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Critical phenomena in gravitational collapse

Critical phenomena in gravitational collapse
Critical phenomena in gravitational collapse
In general relativity black holes can be formed from regular initial data that do not contain a black hole already. The space of regular initial data for general relativity therefore splits naturally into two halves: data that form a black hole in the evolution and data that do not. The spacetimes that are evolved from initial data near the black hole threshold have many properties that are mathematically analogous to a critical phase transition in statistical mechanics. Solutions near the black hole threshold go through an intermediate attractor, called the critical solution. The critical solution is either time-independent (static) or scale-independent (self-similar). In the latter case, the final black hole mass scales as (p - p*)? along any 1-parameter family of data with a regular parameter p such that p = p* is the black hole threshold in that family. The critical solution and the critical exponent ? are universal near the black hole threshold for a given type of matter. We show how the essence of these phenomena can be understood using dynamical systems theory and dimensional analysis. We then review separately the analogy with critical phase transitions in statistical mechanics, and aspects specific to general relativity, such as spacetime singularities. We examine the evidence that critical phenomena in gravitational collapse are generic, and give an overview of their rich phenomenology.
0370-1573
339-405
Gundlach, Carsten
586f1eb5-3185-4b2b-8656-c29c436040fc
Gundlach, Carsten
586f1eb5-3185-4b2b-8656-c29c436040fc

Gundlach, Carsten (2003) Critical phenomena in gravitational collapse. Physics Reports, 376 (6), 339-405. (doi:10.1016/S0370-1573(02)00560-4).

Record type: Article

Abstract

In general relativity black holes can be formed from regular initial data that do not contain a black hole already. The space of regular initial data for general relativity therefore splits naturally into two halves: data that form a black hole in the evolution and data that do not. The spacetimes that are evolved from initial data near the black hole threshold have many properties that are mathematically analogous to a critical phase transition in statistical mechanics. Solutions near the black hole threshold go through an intermediate attractor, called the critical solution. The critical solution is either time-independent (static) or scale-independent (self-similar). In the latter case, the final black hole mass scales as (p - p*)? along any 1-parameter family of data with a regular parameter p such that p = p* is the black hole threshold in that family. The critical solution and the critical exponent ? are universal near the black hole threshold for a given type of matter. We show how the essence of these phenomena can be understood using dynamical systems theory and dimensional analysis. We then review separately the analogy with critical phase transitions in statistical mechanics, and aspects specific to general relativity, such as spacetime singularities. We examine the evidence that critical phenomena in gravitational collapse are generic, and give an overview of their rich phenomenology.

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Published date: 2003

Identifiers

Local EPrints ID: 29196
URI: https://eprints.soton.ac.uk/id/eprint/29196
ISSN: 0370-1573
PURE UUID: 4a1d09d9-641b-4c99-ac64-a280b3db5d33
ORCID for Carsten Gundlach: ORCID iD orcid.org/0000-0001-9585-5375

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Date deposited: 12 May 2006
Last modified: 20 Jul 2018 00:34

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