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In theoretical physics, a dynamical horizon (DH) is a local description (i.e. independent of the global structure of the spacetime) of evolving black hole horizons. In literature there exists two different mathematical formulation of DHs—2+2 formulation developed by Sean Hayward and 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

Isolated horizon
Non-expanding horizon

References
Cross-reference

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.

"Black Holes". University of Cardiff School of Physics and Astronomy. Retrieved 2012-03-08.

Major papers

Ashtekar, Abhay; Krishnan, Badri (2004). "Isolated and Dynamical Horizons and Their Applications". Living Reviews in Relativity 7. arXiv:gr-qc/0407042v3. Bibcode:2004LRR.....7...10A. doi:10.12942/lrr-2004-10.
Schnetter, Erik; Krishnan, Badri; Beyer, Florian (2006). "Introduction to dynamical horizons in numerical relativity". Phys. Rev. D 74. arXiv:gr-qc/0604015v2. Bibcode:2006PhRvD..74b4028S. doi:10.1103/PhysRevD.74.024028.

Other work

Ashtekar, Abhay; Galloway, Gregory J. (2005). "Some uniqueness results for dynamical horizons". Adv. Theor. Math. Phys. 9: 1–30. arXiv:gr-qc/0503109. Bibcode:2005gr.qc.....3109A.
Jaramillo, J. L.; Gourgoulhon, E. (2007). "Dynamical horizons in excised black hole evolutions". Journal of Physics: Conference Series 66. Bibcode:2007JPhCS..66a2048J. doi:10.1088/1742-6596/66/1/012048.
Bartnik, Robert; Isenberg, James (2006). "Spherically symmetric dynamical horizons" (PDF). Classical and Quantum Gravity 23 (7). arXiv:gr-qc/0512091. Bibcode:2006CQGra..23.2559B. doi:10.1088/0264-9381/23/7/020.
Wu, Yu-Huei; Wang, Chih-Hung (2011). "Gravitational radiation and angular momentum flux from a slowly rotating dynamical black hole". Phys. Rev. D 83 (08): 40–44. arXiv:1009.3331. Bibcode:2011PhRvD..83h4044W. doi:10.1103/PhysRevD.83.084044.
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). arXiv:0912.4633. Bibcode:2010PhRvD..81d4034W. doi:10.1103/PhysRevD.81.044034.
Sawayama, Shintaro (2006). "Dynamical horizon of evaporating black hole in Vaidya spacetime". Phys. Rev. D 73. arXiv:gr-qc/0509048v2. Bibcode:2006PhRvD..73f4024S. doi:10.1103/PhysRevD.73.064024.

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