The Mathematical Theory of Black Holes

Front Cover
Clarendon Press, 1998 - Science - 646 pages
Part of the reissued Oxford Classic Texts in the Physical Sciences series, this book was first published in 1983, and has swiftly become one of the great modern classics of relativity theory. It represents a personal testament to the work of the author, who spent several years writing andworking-out the entire subject matter.The theory of black holes is the most simple and beautiful consequence of Einstein's relativity theory. At the time of writing there was no physical evidence for the existence of these objects, therefore all that Professor Chandrasekhar used for their construction were modern mathematical conceptsof space and time. Since that time a growing body of evidence has pointed to the truth of Professor Chandrasekhar's findings, and the wisdom contained in this book has become fully evident.
 

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The mathematical analysis when mixed with intuition physics really complement the gap.But for completion a long way to go and Surprising outcome is there as Nature is more enigmatic than combination physics-mathematics sometimes.
Bohr disliked it because it made the choice of mathematical solution arbitrary. He did not like that a scientist had to choose between equations.
The quantum revolution of the mid-1920s occurred under the direction of both Einstein and Bohr, and their post-revolutionary debates were about making sense of the change. The shocks for Einstein began in 1925 when Werner Heisenberg introduced matrix equations that removed the Newtonian elements of space and time from any underlying reality. The next shock came in 1926 when Max Born proposed that the mechanics was to be understood as a probability without any causal explanation.
Einstein rejected this interpretation. In a 1926 letter to Max Born, Einstein wrote: "I, at any rate, am convinced that He [God] does not throw dice."[5]
Finally, in late 1927, Heisenberg and Born declared at the Solvay Conference that the revolution was over and nothing further was needed. It was at that last stage that Einstein's skepticism turned to dismay. He believed that much had been accomplished, but the reasons for the mechanics still needed to be understood.[4]
Einstein's refusal to accept the revolution as complete reflected his desire to see developed a model for the underlying causes from which these apparent random statistical methods resulted. He did not reject the idea that positions in space-time could never be completely known but did not want to allow the Uncertainty Principle to necessitate a seemingly random, non-deterministic mechanism by which the laws of physics operated. Einstein himself was a great statistical thinker but disagreed that no more needed to be discovered and clarified.[4] Bohr, meanwhile, was dismayed by none of the elements that troubled Einstein. He made his own peace with the contradictions by proposing a Principle of Complementarity that emphasized the role of the observer over the observed.[3]
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Sir Roger Penrose is unique in offering something close to a proof in formal logic that minds are not merely computers. There is a kind of piquant appeal in an argument against the power of formal symbolic systems which is itself clothed largely in formal symbolic terms. Although it is this 'mathematical' argument, based on the famous proof by Gödel of the incompleteness of arithmetic, which has attracted the greatest attention, an important part of Penrose's theory is provided by positive speculations about how consciousness might really work. He thinks that consciousness may depend on a new kind of quantum physics which we don't, as yet, have a theory for, and suggests that the microtubules within brain cells might be the place where the crucial events take place. I think it must be admitted that his negative case against computationalism is much stronger than these positive theories.
You don't think maths tells us anything about the real world then? Well, let's start with the Gödelian argument, anyway. Gödel proved the incompleteness of arithmetic, that is, that there are true statements in arithmetic which can never be proved arithmetically. Actually, the proof goes much wider than that. He provides a way of generating a statement, in any formal algebraic system, which we can see is true, but which cannot be proved within the system. Penrose's point is that any mechanical, algorithmic, process is based on a formal system of some kind. So there will always be some truths that computers can't prove - but which human beings can see are true! So human thought can't be just the running of an algorithm
Citation:The semi blackhole condensate thus acts as a repulsive bump in the centre of the fermionic cloud pushing the fermion cloud out of the centre of the trap and boson cloud acting as an attractor according to laser populated fermion or boson domination. Out of
 

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I Like this book very much.And I Think's that Subrahmanyan Chandrashekar was the greatest astrophysicist of India.

Contents

Introduction
85
An alternative derivation of the Schwarzschild metric
93
the null
123
c The geodesics of the first kind
130
4 THE PERTURBATIONS OF THE SCHWARZSCHILD BLACK
139
wave equation
149
The relations between V and V and Z and Z
160
The elements of the theory of onedimensional potential
166
ELECTROMAGNETIC WAVES IN KERR GEOMETRY
382
The completion of the solution
392
Potential barriers for incident electromagnetic waves
404
The problem of reflexion and transmission
410
Further amplifications and physical interpretation
417
Some general observations on the theory
427
The choice of gauge and the solutions for the spincoefficients
434
Metric perturbations a statement of the problem
443

Perturbations treated via the NewmanPenrose formalism
174
The transformation theory
182
The physical content of the theory
193
The stability of the Schwarzschild blackhole
199
THE REISSNERNORDSTROMSOLUTION
205
An alternative derivation of the ReissnerNordström metric
214
The metric perturbations of the ReissnerNordström solution
226
The transformation theory
245
The problem of reflexion and transmission the scattering
254
The quasinormal modes of the ReissnerNordström black
261
Some general observations on the static blackhole solutions
270
The choice of gauge and the reduction of the equations
278
The derivation of the Kerr metric
286
The uniqueness of the Kerr metric the theorems of Robinson
292
The description of the Kerr spacetime in a NewmanPenrose
299
The nature of the Kerr spacetime
308
THE GEODESICS IN THE KERR SPACEtime
319
The geodesics in the equatorial plane
326
The general equations of geodesic motion and the separability
342
null geodesic
358
The Penrose process
366
Geodesics for aºM
375
The linearization of the remaining Bianchi identities
447
The reduction of system I
453
The separability of V and the functions 9 and 9
464
Four linearized Ricciidentities
470
Explicit solutions for Z and Z2
479
The completion of the solution
485
A retrospect
497
The problem of reflexion and transmission
514
The quasinormal modes of the Kerr blackhole
528
Diracs equation in the NewmanPenrose formalism
543
The conserved current and the reduction of Diracs equations
552
b The separated forms of Diracs equations in oblate
555
OTHER METHODS
563
its derivation and its description
573
The equations governing the coupled electromagnetic
580
A solution of the EinsteinMaxwell equations representing
588
c The linearized versions of the remaining field equations
608
e A variational formulation of the perturbation problem
614
Bibliographical notes
622
Epilogue
637
Copyright

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About the author (1998)

S. Chandrasekhar is at University of Chicago.

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