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El. knyga: Gravitation: Foundations and Frontiers

4.73/5 (21 ratings by Goodreads)
(Inter-University Centre for Astronomy and Astrophysics (IUCAA), Pune, India)
  • Formatas: EPUB+DRM
  • Išleidimo metai: 28-Jan-2010
  • Leidėjas: Cambridge University Press
  • Kalba: eng
  • ISBN-13: 9781139637664
Kitos knygos pagal šią temą:
  • Formatas: EPUB+DRM
  • Išleidimo metai: 28-Jan-2010
  • Leidėjas: Cambridge University Press
  • Kalba: eng
  • ISBN-13: 9781139637664
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"Covering all aspects of gravitation in a contemporary style, this advanced textbook is ideal for graduate students and researchers in all areas of theoretical physics. The 'Foundation' section develops the formalism in six chapters, and uses it in the next four chapters to discuss four key applications - spherical spacetimes, black holes, gravitational waves and cosmology. The six chapters in the 'Frontier' section describe cosmological perturbation theory, quantum fields in curved spacetime, and the Hamiltonian structure of general relativity, among several other advanced topics, some of which are covered in-depth for the first time in a textbook. The modular structure of the book allows different sections to be combined to suit a variety of courses. Over 200 exercises are included to test and develop the reader's understanding. There are also over 30 projects, which help readers make the transition from the book to their own original research"--Provided by publisher.

"The modular structure of the book allows different sections to be combined to suit a variety of courses. Over 225 exercises are included to test and develop the readers' understanding. There are also over 30 projects, which help readers make the transition from the book to their own original research"--Provided by publisher.

Covering all aspects of gravitation in a contemporary style, this advanced textbook is ideal for graduate students and researchers in all areas of theoretical physics. The 'Foundation' section develops the formalism in six chapters, and uses it in the next four chapters to discuss four key applications - spherical spacetimes, black holes, gravitational waves and cosmology. The six chapters in the 'Frontier' section describe cosmological perturbation theory, quantum fields in curved spacetime, and the Hamiltonian structure of general relativity, among several other advanced topics, some of which are covered in-depth for the first time in a textbook. The modular structure of the book allows different sections to be combined to suit a variety of courses. Over 200 exercises are included to test and develop the reader's understanding. There are also over 30 projects, which help readers make the transition from the book to their own original research.

Covering all aspects of gravitation in a contemporary style, this advanced textbook is ideal for graduate students and researchers.

Recenzijos

'This book is immensely impressive. It is full of insights and derivations that do not appear in other books. The serious student will appreciate the extensive coverage of advanced topics, notably of actions. One might say, the book is action-packed.' Andrew J. S. Hamilton, Professor of Astrophysics, University of Colorado, Boulder ' well written throughout presents its material with admirable clarity and patience. It contains many topics that are not easily found in other relativity textbooks, at least not in the detail presented here The book is a valuable contribution to the textbook literature on general relativity and will remain up-to-date for many years to come. It contains 225 exercises (without solutions), many of them highly original, and presents thirty projects that can be used to build a bridge between the exercise level and research work at the level of a master thesis and beyond. It is certainly not possible to cover the whole material in a 1-year course, but its modular structure enables the lecturer to make the selection that is needed for his or her purpose. I plan to use and test the book myself in my next course on relativity and cosmology.' General Relativity and Gravitation 'Every topic is extremely well referenced and current This book is likely to be an essential reference for any galaxy-formation-research student or professor. In the coming years I can see myself dipping into this treasure trove on a very regular basis.' Shaun Cole, The Observatory 'Within minutes of opening the rich, heavy, full, yet succinctly written 728 pages I realised that this is a new and personal view on general relativity, which leads beyond many excellent standard textbooks and offers a challenging training ground for students with its original exercises and study topics [ I] highly recommend it to anyone interested in general relativity and related fields because it offers a modern update if you are a bookworm like me, you must have it, because it is a great read from start to finish.' Cern Courier 'The book is well written throughout and presents its material with admirable clarity and patience. It contains many topics that are not easily found in other relativity textbooks, at least not in the detail presented here The book is a valuable contribution to the textbook literature on general relativity and will remain up-to-date for many years to come I plan to use and test the book myself in my next course on relativity and cosmology.' Institut für Theoretische Physik ' a comprehensive textbook containing both the fundamental and the frontier aspects of gravitation theory. The book is a real pleasure to read by a reader with basic knowledge in mathematics and physics.' Contemporary Physics

Daugiau informacijos

Covering all aspects of gravitation in a contemporary style, this advanced textbook is ideal for graduate students and researchers.
List of exercises
xiii
List of projects
xix
Preface xxi
How to use this book xxvii
Special relativity
1(53)
Introduction
1(1)
The principles of special relativity
1(5)
Transformation of coordinates and velocities
6(7)
Lorentz transformation
8(2)
Transformation of velocities
10(1)
Lorentz boost in an arbitrary direction
11(2)
Four-vectors
13(6)
Four-velocity and acceleration
17(2)
Tensors
19(4)
Tensors as geometrical objects
23(3)
Volume and surface integrals in four dimensions
26(3)
Particle dynamics
29(6)
The distribution function and its moments
35(10)
The Lorentz group and Pauli matrices
45(9)
Scalar and electromagnetic fields in special relativity
54(53)
Intoduction
54(1)
External fields of force
54(1)
Classical scalar field
55(11)
Dynamics of a particle interacting with a scalar field
55(2)
Action and dynamics of the scalar field
57(3)
Energy-momentum tensor for the scalar field
60(2)
Free field and the wave solutions
62(2)
Why does the scalar field lead to an attractive force?
64(2)
Electromagnetic field
66(9)
Charged particle in an electromagnetic field
67(4)
Lorentz transformation of electric and magnetic fields
71(2)
Current vector
73(2)
Motion in the Coulomb field
75(4)
Motion in a constant electric field
79(2)
Action principle for the vector field
81(2)
Maxwell's equations
83(7)
Energy and momentum of the electromagnetic field
90(5)
Radiation from an accelerated charge
95(5)
Larmor formula and radiation reaction
100(7)
Gravity and spacetime geometry: the inescapable connection
107(29)
Introduction
107(1)
Field theoretic approaches to gravity
107(1)
Gravity as a scalar field
108(5)
Second rank tensor theory of gravity
113(12)
The principle of equivalence and the geometrical description of gravity
125(11)
Uniformly accelerated observer
126(2)
Gravity and the flow of time
128(8)
Metric tensor, geodesics and covariant derivative
136(53)
Introduction
136(1)
Metric tensor and gravity
136(5)
Tensor algebra in curved spacetime
141(5)
Volume and surface integrals
146(3)
Geodesic curves
149(13)
Properties of geodesic curves
154(2)
Affine parameter and null geodesics
156(6)
Covariant derivative
162(8)
Geometrical interpretation of the covariant derivative
163(4)
Manipulation of covariant derivatives
167(3)
Parallel transport
170(3)
Lie transport and Killing vectors
173(8)
Fermi---Walker transport
181(8)
Curvature of spacetime
189(50)
Introduction
189(1)
Three perspectives on the spacetime curvature
189(11)
Parallel transport around a closed curve
189(3)
Non-commutativity of covariant derivatives
192(4)
Tidal acceleration produced by gravity
196(4)
Properties of the curvature tensor
200(8)
Algebraic properties
200(3)
Bianchi identity
203(1)
Ricci tensor, Weyl tensor and conformal transformations
204(4)
Physics in curved spacetime
208(16)
Particles and photons in curved spacetime
209(1)
Ideal fluid in curved spacetime
210(7)
Classical field theory in curved spacetime
217(4)
Geometrical optics in curved spacetime
221(3)
Geodesic congruence and Raychaudhuri's equation
224(7)
Timelike congruence
225(3)
Null congruence
228(2)
Integration on null surfaces
230(1)
Classification of spacetime curvature
231(8)
Curvature in two dimensions
232(1)
Curvature in three dimensions
233(1)
Curvature in four dimensions
234(5)
Einstein's field equations and gravitational dynamics
239(54)
Introduction
239(1)
Action and gravitational field equations
239(22)
Properties of the gravitational action
242(2)
Variation of the gravitational action
244(3)
A digression on an alternative form of action functional
247(3)
Variation of the matter action
250(8)
Gravitational field equations
258(3)
General properties of gravitational field equations
261(7)
The weak field limit of gravity
268(11)
Metric of a stationary source in linearized theory
271(5)
Metric of a light beam in linearized theory
276(3)
Gravitational energy-momentum pseudo-tensor
279(14)
Spherically symmetric geometry
293(47)
Introduction
293(1)
Metric of a spherically symmetric spacetime
293(20)
Static geometry and Birkoff's theorem
296(8)
Interior solution to the Schwarzschild metric
304(7)
Embedding diagrams to visualize geometry
311(2)
Vaidya metric of a radiating source
313(1)
Orbits in the Schwarzschild metric
314(15)
Precession of the perihelion
318(5)
Deflection of an ultra-relativistic particle
323(3)
Precession of a gyroscope
326(3)
Effective potential for orbits in the Schwarzschild metric
329(5)
Gravitational collapse of a dust sphere
334(6)
Black holes
340(59)
Introduction
340(1)
Horizons in spherically symmetric metrics
340(3)
Kruskal---Szekeres coordinates
343(15)
Radial infall in different coordinates
350(6)
General properties of maximal extension
356(2)
Penrose---Carter diagrams
358(7)
Rotating black holes and the Kerr metric
365(16)
Event horizon and infinite redshift surface
368(4)
Static limit
372(2)
Penrose process and the area of the event horizon
374(4)
Particle orbits in the Kerr metric
378(3)
Super-radiance in kerr geometry
381(4)
Horizons as null surfaces
385(14)
Gravitational waves
399(53)
Introduction
399(1)
Propagating modes of gravity
399(3)
Gravitational waves in a flat spacetime background
402(11)
Effect of the gravitational wave on a system of particles
409(4)
Propagation of gravitational waves in the curved spacetime
413(3)
Energy and momentum of the gravitational wave
416(6)
Generation of gravitational waves
422(12)
Quadrupole formula for the gravitational radiation
427(2)
Back reaction due to the emission of gravitational waves
429(5)
General relativistic effects in binary systems
434(18)
Gravitational radiation from binary pulsars
434(4)
Observational aspects of binary pulsars
438(5)
Gravitational radiation from coalescing binaries
443(9)
Relativistic cosmology
452(50)
Introduction
452(1)
The Friedmann spacetime
452(5)
Kinematics of the Friedmann model
457(9)
The redshifting of the momentum
458(3)
Distribution functions for particles and photons
461(1)
Measures of distance
462(4)
Dynamics of the Friedmann model
466(13)
The de Sitter spacetime
479(4)
Brief thermal history of the universe
483(4)
Decoupling of matter and radiation
484(3)
Gravitational lensing
487(6)
Killing vectors and the symmetries of the space
493(9)
Maximally symmetric spaces
494(2)
Homogeneous spaces
496(6)
Differential forms and exterior calculus
502(28)
Introduction
502(1)
Vectors and 1-forms
502(8)
Differential forms
510(3)
Integration of forms
513(3)
The Hodge duality
516(3)
Spin connection and the curvature 2-forms
519(11)
Einstein-Hilbert action and curvature 2-forms
523(3)
Gauge theories in the language of forms
526(4)
Hamiltonian structure of general relativity
530(30)
Introduction
530(1)
Einstein's equations in (1+3)-form
530(5)
Gauss---Codazzi equations
535(5)
Gravitational action in (1+3)-form
540(12)
The Hamiltonian for general relativity
542(3)
The surface term and the extrinsic curvature
545(2)
Variation of the action and canonical momenta
547(5)
Junction conditions
552(8)
Collapse of a dust sphere and thin-shell
554(6)
Evolution of cosmological perturbations
560(31)
Introduction
560(1)
Structure formation and linear perturbation theory
560(1)
Perturbation equations and gauge transformations
560(12)
Evolution equations for the source
560(12)
Perturbations in dark matter and radiation
572(10)
Evolution of modes with λ» dH
573(1)
Evolution of modes with λ« dH in the radiation dominated phase
574(3)
Evolution in the matter dominated phase
577(1)
An alternative description of the matter---radiation system
578(4)
Transfer function for the matter perturbations
582(2)
Application: temperature anisotropies of CMBR
584(7)
The Sachs---Wolfe effect
586(5)
Quantum field theory in curved spacetime
591(52)
Introduction
591(1)
Review of some key results in quantum field theory
591(11)
Bogolyubov transformations and the particle concept
596(2)
Path integrals and Euclidean time
598(4)
Exponential redshift and the thermal spectrum
602(3)
Vacuum state in the presence of horizons
605(4)
Vacuum functional from a path integral
609(9)
Hawking radiation from black holes
618(7)
Quantum field theory in a Friedmann universe
625(6)
General formalism
625(3)
Application: power law expansion
628(3)
Generation of initial perturbations from inflation
631(12)
Background evolution
632(2)
Perturbations in the inflationary models
634(9)
Gravity in higher and lower dimensions
643(27)
Introduction
643(1)
Gravity in lower dimensions
644(2)
Gravity and black hole solutions in(1+2) dimensions
644(2)
Gravity in two dimensions
646(1)
Gravity in higher dimensions
646(7)
Black holes in higher dimensions
648(1)
Brane world models
648(5)
Actions with holography
653(10)
Surface term and the entropy of the horizon
663(7)
Gravity as an emergent phenomenon
670(19)
Introduction
670(1)
The notion of an emergent phenomenon
671(2)
Some intriguing features of gravitational dynamics
673(6)
Einstein's equations as a thermodynamic identity
673(3)
Gravitational entropy and the boundary term in the action
676(1)
Horizon thermodynamics and Lanczos-Lovelock theories
677(2)
An alternative perspective on gravitational dynamics
679(10)
Notes 689(6)
Index 695
T. Padmanabhan is a Distinguished Professor and Dean of Core Academic Programmes at the Inter-University Centre for Astronomy and Astrophysics (IUCAA), Pune. He is a renowned theoretical physicist and cosmologist with nearly 30 years of research and teaching experience both in India and abroad. Professor Padmanabhan has published over 200 research papers and nine books, including six graduate-level textbooks. These include the Structure Formation in the Universe and Theoretical Astrophysics, a comprehensive 3-volume course. His research work has won prizes from the Gravity Research Foundation (USA) five times, including the First Prize in 2008. In 2007 he received the Padma Shri, the medal of honour from the President of India, in recognition of his achievements.