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| {{short description|Region outside of a rotating black hole's event horizon}} | |||
| ], equatorial perspective.<ref>{{cite arXiv|last=Visser|first=Matt|title=The Kerr spacetime: A brief introduction|date=15 Jan 2008| |
], equatorial perspective.<ref>{{cite arXiv |last=Visser |first=Matt |title=The Kerr spacetime: A brief introduction |date=15 Jan 2008 |eprint=0706.0622 |page=35|class=gr-qc }}</ref>]] | ||
| ⚫ | |||
| ⚫ | In ], the '''ergosphere''' is a region located outside a ]'s outer ]. Its name was proposed by ] and ] during the ] in 1971 and is derived {{ety|grc|''ἔργον'' (ergon)|work}}. It received this name because it is theoretically possible to ] from this region. The ergosphere touches the event horizon at the poles of a rotating black hole and extends to a greater radius at the equator. A black hole with modest ] has an ergosphere with a shape approximated by an ], while faster spins produce a more pumpkin-shaped ergosphere. The equatorial (maximal) radius of an ergosphere is the ], the radius of a non-rotating black hole. The polar (minimal) radius is also the polar (minimal) radius of the event horizon which can be as little as half the Schwarzschild radius for a maximally rotating black hole.<ref>{{cite web |url=http://physics.ucsd.edu/students/courses/winter2010/physics161/p161.26feb10.pdf |title=Physics 161: Black Holes: Lecture 22 |access-date=2011-10-19 |url-status=live |archive-url=https://web.archive.org/web/20120403010009/http://physics.ucsd.edu/students/courses/winter2010/physics161/p161.26feb10.pdf |archive-date=2012-04-03 |last=Griest |first=Kim |date=26 February 2010}}</ref> | ||
| ⚫ | As a black hole rotates, it twists spacetime in the direction of the rotation at a speed that decreases with distance from the event horizon.<ref>Misner 1973, p.879</ref> This process is known as the ] or ].<ref>Darling |
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| ==Rotation== | |||
| ⚫ | ].]] | ||
| ⚫ | As a black hole rotates, it twists spacetime in the direction of the rotation at a speed that decreases with distance from the event horizon.<ref>Misner 1973, p. 879.</ref> This process is known as the ] or ].<ref>{{cite web |last=Darling |first=David |url=http://www.daviddarling.info/encyclopedia/L/Lense-Thiring_effect.html |title=Lense-Thiring Effect |archive-url=https://web.archive.org/web/20090811155132/http://www.daviddarling.info/encyclopedia/L/Lense-Thiring_effect.html |archive-date=2009-08-11 |url-status=live}}</ref> Because of this dragging effect, an object within the ergosphere cannot appear stationary with respect to an outside observer at a great distance unless that object were to move at faster than the speed of light (an impossibility) with respect to the local spacetime. The speed necessary for such an object to appear stationary decreases at points further out from the event horizon, until at some distance the required speed is negligible. | ||
| ⚫ | A suspended plumb, held stationary outside the ergosphere, will experience an infinite/diverging radial pull as it approaches the static limit. At some point it will start to fall, resulting in a gravitomagnetically induced spinward motion. |
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| The set of all such points defines the ergosphere surface, called '''ergosurface<!--redirect-->'''. The outer surface of the ergosphere is called the ''static surface'' or ''static limit''. This is because ] change from being time-like outside the static limit to being space-like inside it.<ref>Misner 1973, p. 879.</ref> It is the speed of light that arbitrarily defines the ergosphere surface. Such a surface would appear as an oblate that is coincident with the event horizon at the pole of rotation, but at a greater distance from the event horizon at the equator. Outside this surface, space is still dragged, but at a lesser rate.{{Citation needed|date=September 2020}} | |||
| ⚫ | |||
| ==Radial pull== | |||
| ⚫ | The size of the ergosphere, the distance between the ergosurface and the event horizon, is not necessarily proportional to the radius of the event horizon, but rather to the black hole's gravity and its angular momentum. A point at the poles does not move, and thus has no angular momentum, while at the equator a point would have its greatest angular momentum. This variation of angular momentum that extends from the poles to the equator is what gives the ergosphere its |
||
| ⚫ | ]).]] | ||
| ⚫ | A suspended ], held stationary outside the ergosphere, will experience an infinite/diverging radial pull as it approaches the static limit. At some point it will start to fall, resulting in a ] spinward motion. An implication of this dragging of space is the existence of ] within the ergosphere. | ||
| Since the ergosphere is outside the event horizon, it is still possible for objects that enter that region with sufficient velocity to escape from the gravitational pull of the black hole. An object can gain energy by entering the black hole's rotation and then escaping from it, thus taking some of the black hole's energy with it (making the maneuver similar to the exploitation of the ] around "normal" space objects). | |||
| ⚫ | This process of removing energy from a rotating black hole was proposed by the mathematician ] in 1969 and is called the ].<ref>{{cite journal |last1=Bhat |first1=Manjiri |last2=Dhurandhar |first2=Sanjeev |last3=Dadhich |first3=Naresh |url=http://www.ias.ac.in/jarch/jaa/6/85-100.pdf |title=Energetics of the Kerr–Newman Black Hole by the Penrose Process |date=10 January 1985 |journal=Journal of Astrophysics and Astronomy |volume=6 |issue=2 |pages=85–100 |bibcode=1985JApA....6...85B |doi=10.1007/BF02715080|s2cid=53513572 }}</ref> The maximal amount of energy gain possible for a single particle via this process is 20.7% in terms of its mass equivalence,<ref>Chandrasekhar, p. 369.</ref> and if this process is repeated by the same mass, the theoretical maximal energy gain approaches 29% of its original mass-energy equivalent.<ref>Carroll, p. 271.</ref> As this energy is removed, the black hole loses angular momentum, and thus the limit of zero rotation is approached as spacetime dragging is reduced{{reference needed|date=November 2023}}. In the limit, the ergosphere no longer exists. This process is considered a possible explanation for a source of energy of such energetic phenomena as ]s.<ref>{{cite journal |last=Nagataki |first=Shigehiro |title=Rotating BHs as Central Engines of Long GRBs: Faster is Better |journal=Publications of the Astronomical Society of Japan |date=28 June 2011 |arxiv=1010.4964 |doi=10.1093/pasj/63.6.1243 |volume=63 |issue=6 |pages=1243–1249 |bibcode=2011PASJ...63.1243N|s2cid=118666120 }}</ref> Results from computer models show that the Penrose process is capable of producing the high-energy particles that are observed being emitted from ]s and other active galactic nuclei.<ref>{{cite journal |last1=Kafatos |first1=Menas |last2=Leiter |first2=D. |title=Penrose pair production as a power source of quasars and active galactic nuclei |journal=The Astrophysical Journal |date=1979 |volume=229 |pages=46–52 |citeseerx=10.1.1.924.9607 |bibcode=1979ApJ...229...46K |doi=10.1086/156928}}</ref> | ||
| ==Ergosphere size== | |||
| ⚫ | The size of the ergosphere, the distance between the ergosurface and the event horizon, is not necessarily proportional to the radius of the event horizon, but rather to the black hole's gravity and its angular momentum. A point at the poles does not move, and thus has no angular momentum, while at the equator a point would have its greatest angular momentum. This variation of angular momentum that extends from the poles to the equator is what gives the ergosphere its oblate shape. As the mass of the black hole or its rotation speed increases, the size of the ergosphere increases as well.<ref>{{cite journal |last=Visser |first=Matt |title=Acoustic black holes: horizons, ergospheres, and Hawking radiation |journal=Classical and Quantum Gravity |year=1998 |arxiv=gr-qc/9712010 |doi=10.1088/0264-9381/15/6/024 |volume=15 |issue=6 |pages=1767–1791 |bibcode=1998CQGra..15.1767V|s2cid=5526480 }}</ref> | ||
| ==References== | ==References== | ||
| Line 15: | Line 24: | ||
| ==Further reading== | ==Further reading== | ||
| * {{Cite book| last1=Chandrasekhar | first1=Subrahmanyan | |
* {{Cite book| last1=Chandrasekhar | first1=Subrahmanyan |author-link1=Subrahmanyan Chandrasekhar |title=Mathematical Theory of Black Holes|publisher=]|date=1999|isbn=0-19-850370-9 }} | ||
| * {{Cite book|last2=Thorne | first2=Kip S. |last1=Misner | first1=Charles |last3=Wheeler | first3=John |author2-link=Kip Thorne |author1-link=Charles W. Misner| author3-link=John Archibald Wheeler |title=Gravitation|publisher=]|date=1973|isbn=0-7167-0344-0 |
* {{Cite book|last2=Thorne | first2=Kip S. |last1=Misner | first1=Charles |last3=Wheeler | first3=John |author2-link=Kip Thorne |author1-link=Charles W. Misner| author3-link=John Archibald Wheeler |title=Gravitation|publisher=]|date=1973|isbn=0-7167-0344-0 }} | ||
| * {{Cite book |last=Carroll |first=Sean |title=Spacetime and Geometry: An Introduction to General Relativity |date=2003 |isbn=0-8053-8732-3}} | * {{Cite book |last=Carroll |first=Sean |title=Spacetime and Geometry: An Introduction to General Relativity |date=2003 |publisher=Addison Wesley |isbn=0-8053-8732-3}} | ||
| ==External links== | ==External links== | ||
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| * | * | ||
| {{Black holes}} | {{Black holes|state=collapsed}} | ||
| {{Portal bar|Astronomy|Stars|Spaceflight|Outer space|Solar System}} | |||
| ] | ] | ||
| ] | |||
Latest revision as of 16:49, 8 January 2025
Region outside of a rotating black hole's event horizon
In astrophysics, the ergosphere is a region located outside a rotating black hole's outer event horizon. Its name was proposed by Remo Ruffini and John Archibald Wheeler during the Les Houches lectures in 1971 and is derived from Ancient Greek ἔργον (ergon) 'work'. It received this name because it is theoretically possible to extract energy and mass from this region. The ergosphere touches the event horizon at the poles of a rotating black hole and extends to a greater radius at the equator. A black hole with modest angular momentum has an ergosphere with a shape approximated by an oblate spheroid, while faster spins produce a more pumpkin-shaped ergosphere. The equatorial (maximal) radius of an ergosphere is the Schwarzschild radius, the radius of a non-rotating black hole. The polar (minimal) radius is also the polar (minimal) radius of the event horizon which can be as little as half the Schwarzschild radius for a maximally rotating black hole.
Rotation
As a black hole rotates, it twists spacetime in the direction of the rotation at a speed that decreases with distance from the event horizon. This process is known as the Lense–Thirring effect or frame-dragging. Because of this dragging effect, an object within the ergosphere cannot appear stationary with respect to an outside observer at a great distance unless that object were to move at faster than the speed of light (an impossibility) with respect to the local spacetime. The speed necessary for such an object to appear stationary decreases at points further out from the event horizon, until at some distance the required speed is negligible.
The set of all such points defines the ergosphere surface, called ergosurface. The outer surface of the ergosphere is called the static surface or static limit. This is because world lines change from being time-like outside the static limit to being space-like inside it. It is the speed of light that arbitrarily defines the ergosphere surface. Such a surface would appear as an oblate that is coincident with the event horizon at the pole of rotation, but at a greater distance from the event horizon at the equator. Outside this surface, space is still dragged, but at a lesser rate.
Radial pull
A suspended plumb, held stationary outside the ergosphere, will experience an infinite/diverging radial pull as it approaches the static limit. At some point it will start to fall, resulting in a gravitomagnetically induced spinward motion. An implication of this dragging of space is the existence of negative energies within the ergosphere.
Since the ergosphere is outside the event horizon, it is still possible for objects that enter that region with sufficient velocity to escape from the gravitational pull of the black hole. An object can gain energy by entering the black hole's rotation and then escaping from it, thus taking some of the black hole's energy with it (making the maneuver similar to the exploitation of the Oberth effect around "normal" space objects).
This process of removing energy from a rotating black hole was proposed by the mathematician Roger Penrose in 1969 and is called the Penrose process. The maximal amount of energy gain possible for a single particle via this process is 20.7% in terms of its mass equivalence, and if this process is repeated by the same mass, the theoretical maximal energy gain approaches 29% of its original mass-energy equivalent. As this energy is removed, the black hole loses angular momentum, and thus the limit of zero rotation is approached as spacetime dragging is reduced. In the limit, the ergosphere no longer exists. This process is considered a possible explanation for a source of energy of such energetic phenomena as gamma-ray bursts. Results from computer models show that the Penrose process is capable of producing the high-energy particles that are observed being emitted from quasars and other active galactic nuclei.
Ergosphere size
The size of the ergosphere, the distance between the ergosurface and the event horizon, is not necessarily proportional to the radius of the event horizon, but rather to the black hole's gravity and its angular momentum. A point at the poles does not move, and thus has no angular momentum, while at the equator a point would have its greatest angular momentum. This variation of angular momentum that extends from the poles to the equator is what gives the ergosphere its oblate shape. As the mass of the black hole or its rotation speed increases, the size of the ergosphere increases as well.
References
- Visser, Matt (15 Jan 2008). "The Kerr spacetime: A brief introduction". p. 35. arXiv:0706.0622 .
- Griest, Kim (26 February 2010). "Physics 161: Black Holes: Lecture 22" (PDF). Archived (PDF) from the original on 2012-04-03. Retrieved 2011-10-19.
- Misner 1973, p. 879.
- Darling, David. "Lense-Thiring Effect". Archived from the original on 2009-08-11.
- Misner 1973, p. 879.
- Bhat, Manjiri; Dhurandhar, Sanjeev; Dadhich, Naresh (10 January 1985). "Energetics of the Kerr–Newman Black Hole by the Penrose Process" (PDF). Journal of Astrophysics and Astronomy. 6 (2): 85–100. Bibcode:1985JApA....6...85B. doi:10.1007/BF02715080. S2CID 53513572.
- Chandrasekhar, p. 369.
- Carroll, p. 271.
- Nagataki, Shigehiro (28 June 2011). "Rotating BHs as Central Engines of Long GRBs: Faster is Better". Publications of the Astronomical Society of Japan. 63 (6): 1243–1249. arXiv:1010.4964. Bibcode:2011PASJ...63.1243N. doi:10.1093/pasj/63.6.1243. S2CID 118666120.
- Kafatos, Menas; Leiter, D. (1979). "Penrose pair production as a power source of quasars and active galactic nuclei". The Astrophysical Journal. 229: 46–52. Bibcode:1979ApJ...229...46K. CiteSeerX 10.1.1.924.9607. doi:10.1086/156928.
- Visser, Matt (1998). "Acoustic black holes: horizons, ergospheres, and Hawking radiation". Classical and Quantum Gravity. 15 (6): 1767–1791. arXiv:gr-qc/9712010. Bibcode:1998CQGra..15.1767V. doi:10.1088/0264-9381/15/6/024. S2CID 5526480.
Further reading
- Chandrasekhar, Subrahmanyan (1999). Mathematical Theory of Black Holes. Oxford University Press. ISBN 0-19-850370-9.
- Misner, Charles; Thorne, Kip S.; Wheeler, John (1973). Gravitation. W. H. Freeman and Company. ISBN 0-7167-0344-0.
- Carroll, Sean (2003). Spacetime and Geometry: An Introduction to General Relativity. Addison Wesley. ISBN 0-8053-8732-3.
