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## Black Hole Disasters

February 19th, 2017

Given the current situation, the destruction of planet Earth through an encounter with a black hole is a low-probability scenario that should elicit relatively little concern.

Nonetheless, the industry surrounding black holes and their various associated activities generates a non-negligible economic contribution. By way of setting scale, an article in this week’s New York Times points to the statistic that the total US commercial honeybee pollination industry has an annual value of order $500 million, with slim margins and the ongoing specter of colony collapse disorder. The movie Interstellar, by contrast, generated$675 million in receipts based on a \$165 million production budget. Having seen the movie, I would hazard a guess that a significant, if not decisive, factor in the box office draw centered on the numerical calculation of ray bundle propagation through the curved spacetime of a spinning Kerr black hole, as described by James, Tunzelmann, Franklin & Thorne (2015).

Figure 16 from James et al. (2015)

Activities as diverse as the technology development and staffing of LIGO, the awarding of multi-million dollar prizes, and lurid television documentaries are all parts of the thriving Black-Holes-as-a-Business paradigm. Sure, I’m being a little facetious here, but not really… It’s a real phenomenon.

As far as planets are concerned, disasters associated with black hole encounters can be divided into three very distinct categories. Throughout the visible universe, over the course of cosmic time, a very large number of Earth-sized planets have come to untimely demise by crossing the event horizon of a supermassive black hole. Rather preposterously, this was the premise underlying a recent episode of History Channel’s The End. As a practical matter, we would have of order 500 million years of advance notice if a rogue M87-style supermassive black hole — presumably ejected during a 3-body encounter in a massive galaxy merger — were impinging on the Local Group. When an inhabited planet enters an isolated billion solar mass Schwarzschild black hole, there is a period measured in hours where one sails comfortably numbed through a bizarre GR-mediated light show. Things get bad only in the last thirty minutes or so before the encounter with the singularity.

A second genre of black hole disaster occurs whenever a planet encounters an ordinary Cygnus X-1 style black hole, or indeed, any black hole with a mass ranging from roughly planetary heft to millions of solar masses. In these events, a planet is generally tidally shredded before encountering the event horizon, and from an on-the-ground perspective, the histrionics fall broadly into the type experienced by the planet Theia ~4.51 billion years ago. In both the near term, as well as the extremely long term, Earth stands effectively zero chance of succumbing to black hole-mediated tidal destruction.

Primordial black holes might actually pose a non-absurdist threat. While still fully speculative, it has been proposed that density fluctuations in the early universe created black holes, and in the 10^17 to 10^26 gram mass range there is currently little actual constraint on their existence. Papers have been published that elucidate the seismic disturbances that would result, for example, from the collision of a 10^15 gram black hole traveling at 200 km/s through the Earth.

Generation of seismic waves in Earth following the passage of a 10^15 gram black hole with speed ~200 km/sec From Figure 2 of Luo et al. 2012.

In general, an encounter with a primordial black hole provides a hydrogen bomb-level of devastation at the entry and exit points, but no further consequences as the marauding black hole speeds away into interstellar space. In the early 1970s, a black hole encounter was briefly a credible model (at the got published in Nature level of credibility) for explaining the Tunguska impact.

A singularly unfortunate scenario results if Earth manages to capture a primordial black hole into an orbit with perigee inside Earth. This is hard, but not impossible, if the black hole is a member of a binary pair. The physics of the capture would be similar to the event that is thought to have given rise to Triton in orbit around Neptune. For those interested in details, I attach here some irresponsible order-of-magnitude notes that outline what I believe would happen if Earth were to collect an Enceladus-mass black hole in its thrall.

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