Dynamical horizon

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). It provides a description of a black hole that is evolving (e.g. one that has a non-zero mass–energy influx). 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

• Isolated horizon
• Non-expanding horizon

References

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. Retrieved 2012-03-08.

Major papers

• Ashtekar, Abhay; Krishnan, Badri (2004). "Isolated and Dynamical Horizons and Their Applications". Living Reviews in Relativity. 7 (1): 10. arXiv:gr-qc/0407042v3. Bibcode:2004LRR.....7...10A. doi:10.12942/lrr-2004-10. PMC 5253930. PMID 28163644.
• Schnetter, Erik; Krishnan, Badri; Beyer, Florian (2006). "Introduction to dynamical horizons in numerical relativity". Phys. Rev. D. 74 (2): 024028. arXiv:gr-qc/0604015v2. Bibcode:2006PhRvD..74b4028S. doi:10.1103/PhysRevD.74.024028. S2CID 35349561.

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. doi:10.4310/atmp.2005.v9.n1.a1. S2CID 7484560.
• Jaramillo, J. L.; Gourgoulhon, E. (2007). "Dynamical horizons in excised black hole evolutions". Journal of Physics: Conference Series. 66 (1): 012048. 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): 2559–2569. arXiv:gr-qc/0512091. Bibcode:2006CQGra..23.2559B. doi:10.1088/0264-9381/23/7/020. S2CID 12321797.
• 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. arXiv:1009.3331. Bibcode:2011PhRvD..83h4044W. doi:10.1103/PhysRevD.83.084044. S2CID 117028848.
• 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. arXiv:0912.4633. Bibcode:2010PhRvD..81d4034W. doi:10.1103/PhysRevD.81.044034. S2CID 118490680.
• Sawayama, Shintaro (2006). "Dynamical horizon of evaporating black hole in Vaidya spacetime". Phys. Rev. D. 73 (6): 064024. arXiv:gr-qc/0509048v2. Bibcode:2006PhRvD..73f4024S. doi:10.1103/PhysRevD.73.064024.