Homogeneous Einstein Metrics on SU(n) Manifolds, Hoop Conjecture for Black Rings, and Ergoregions in Magnetised Black Hole Spacetimes
This Dissertation covers three aspects of General Relativity: inequivalent Einstein metrics on Lie Group Manifolds, proving the Hoop Conjecture for Black Rings, and investigating ergoregions in magnetised black hole spacetimes. A number of analytical and numerical techniques are employed to that end...
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ndltd-tamu.edu-oai-repository.tamu.edu-1969.1-1492622013-10-04T04:55:02ZHomogeneous Einstein Metrics on SU(n) Manifolds, Hoop Conjecture for Black Rings, and Ergoregions in Magnetised Black Hole SpacetimesMujtaba, Abid HasanEinstein metricsSU(n)Hoop ConjectureBlack RingsErgoregionsKerr-NewmanMelvinThis Dissertation covers three aspects of General Relativity: inequivalent Einstein metrics on Lie Group Manifolds, proving the Hoop Conjecture for Black Rings, and investigating ergoregions in magnetised black hole spacetimes. A number of analytical and numerical techniques are employed to that end. It is known that every compact simple Lie Group admits a bi-invariant homogeneous Einstein metric. We use two ansatze to probe the existence of additional inequivalent Einstein metrics on the Lie Group SU (n). We provide an explicit construction of 2k + 1 and 2k inequivalent Einstein metrics on SU (2k) and SU (2k + 1) respectively. We prove the Hoop Conjecture for neutral and charged, singly and doubly rotating black rings. This allows one to determine whether a rotating mass distribution has an event horizon, that it is in fact a black ring. We investigate ergoregions in magnetised black hole spacetimes. We show that, in general, rotating charged black holes (Kerr-Newman) immersed in an external magnetic field have ergoregions that extend to infinity near the central axis unless we restrict the charge to q = amB and keep B below a maximal value. Additionally, we show that as B is increased from zero the ergoregion adjacent to the event horizon shrinks, vanishing altogether at a critical value, before reappearing and growing until it is no longer bounded as B becomes greater than the maximal value.Pope, Christopher NSezgin, ErginDutta, BhaskarFulling, Stephen2013-10-02T21:27:29Z2013-10-02T21:27:29Z2013-052013-01-09May 20132013-10-02T21:27:29ZThesistextapplication/pdfhttp://hdl.handle.net/1969.1/149262 |
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Einstein metrics SU(n) Hoop Conjecture Black Rings Ergoregions Kerr-Newman Melvin |
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Einstein metrics SU(n) Hoop Conjecture Black Rings Ergoregions Kerr-Newman Melvin Mujtaba, Abid Hasan Homogeneous Einstein Metrics on SU(n) Manifolds, Hoop Conjecture for Black Rings, and Ergoregions in Magnetised Black Hole Spacetimes |
description |
This Dissertation covers three aspects of General Relativity: inequivalent Einstein metrics on Lie Group Manifolds, proving the Hoop Conjecture for Black Rings, and investigating ergoregions in magnetised black hole spacetimes. A number of analytical and numerical techniques are employed to that end.
It is known that every compact simple Lie Group admits a bi-invariant homogeneous Einstein metric. We use two ansatze to probe the existence of additional inequivalent Einstein metrics on the Lie Group SU (n). We provide an explicit construction of 2k + 1 and 2k inequivalent Einstein metrics on SU (2k) and SU (2k + 1) respectively.
We prove the Hoop Conjecture for neutral and charged, singly and doubly rotating black rings. This allows one to determine whether a rotating mass distribution has an event horizon, that it is in fact a black ring.
We investigate ergoregions in magnetised black hole spacetimes. We show that, in general, rotating charged black holes (Kerr-Newman) immersed in an external magnetic field have ergoregions that extend to infinity near the central axis unless we restrict the charge to q = amB and keep B below a maximal value. Additionally, we show that as B is increased from zero the ergoregion adjacent to the event horizon shrinks, vanishing altogether at a critical value, before reappearing and growing until it is no longer bounded as B becomes greater than the maximal value. |
author2 |
Pope, Christopher N |
author_facet |
Pope, Christopher N Mujtaba, Abid Hasan |
author |
Mujtaba, Abid Hasan |
author_sort |
Mujtaba, Abid Hasan |
title |
Homogeneous Einstein Metrics on SU(n) Manifolds, Hoop Conjecture for Black Rings, and Ergoregions in Magnetised Black Hole Spacetimes |
title_short |
Homogeneous Einstein Metrics on SU(n) Manifolds, Hoop Conjecture for Black Rings, and Ergoregions in Magnetised Black Hole Spacetimes |
title_full |
Homogeneous Einstein Metrics on SU(n) Manifolds, Hoop Conjecture for Black Rings, and Ergoregions in Magnetised Black Hole Spacetimes |
title_fullStr |
Homogeneous Einstein Metrics on SU(n) Manifolds, Hoop Conjecture for Black Rings, and Ergoregions in Magnetised Black Hole Spacetimes |
title_full_unstemmed |
Homogeneous Einstein Metrics on SU(n) Manifolds, Hoop Conjecture for Black Rings, and Ergoregions in Magnetised Black Hole Spacetimes |
title_sort |
homogeneous einstein metrics on su(n) manifolds, hoop conjecture for black rings, and ergoregions in magnetised black hole spacetimes |
publishDate |
2013 |
url |
http://hdl.handle.net/1969.1/149262 |
work_keys_str_mv |
AT mujtabaabidhasan homogeneouseinsteinmetricsonsunmanifoldshoopconjectureforblackringsandergoregionsinmagnetisedblackholespacetimes |
_version_ |
1716603950352826368 |