dynamical horizon
{{primary sources|date=March 2012}}
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 {{harvnb|Ashtekar|Krishnan|2004}}).{{sfn|Duggal|Şahin|2010|p=118}} It provides a description of a black hole that is evolving (e.g. one that has a non-zero mass–energy influx).{{sfn|Duggal|Şahin|2010|p=118}} 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:
{{quote|text=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.
|sign=Definition 3.3.2|source={{harvnb|Duggal|Şahin|2010|p=118}}}}
See also
References
=Cross-reference=
{{reflist|20em}}
=Sources used=
{{refbegin}}
- {{cite book|title=Differential geometry of lightlike submanifolds|first1=Krishan L.|last1=Duggal|first2=Bayram|last2=Şahin|publisher=Springer|year=2010|isbn=978-3-0346-0250-1|chapter=Dynamical horizons}}
{{refend}}
Further reading
=Broad outlines=
- {{cite web|url=http://www.astro.cardiff.ac.uk/research/gravity/researchactivities/?page=blackholes|publisher=University of Cardiff School of Physics and Astronomy|title=Black Holes|access-date=2012-03-08}}
=Major papers=
- {{cite journal|first1=Abhay|last1=Ashtekar|authorlink1=Abhay Ashtekar|first2=Badri|last2=Krishnan|title=Isolated and Dynamical Horizons and Their Applications|journal=Living Reviews in Relativity|volume=7|year=2004|issue=1|arxiv=gr-qc/0407042v3|bibcode=2004LRR.....7...10A|doi=10.12942/lrr-2004-10|pmid=28163644|pmc=5253930|page=10|doi-access=free }}
- {{cite journal|journal=Phys. Rev. D|volume=74|year=2006|issue=2|doi=10.1103/PhysRevD.74.024028|arxiv=gr-qc/0604015v2|title=Introduction to dynamical horizons in numerical relativity|first1=Erik|last1=Schnetter|first2=Badri|last2=Krishnan|first3=Florian|last3=Beyer|page=024028|bibcode = 2006PhRvD..74b4028S |s2cid=35349561}}
=Other work=
- {{cite journal|arxiv=gr-qc/0503109|first1=Abhay|last1=Ashtekar|authorlink1=Abhay Ashtekar|first2=Gregory J.|last2=Galloway|title=Some uniqueness results for dynamical horizons|journal=Adv. Theor. Math. Phys.|volume=9|year=2005|pages=1–30|bibcode = 2005gr.qc.....3109A|doi=10.4310/atmp.2005.v9.n1.a1 |s2cid=7484560}}
- {{cite journal|first1=J. L.|last1=Jaramillo|first2=E.|last2=Gourgoulhon|year=2007|journal=Journal of Physics: Conference Series|volume=66|doi=10.1088/1742-6596/66/1/012048|title=Dynamical horizons in excised black hole evolutions |issue=1|bibcode = 2007JPhCS..66a2048J|page=012048 |doi-access=free}}
- {{cite journal|first1=Robert|last1=Bartnik|first2=James|last2=Isenberg|year=2006|journal=Classical and Quantum Gravity|volume=23|issue=7|doi=10.1088/0264-9381/23/7/020|url=http://www.newton.ac.uk/preprints/NI05079.pdf|title=Spherically symmetric dynamical horizons |arxiv = gr-qc/0512091 |bibcode = 2006CQGra..23.2559B |pages=2559–2569 |s2cid=12321797}}
- {{cite journal|journal=Phys. Rev. D|volume=83|issue=8|pages=40–44|year=2011|title=Gravitational radiation and angular momentum flux from a slowly rotating dynamical black hole|last1=Wu|first1=Yu-Huei|last2=Wang|first2=Chih-Hung|doi=10.1103/PhysRevD.83.084044|bibcode = 2011PhRvD..83h4044W |arxiv = 1009.3331 |s2cid=117028848}}
- {{cite journal|first1=Shao-Feng|last1=Wu|first2=Xian-Hui|last2=Ge|first3=Peng-Ming|last3=Zhang|first4=Guo-Hong|last4=Yang|journal=Phys. Rev. D|volume=81|issue=4|year=2010|title=Dynamical horizon entropy and equilibrium thermodynamics of generalized gravity theories|page=044034|doi=10.1103/PhysRevD.81.044034|bibcode = 2010PhRvD..81d4034W |arxiv = 0912.4633 |s2cid=118490680}}
- {{cite journal|arxiv=gr-qc/0509048v2|journal=Phys. Rev. D|volume=73|year=2006|title=Dynamical horizon of evaporating black hole in Vaidya spacetime|first1=Shintaro|last1=Sawayama|issue=6|page=064024|bibcode = 2006PhRvD..73f4024S |doi = 10.1103/PhysRevD.73.064024 }}
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