Singularities and Black Holes

A spacetime singularity is a breakdown in the geometrical structure of space and time. It is a topic of ongoing physical and philosophical research to clarify both the nature and significance of such pathologies. Because it is the fundamental geometry that is breaking down, spacetime singularities are often viewed as an end, or “edge,” of spacetime itself. However, numerous difficulties arise when one tries to make this notion more precise.

Our current theory of spacetime, general relativity, not only allows for singularities, but tells us that they are unavoidable in some real-life 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 contain a spacetime singularity at their center; thus we cannot fully understand a black hole without also understanding the nature of singularities. However, black holes raise several additional conceptual issues. As purely gravitational entities, black holes are at the heart of many attempts to formulate a theory of quantum gravity. Although they are regions of spacetime, black holes are also thermodynamical entities, with a temperature and an entropy; however, it is far from clear what statistical physics underlies these thermodynamical facts. The evolution of black holes is also 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. This has led to a debate over what fundamental physical principles are likely to be preserved in, or violated by, a full quantum theory of gravity.

• 1. Spacetime Singularities
  • 1.1 Path Incompleteness
  • 1.2 Boundary Constructions
  • 1.3 Curvature Pathology
• 2. The Significance of Singularities
  • 2.1 Definitions and Existence of Singularities
  • 2.2 The Breakdown of General Relativity?
• 3. Black Holes
  • 3.1 The Geometrical Nature of Black Holes
• 4. Naked Singularities and the Cosmic Censorship Hypothesis
• 5. Quantum Black Holes
  • 5.1 Black Hole Thermodynamics
  • 5.2 The Generalized Second Law of Thermodynamics
  • 5.3 Information Loss Paradox

The physical investigation of spacetime singularities and black holes has touched on numerous philosophical issues. To begin, we were confronted with the question of the definition and significance of singularities. Should they be defined in terms of incomplete paths, missing points, or curvature pathology? Should we even think that there is a single correct answer to this question? Need we include such things in our ontology, or do they instead merely indicate the break-down of a particular physical theory? Are they “edges” of spacetime, or merely inadequate descriptions that will be dispensed with by a truly fundamental theory of quantum gravity?

This has obvious connections to the issue of how we are to interpret the ontology of merely effective physical descriptions. The debate over the information loss paradox also highlights the conceptual importance of the relationship between different effective theories. At root, the debate is over where and how our effective physical theories will break down: when can they be trusted, and where must they be replaced by a more adequate theory?

Black holes appear to be crucial for our understanding of the relationship between matter and spacetime. As discussed in Section 3, When matter forms a black hole, it is transformed into a purely gravitational entity. When a black hole evaporates, spacetime curvature is transformed into ordinary matter. Thus black holes offer an important arena for investigating the ontology of spacetime and ordinary objects.

Black holes were also seen to provide an important testing ground to investigate the conceptual problems underlying quantum theory and general relativity. The question of whether black hole evolution is unitary raises the issue of how the unitary evolution of standard quantum mechanics serves to guarantee that no experiment can reveal a violation of energy conservation or of microcausality. Likewise, the debate over the information loss paradox can be seen as a debate over whether spacetime or an abstract dynamical state space (Hilbert space) should be viewed as being more fundamental. Might spacetime itself be an emergent entity belonging only to an effective physical theory?

Singularities and black holes are arguably our best windows into the details of quantum gravity, which would seem to be the best candidate for a truly fundamental physical description of the world (if such a fundamental description exists). As such, they offer glimpses into deepest nature of matter, dynamical laws, and space and time; and these glimpses seem to call for a conceptual revision at least as great as that required by quantum mechanics or relativity theory alone.