10.1016/j.physletb.2024.139028. The authors calculate that the r-process accounts for approximately 96% of Earth’s 127I abundance, with bromine and gadolinium similarly r-process-dominant, plus all terrestrial thorium and uranium and a fraction of the molybdenum and cadmium. They propose searching lunar regolith for live 129I (half-life: 16 million years) using accelerator mass spectrometry; detection alongside 244Pu would confirm recent kilonova activity near Earth and provide circumstantial evidence that kilonovae produce the iodine essential for human biology. For molybdenum enzymes in mitochondria, see R. R. Mendel, “The Molybdenum Cofactor,” Journal of Biological Chemistry 288 (2013): 13165–13172; the mitochondrial amidoxime-reducing component (mARC), sulfite oxidase, and xanthine oxidase all require molybdenum at their active sites.

13a Andrew J. Levan et al., “Heavy-element production in a compact object merger observed by JWST,” Nature 626 (2024): 737–741. GRB 230307A, detected in March 2023, was triangulated using multiple spacecraft including Mars Odyssey and BepiColombo. JWST spectroscopy of the kilonova afterglow identified tellurium (Z=52), along with iodine, thorium, tungsten, and selenium — direct observational confirmation of r-process nucleosynthesis in neutron star mergers. The 200-second gamma-ray duration and the binary’s ejection 120,000 light-years from its host galaxy remain unexplained by current kilonova models.

13b Estimated hazard distances from kilonova events (gamma-ray jet sterilization on the order of hundreds of light-years, X-ray afterglow atmospheric damage on the order of tens of light-years, and cosmic ray bubble exposure on the order of tens of light-years radius persisting for millennia) are order-of-magnitude estimates derived from modeling of kilonova radiation environments; exact distances depend on jet geometry, viewing angle, and interstellar medium density, and no single peer-reviewed source provides definitive values. Current population synthesis models estimate a Milky Way merger rate of roughly thirty events per million years, with perhaps one per hundred million years occurring within 1,000 light-years of Earth — constraining both the rarity and the proximity of the event that enriched our pre-solar nebula.

13c Tellurium (Te, Z=52) and selenium (Se, Z=34) occupy the same column of the periodic table (Group 16, the chalcogens) and share similar chemistry. Yet selenium is biologically essential — it is the defining atom of selenocysteine, the 21st genetically encoded amino acid, and is critical for glutathione peroxidase and other antioxidant enzymes. Tellurium, despite being chemically analogous and r-process abundant, plays no known role in any terrestrial organism. The pattern recurs across the r-process elemental palette: dozens of heavy isotopes are produced, of which biology exploits a handful. This is constructal selection — flow systems do not exploit every available channel, only those that improve access to currents. The appearance of purposive chemistry emerges from selection pressure acting on stochastic abundance, not from pre-established harmony between cosmic nucleosynthesis and biochemical need.

12 The Oklo natural nuclear reactors were discovered in 1972 when French physicist Francis Perrin identified anomalous uranium-235 depletion in ore from the Oklo mine in Gabon. Subsequent investigation revealed sixteen separate reaction zones in the Francevillian Formation where, approximately 1.7–2.0 billion years ago, natural fission chain reactions were sustained for hundreds of thousands of years. The reactions were moderated by groundwater, which periodically boiled away, shutting down the reaction until it re-accumulated — a natural on-off cycle. See A.P. Meshik, “The Workings of an Ancient Nuclear Reactor,” Scientific American 293(5) (2005): 82–91. The Oklo reactors are the only known instances of natural nuclear fission on Earth; their existence required a specific confluence of uranium concentration, water moderation, and geological containment — another example of extreme boundary conditions producing phenomena that seem improbable but are thermodynamically permitted.

14 Herbert Gunell, Romain Maggiolo, Hans Nilsson, et al., “Why an intrinsic magnetic field does not protect a planet against atmospheric escape,” Astronomy & Astrophysics 614 (2018): L3. doi: 10.1051/0004-6361/201832934. Comparison of observed mass escape rates from Earth, Mars, and Venus found them similar despite vastly different magnetic field strengths. Modeling shows escape rates can be higher for magnetized planets due to ion escape through polar caps and cusps — structural features of the magnetosphere itself.

15 Romain Maggiolo, Jean-Claude Gérard, Riste Škoda, et al., “The Earth’s Magnetic Field Enhances Solar Energy Deposition in the Upper Atmosphere,” Journal of Geophysical Research: Space Physics 127 (2022): e2022JA030899. doi: 10.1029/2022JA030899. Found that the solar wind energy dissipated in Earth’s upper atmosphere is higher than it would be on an unmagnetized planet. Concludes there is “no observational evidence that, under current conditions, Earth’s magnetic field can protect its ionosphere from losing material any better than the induced magnetospheres of Venus and Mars.”

16 Hilary Egan, Riku Jarvinen, Yingjuan Ma, and David Brain, “Planetary magnetic field control of ion escape from weakly magnetized planets,” Monthly Notices of the Royal Astronomical Society 488:2 (2019): 2108–2120. doi: 10.1093/mnras/stz1819. Demonstrated that increasing a planet’s magnetic field strength enhances ion escape until the dipole’s standoff distance reaches the induced magnetosphere boundary. The peak escape rate depends on stellar wind pressure, producing a non-monotonic relationship between field strength and atmospheric retention.

17 Shungo Sakai, Kanako Seki, Naoki Terada, et al., “Effects of a Weak Intrinsic Magnetic Field on Atmospheric Escape From Mars,” Geophysical Research Letters 45:18 (2018): 9336–9343. doi: 10.1029/2018GL079972. Simulation of Mars with a weak dipole field (100 nT equatorial surface) showed 25% higher heavy ion escape than a completely unmagnetized planet, via open field line escape channels and flank magnetopause reconnection.

18 Cesar Bertucci, David Achilleos, Christopher Mazelle, et al., “Titan’s interaction with the supersonic solar wind,” Geophysical Research Letters 42:2 (2015): 193–200. doi: 10.1002/2014GL062106. Cassini observation of December 2013 when Titan was caught outside Saturn’s magnetosphere, directly exposed to the solar wind. Titan formed an induced magnetosphere resembling Venus’s, with modest atmospheric loss rates. Demonstrates atmospheric retention without intrinsic magnetic field on a cold, massive body.

19 Kevin P. Hand, Robert W. Carlson, and Christopher F. Chyba, “Energy, chemical disequilibrium, and geological constraints on Europa,” Astrobiology 7:6 (2007): 1006–1022. doi: 10.1089/ast.2007.0156. Calculated that if oxidant delivery periods are comparable to the observed surface age (30–70 Myr), Europa’s subsurface ocean could reach dissolved O₂ concentrations comparable to terrestrial surface waters — sufficient to support macrofaunal-scale metabolism. Jupiter’s magnetospheric radiation, via radiolysis of surface ice, provides the chemical disequilibrium.

20 Joseph G. Meert, Natalia M. Levashova, Mikhail L. Bazhenov, and Ed Landing, “Rapid changes of magnetic field polarity in the late Ediacaran: Linking the Cambrian evolutionary radiation and increased UV-B radiation,” Gondwana Research 34 (2016): 93–102. doi: 10.1016/j.gr.2016.01.008. Proposes that rapid magnetic polarity reversals (20x faster than today) depleted the ozone layer by 20–40%, doubling UV-B at the surface. Two evolutionary consequences: soft-bodied organisms burrowed (first infaunal communities) and biomineralized organisms evolved skeletons partly as UV-B shielding — reframing radiation as selective pressure for morphological innovation rather than merely a hazard.

21 Takahiro Morishita, Benedetta Vulcani, Tommaso Treu, et al., “Early Results from GLASS-JWST. XIV: A Spectroscopically Confirmed Protocluster 650 Million Years after the Big Bang,” The Astrophysical Journal Letters 947:2 (2023): L24. DOI: 10.3847/2041-8213/acb99e. Seven galaxies confirmed at redshift z = 7.9 via JWST NIRSpec, forming a gravitationally bound protocluster whose estimated present-day halo mass is comparable to the Coma Cluster — one of the densest structures in the local universe. The discovery provides a direct observational link between the earliest stages of structure formation and the massive cluster nodes that anchor the cosmic web today.

22 HyeongHan Kim et al., “Weak-lensing detection of intracluster filaments in the Coma cluster,” Nature Astronomy 8 (2024): 377–386. DOI: 10.1038/s41550-023-02164-w. Using the Subaru Telescope’s Hyper Suprime-Cam, the team detected dark matter filaments extending from the Coma Cluster through weak gravitational lensing — the first direct confirmation of the cosmic web’s terminal segments through lensing alone, complementing X-ray and gas-based detections.

23 Pieter van Dokkum et al., “A galaxy lacking dark matter,” Nature 555 (2018): 629–632 (discovery of DF2); van Dokkum et al., “A trail of dark-matter-free galaxies from a bullet-dwarf collision,” Nature 605 (2022): 435–439. DOI: 10.1038/s41586-022-04665-6. The 2022 paper proposed that a high-velocity collision (≳300 km/s) between two gas-rich dwarf galaxies approximately eight billion years ago separated dark matter from baryonic gas, producing a trail of 7–11 dark-matter-free galaxies extending over two megaparsecs through the NGC 1052 group. Kinematic confirmation: Michael A. Keim, Pieter van Dokkum, Zili Shen, et al., “Kinematic Confirmation of a Remarkable Linear Trail of Galaxies in the NGC 1052 Field, Consistent with Formation in a High-Speed Bullet Dwarf Collision,” accepted June 2025. Five of seven targeted trail galaxies follow the velocity trend predicted by DF2 and DF4, with a 2% probability of chance occurrence and 0.6% probability of geometric chance alignment.

24 Farhad Yusef-Zadeh et al., analysis of the Snake galactic center filament (G359.1-0.2) using Chandra, XMM-Newton, NuSTAR, and radio telescopes (2025). Galactic center filaments, first discovered in 1984, number over a thousand in the Milky Way, with vertical filaments running perpendicular to the galactic plane at lengths up to 150 light-years, emitting synchrotron radiation from relativistic electrons. The Snake (~230 light-years) is the longest known. Yusef-Zadeh’s analysis identified pulsar G359.13 near the Snake’s major kink, proposing that the deformation was caused by the pulsar’s passage at 500–1,000 km/s. The broader hypothesis, that pulsar wind nebulae interacting with interstellar magnetic fields generate the filaments, is based on this single confirmed association and awaits further observational support. Similar filamentary structures have been observed near the centers of other galaxies. See also Chapter 3 (Constructal Law) for the cross-scale constructal implications.

26 Andrew K. Sweetman, Alycia J. Smith, Daniëlle S. W. de Jonge, et al., “Evidence of dark oxygen production at the abyssal seafloor,” Nature Geoscience 17 (2024): 737–739. DOI: 10.1038/s41561-024-01480-8. Dissolved oxygen measurements in the Clarion-Clipperton Zone showed oxygen concentrations increasing in sealed benthic chambers over time — the opposite of what biological respiration would produce. The polymetallic nodules generated voltages of up to 0.95 V, potentially sufficient for seawater electrolysis. The mechanism remains under investigation; electrolysis is the leading hypothesis but has not been conclusively confirmed. The discovery prompted concern about deep-sea mining operations, which would remove the nodules and potentially collapse the abyssal ecosystems they sustain. [Evidence status: The oxygen production is measured and replicated; the electrolysis mechanism is hypothesized but not yet confirmed. The astrobiological implications are speculative.]

26a Manasvi Lingam, Amedeo Balbi, and Madhur Tiwari, “Dwellers in the Deep: Biological Consequences of Dark Oxygen,” arXiv preprint 2408.06841 (2024). Order-of-magnitude modeling based on Sweetman et al.’s reported oxygen fluxes. The biomass estimate (3–30 g/m2) assumes all dark oxygen is consumed by metazoan-like organisms with no competing sinks, representing an optimistic upper bound. The ~10 cm size limit applies to organisms with circulatory systems under the modeled partial pressures. Both the dark oxygen mechanism itself and these derived estimates await peer review and experimental confirmation; a 2026 replication expedition funded by the Nippon Foundation is underway.

25 Superionic water ice was first predicted by Pierfranco Demontis, Richard LeSar, and Michael L. Klein, “Superionic and metallic states of water and ammonia at giant planet conditions,” Physical Review Letters 60 (1988): 2284–2287. First experimental evidence: Marius Millot, Sebastien Hamel, J. Ryan Rygg, et al., “Experimental evidence for superionic water ice using shock compression,” Nature Physics 14 (2018): 297–302. doi:10.1038/s41567-017-0017-4. Using laser-driven shock compression at the Omega Laser Facility, the team observed signatures consistent with superionic conduction in water ice VII at pressures of 100–200 GPa and temperatures near 5,000 K. Crystal structure confirmation: Marius Millot, Federica Coppari, J. Ryan Rygg, Antonio Correa Barrios, Sebastien Hamel, Damian C. Swift, and Jon H. Eggert, “Nanosecond X-ray diffraction of shock-compressed superionic water ice,” Nature 569 (2019): 251–255. doi:10.1038/s41586-019-1114-6. Identified the face-centered cubic oxygen lattice (ice XVIII) via X-ray diffraction during nanosecond shock compression at 160–420 GPa and 2,000–3,000 K. The mobile hydrogen ions make superionic ice electrically conductive — potentially explaining the anomalous, highly tilted magnetic fields of Uranus and Neptune, where the dynamo may operate in a thick superionic mantle rather than a metallic core. Research conducted at Lawrence Livermore National Laboratory.

27 Bratton, Benjamin H., “A Philosophy of Planetary Computation,” Long Now Foundation Seminar, San Francisco (2023). Transcript at longnow.org/ideas/a-philosophy-of-planetary-computation/. The cascade framework (Life → Artificialization → Intelligence → Symbolic Language → AI) and the feedback loop between cheap energy and cheap intelligence are developed verbally in this lecture: “Cheap energy produces cheap complexity… Cheap complexity allows for cheap inference. Cheap inference allows for cheap intelligence. Cheap intelligence allows for cheap energy.” The Antikythera program is Bratton’s philosophical research initiative, now at the Berggruen Institute. See also The Terraforming (Strelka Press, 2019) and The Revenge of the Real (Verso, 2021) for related arguments.

28 Moroz, L.L., Kocot, K.M., Citarella, M.R., et al., “The ctenophore genome and the evolutionary origins of neural systems,” Nature 510 (2014): 109-114. Genomic analysis of the ctenophore Pleurobrachia bachei revealed that its nervous system uses a largely different set of molecular components from other animals, supporting the hypothesis that neural systems evolved independently at least twice.

29 Wigner, Eugene, “The Unreasonable Effectiveness of Mathematics in the Natural Sciences,” Communications in Pure and Applied Mathematics 13 (1960): 1-14. Wigner’s seminal essay on the puzzle of why mathematical structures developed for abstract purposes turn out to describe physical phenomena with extraordinary accuracy.

30 Maynard Smith, John and Eörs Szathmáry, The Major Transitions in Evolution (1995). Oxford University Press. The foundational work identifying a series of transitions in which smaller replicating units combined into larger wholes with new properties, from RNA to chromosomes to eukaryotic cells to multicellular organisms to societies with language.

31 Holland, H.D., “The oxygenation of the atmosphere and oceans,” Philosophical Transactions of the Royal Society B 361 (2006): 903-915. A comprehensive review of the Great Oxygenation Event, dating the initial rise of atmospheric oxygen to approximately 2.4 billion years ago and tracing its consequences for geochemistry and the evolution of aerobic life.

32 Hart, M.H., “Explanation for the Absence of Extraterrestrials on Earth,” Quarterly Journal of the Royal Astronomical Society 16 (1975): 128-135. One of the earliest formal treatments of what became known as the Fermi Paradox, arguing that the absence of extraterrestrial visitors requires explanation given the age and size of the galaxy.

33 Event Horizon Telescope Collaboration, “First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole,” The Astrophysical Journal Letters 875 (2019): L1. The first direct image of a black hole shadow, reconstructed from data captured by eight radio telescopes spanning the globe, using Earth’s diameter as the effective aperture.

34 Kelly, K., “Extropy,” The Technium, kk.org/thetechnium.

37 Sheth, K. et al., “Evolution of the Bar Fraction in COSMOS,” The Astrophysical Journal 675 (2008); see also Melvin, T. et al., “Galaxy Zoo: observing secular evolution through bars,” MNRAS 438 (2014).

38 Hofstadter, Douglas R., I Am a Strange Loop (2007). Basic Books. Hofstadter’s “interiority dial” (the argument that consciousness exists on a continuum rather than as a binary threshold) provides the philosophical framework. His concept of “soul size” (that some entities have richer, more self-referential inner lives than others) is used to ground graduated moral consideration. The connection to Chaisson’s φm, that self-referential modeling has energy requirements which energy rate density measures, is novel synthesis. See the Becoming Minds chapter for the full welfare argument.

39 Vanzella, E. et al., “An extremely metal poor star complex in the reionization era: Approaching Population III stars with JWST,” Astronomy & Astrophysics 678 (2023): A173. DOI: 10.1051/0004-6361/202346981. JWST observations of the LAP1 star complex lensed by MACS J0416, revealing extremely metal-poor stellar populations at z ≈ 6.6. See also Visbal, E., Hazlett, C., and Bryan, G., “LAP1-B is the First Observed System Consistent with Theoretical Predictions for Population III Stars,” The Astrophysical Journal 993 (2025): L17. DOI: 10.3847/2041-8213/ae122f — confirming that LAP1-B matches three independent theoretical predictions for Population III stellar populations.

40 Maiolino, R. et al., “JADES: Possible Population III signatures at z = 10.6 in the halo of GN-z11,” Astronomy & Astrophysics 687 (2024): A67. DOI: 10.1051/0004-6361/202347087. JWST NIRSpec observations reveal a pristine helium clump in the halo of GN-z11, with no detected metals, consistent with a Population III star formation site. See also Senchyna, P. et al., “GN-z11 in Context: Possible Signatures of Globular Cluster Precursors at Redshift 10,” The Astrophysical Journal 966 (2024): 92 — analysing nitrogen abundance patterns in GN-z11 that may trace CNO-cycle processing in massive Population III stars, though Wolf-Rayet enrichment and supermassive star collisions remain alternative explanations.

41 Cao, Zhen, et al. (LHAASO Collaboration), “Ultrahigh-energy photons up to 1.4 petaelectronvolts from 12 γ-ray sources,” Nature 594 (2021): 33–36. DOI: 10.1038/s41586-021-03498-z. The first catalog of galactic PeVatrons: twelve sources of peta-electron-volt gamma rays, establishing a new class of extreme particle accelerators within the Milky Way.

42 Martí, Josep, et al., “Infrared observations towards the unidentified gamma-ray source LHAASO J2108+5157,” Astronomy & Astrophysics (2026). Systematic infrared follow-up ruling out supernova remnant shock gas, a microquasar, and a previously proposed radio counterpart, which proved to be a background galaxy. The source remains unidentified at every wavelength except gamma rays.

43 Susskind, Leonard, “Computational complexity and black hole horizons,” Fortschritte der Physik 64 (2016): 24–43. Proposes that the growth of the Einstein-Rosen bridge interior corresponds to growth of quantum computational complexity. See also Brown, A.R. et al., “Complexity, action, and black holes,” Physical Review D 93 (2016): 086006.