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The many definitions of a black hole


Although black holes are objects of central importance across many fields of physics, there is no agreed upon definition for them, a fact that does not seem to be widely recognized. Physicists in different fields conceive of and reason about them in radically different, and often conflicting, ways. All those ways, however, seem sound in the relevant contexts. After examining and comparing many of the definitions used in practice, I consider the problems that the lack of a universally accepted definition leads to, and discuss whether one is in fact needed for progress in the physics of black holes. I conclude that, within reasonable bounds, the profusion of different definitions is in fact a virtue, making the investigation of black holes possible and fruitful in all the many different kinds of problems about them that physicists consider, although one must take care in trying to translate results between fields.

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I am grateful to all the many physicists and philosophers who responded to my questions with thoughtful enthusiasm—you are too many to name, but you know who you are. This Perspective would have been much poorer without the illumination of your discussions. I must, however, single out A. Ashtekar, B. Bonga, P. Chesler, B. Geroch, D. Giulini, G. ’t Hooft, T. Jacobson, C. Kiefer, A. Loeb, J. Maldacena, D. Marolf, R. Narayan, D. Oriti, C. Rovelli, K. Thébault, B. Unruh, B. Wald, D. Wallace, and S.-T. Yau for supererogatory input and further discussion. I thank B. Unruh and B. Wald also for their recollections of the attitude of relativists in the 1960s and 1970s to black holes, as well as A. Loeb and R. Narayan for discussion about the reception of the idea in the community of astrophysicists at the same time. Some of this work was completed at the Black Hole Initiative at Harvard University, which is funded through a grant from the John Templeton Foundation. The rest was completed at the Munich Center for Mathematical Philosophy, in part funded by a grant from the Deutsche Forschungsgemeinschaft (grant number CU 338/1-1 AOBJ 628412).

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Correspondence to Erik Curiel.

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Curiel, E. The many definitions of a black hole. Nat Astron 3, 27–34 (2019).

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