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Curiel, Erik ORCID logoORCID: https://orcid.org/0000-0002-5812-3033 (2019): Singularities and Black Hole. In: Zalta, Edward (ed.) : The Stanford Encyclopedia of Philosophy. Spring 2019.

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A spacetime singularity is a breakdown in spacetime, either in its geometry or in some other basic physical structure. It is a topic of ongoing physical and philosophical research to clarify both the nature and significance of such pathologies. When it is the fundamental geometry that breaks down, spacetime singularities are often viewed as an end, or “edge”, of spacetime itself. Numerous difficulties, however, arise when one tries to make this notion more precise. Breakdowns in other physical structures pose other problems, just as difficult. Our current theory of spacetime, general relativity, not only allows for singularities, but tells us that they are unavoidable in some real-world circumstances. Thus we apparently need to understand the ontology of singularities if we are to grasp the nature of space and time in the actual universe. The possibility of singularities also carries potentially important implications for the issues of physical determinism and the scope of physical laws.

Black holes are regions of spacetime from which nothing, not even light, can escape. A typical black hole is the result of the gravitational force becoming so strong that one would have to travel faster than light to escape its pull. Such black holes generically contain a spacetime singularity at their center; thus we cannot fully understand a black hole without also understanding the nature of singularities. Black holes, however, raise several additional conceptual problems and questions on their own. When quantum effects are taken into account, black holes, although they are nothing more than regions of spacetime, appear to become thermodynamical entities, with a temperature and an entropy. This seems to point to a deep and hitherto unsuspected connection among our three most fundamental theories, general relativity, quantum field theory and thermodynamics. It is far from clear, however, what it may mean to attribute thermodynamical properties to black holes. At the same time, some of these thermodynamical properties of black holes now seem amenable to direct testing in terrestrial laboratories by observing the behavior of “analogue” systems composed of ordinary material. This all raises problems about inter-theory relations, in particular about relations between the “same” quantity as it appears in different theories. It also bears on the meaning and status of the Second Law of thermodynamics, with possible implications for characterizing a cosmological arrow of time.

Finally, the evolution of black holes is apparently in conflict with standard quantum evolution, for such evolution rules out the sort of increase in entropy that seems to be required when black holes are present. Indeed, as purely gravitational entities with striking quantum properties, what we know about black holes lies at the heart of and guides many attempts to formulate a theory of quantum gravity. This has led to a debate over what seemingly fundamental physical principles are likely to be preserved in, or violated by, a full quantum theory of gravity.

Because so few philosophers have worked on these issues, many questions and problems of great possible interest have not been investigated philosophically at all; others have had only the barest starts made on them; consequently, several sections discussed in this article merely raise questions and point to problems that deserve philosophical attention. The field is wide open for expansive and intensive exploration.

All the technical material required to delve more deeply into the subject of this entry can be found in any of a number of excellent classic and recent sources, including: Hawking and Ellis (1973); Geroch and Horowitz (1979); Wald (1984, 1994); Brout et al (1995); Malament (2007, 2012); and Manchak (2013). The reader unfamiliar with general relativity may find it helpful to review the Hole Argument entry's Beginner's Guide to Modern Spacetime Theories, which presents a brief and accessible introduction to the concepts of a spacetime manifold, a metric, and a worldline.

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