Astronomy:Dynamical horizon
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In theoretical physics, a dynamical horizon (DH) is a local description (i.e. independent of the global structure of space–time) of evolving black-hole horizons. In the literature there exist two different mathematical formulations of DHs—the 2+2 formulation developed first by Sean Hayward and the 3+1 formulation developed by Abhay Ashtekar and others (see Ashtekar & Krishnan 2004).[1] It provides a description of a black hole that is evolving (e.g. one that has a non-zero mass–energy influx).[1] A related formalism, for black holes with zero influx, is an isolated horizon.
Formal definition
The formal definition of a dynamical horizon is as follows:
A smooth, three-dimensional, space-like submanifold (possibly with boundary) Σ of space–time M is said to be a dynamical horizon if it can be foliated by a family of closed 2-manifolds such that on each leaf L
- the expansion Θ(ℓ) of one null normal ℓ is zero (i.e. it vanishes); and
- the expansion Θ(n) of the other null normal n is negative.
—Definition 3.3.2, Duggal & Şahin 2010, p. 118
See also
References
Cross-reference
- ↑ 1.0 1.1 Duggal & Şahin 2010, p. 118.
Sources used
- Duggal, Krishan L.; Şahin, Bayram (2010). "Dynamical horizons". Differential geometry of lightlike submanifolds. Springer. ISBN 978-3-0346-0250-1.
Further reading
Broad outlines
- "Black Holes". University of Cardiff School of Physics and Astronomy. http://www.astro.cardiff.ac.uk/research/gravity/researchactivities/?page=blackholes.
Major papers
- Ashtekar, Abhay; Krishnan, Badri (2004). "Isolated and Dynamical Horizons and Their Applications". Living Reviews in Relativity 7 (1): 10. doi:10.12942/lrr-2004-10. PMID 28163644. PMC 5253930. Bibcode: 2004LRR.....7...10A. http://relativity.livingreviews.org/Articles/lrr-2004-10/. Retrieved 2012-03-08.
- Schnetter, Erik; Krishnan, Badri; Beyer, Florian (2006). "Introduction to dynamical horizons in numerical relativity". Phys. Rev. D 74 (2): 024028. doi:10.1103/PhysRevD.74.024028. Bibcode: 2006PhRvD..74b4028S.
Other work
- Ashtekar, Abhay; Galloway, Gregory J. (2005). "Some uniqueness results for dynamical horizons". Adv. Theor. Math. Phys. 9: 1–30. doi:10.4310/atmp.2005.v9.n1.a1. Bibcode: 2005gr.qc.....3109A.
- Jaramillo, J. L.; Gourgoulhon, E. (2007). "Dynamical horizons in excised black hole evolutions". Journal of Physics: Conference Series 66 (1): 012048. doi:10.1088/1742-6596/66/1/012048. Bibcode: 2007JPhCS..66a2048J.
- Bartnik, Robert; Isenberg, James (2006). "Spherically symmetric dynamical horizons". Classical and Quantum Gravity 23 (7): 2559–2569. doi:10.1088/0264-9381/23/7/020. Bibcode: 2006CQGra..23.2559B. http://www.newton.ac.uk/preprints/NI05079.pdf.
- Wu, Yu-Huei; Wang, Chih-Hung (2011). "Gravitational radiation and angular momentum flux from a slowly rotating dynamical black hole". Phys. Rev. D 83 (8): 40–44. doi:10.1103/PhysRevD.83.084044. Bibcode: 2011PhRvD..83h4044W.
- Wu, Shao-Feng; Ge, Xian-Hui; Zhang, Peng-Ming; Yang, Guo-Hong (2010). "Dynamical horizon entropy and equilibrium thermodynamics of generalized gravity theories". Phys. Rev. D 81 (4): 044034. doi:10.1103/PhysRevD.81.044034. Bibcode: 2010PhRvD..81d4034W.
- Sawayama, Shintaro (2006). "Dynamical horizon of evaporating black hole in Vaidya spacetime". Phys. Rev. D 73 (6): 064024. doi:10.1103/PhysRevD.73.064024. Bibcode: 2006PhRvD..73f4024S.
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