Cosmological relativity: the special and general theories for the structure of the universe
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore [u.a.]
World Scientific
2006
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XI, 138 S. graph. Darst. |
| ISBN: | 9812700757 9789812700759 |
Staff View
MARC
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| 245 | 1 | 0 | |a Cosmological relativity |b the special and general theories for the structure of the universe |c Moshe Carmeli |
| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 2006 | |
| 300 | |a XI, 138 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Cosmology | |
| 650 | 4 | |a Special relativity (Physics) | |
| 650 | 4 | |a Space and time | |
| 650 | 0 | 7 | |a Kosmologie |0 (DE-588)4114294-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Relativitätstheorie |0 (DE-588)4049363-5 |2 gnd |9 rswk-swf |
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Record in the Search Index
| _version_ | 1804138108916072448 |
|---|---|
| adam_text | Contents
Preface
v
1
Introduction
1
1.1
Remarks on cosmological special relativity
.... 1
2
Cosmological Special Relativity
3
2.1
The Galileo transformation and its
generalization
.................... 3
2.1.1
The Galileo transformation
........ 3
2.1.2
Difficulties with light
............ 5
2.1.3
Role of velocity in classical physics
.... 5
2.2
Nonrelativistic cosmological transformation
.... 6
2.2.1
Nonrelativistic transformation
....... 6
2.2.2
Difficulties at the Big Bang
........ 6
2.3
Extension to the
Lorentz
transformation
..... 8
2.3.1
Invariance
of light propagation
....... 8
2.3.2
The
Lorentz
transformation
........ 8
2.4
Extension to the cosmological transformation
. . 9
2.4.1
Invariance
of the Big Bang time
...... 9
2.4.2
The cosmological transformation
..... 9
2.5
Temperature of the Universe
............ 10
2.5.1
Conclusions
................. 11
2.6
Line elements in Einstein s special relativity
and in cosmological special relativity
....... 11
2.6.1
Line element in Einstein s relativity
.... 11
VII
viii
Contents
2.6.2
Light propagation
.............. 12
2.6.3
Line element in cosmological special
relativity
................... 12
2.6.4
Hubble s expansion
............. 12
2.7
Inflation of the Universe
.............. 15
2.7.1
Matter density
............... 15
2.7.2
Ratio of volumes
.............. 16
2.8
Minimal acceleration in Nature
.......... 16
2.8.1
Relation to Pioneer spacecrafts
...... 17
2.9
Redshift and cosmic time
.............. 17
2.10
Field equations of a different kind
......... 19
2.10.1
Examples
.................. 21
2.11
Cosmological special relativity in five
dimensions
...................... 22
2.11.1
Subtransformations
............. 23
2.11.2
Electrodynamics in five dimensions
.... 24
2.11.3
Field equations
............... 25
2.12
Generalized Maxwell s equations
.......... 25
2.12.1
The mix-up
................. 26
2.12.2
Does the Cabibbo angle describe a
rotation in the time-velocity plane?
.... 28
3
Elements of General Relativity
29
3.1
Riemannian geometry
................ 29
3.1.1
Transformation of coordinates
....... 29
3.1.2
Contravariant
vectors
............ 30
3.1.3
Invariants. Covariant vectors
........ 31
3.1.4
Tensors
................... 32
3.1.5
Metric tensor
................ 32
3.1.6 Christoffel
symbols
............. 33
3.1.7
Covariant differentiation
.......... 34
3.1.8
Riemann,
Ricci
and Einstein tensors
... 36
3.1.9
Geodesies
.................. 37
3.1.10
Bianchi
identities
.............. 38
3.2
Principle of equivalence
............... 39
Contents
ix
3.2.1
Null experiments.
Eötvös
experiment
... 39
3.3
Principle of general covariance
........... 41
3.4
Gravitational field equations
............ 42
3.4.1
Einstein s field equations
.......... 43
3.4.2
Deduction of Einstein s equations from
variational principle
............. 44
3.4.3
The electromagnetic energy-momentum
tensor
.................... 45
3.5
The
Schwarzschild
metric
.............. 46
3.6
Experimental tests of general relativity
...... 51
3.6.1
Gravitational red shift
........... 51
3.6.2
Effects on planetary motion
........ 52
3.6.3
Deflection of light
.............. 56
3.6.4
Gravitational radiation experiments
.... 59
3.6.5
Radar experiment
.............. 59
3.6.6
Low-temperature experiments
....... 60
3.7
Equations of motion
................ 61
3.7.1
Geodesic postulate
............. 61
3.7.2
Equations of motion as a consequence of
field equations
................ 61
3.7.3
Self-action terms
.............. 63
3.7.4
Einstein-Infeld-Hoffmann method
..... 67
3.7.5
Newtonian equation of motion
....... 69
3.7.6
Einstein-Infeld-Hoffmann equation
.... 70
3.8
Decomposition of the Riemann tensor
....... 71
4
COSMOLOGICAL GENERAL RELATIVITY
73
4.1
Introduction
..................... 73
4.2
Space and velocity
................. 74
4.3
Gravitational field equations
............ 74
4.3.1
Universe expansion
............. 75
4.3.2
Energy-momentum tensor
......... 75
4.3.3
Independent field equations
........ 76
4.4
Solution of the field equations
........... 76
4.4.1
Simple solution
............... 76
Contents
4.4.2
Pressure
................... 77
4.4.3 Line
element
................. 77
4.5
Physical meaning
.................. 77
4.5.1
Пт
> 1:................... 78
4.5.2
Пт
< 1:................... 78
4.5.3
Qm
= 1:................... 78
4.6
The accelerating Universe
............. 78
4.6.1
Tri-phase expansion
............. 79
4.7
Theory versus experiment
............. 80
4.7.1
Value of the Big Bang time
r
....... 80
4.7.2
Value of
Ω£η
................ 82
4.8
Comparison with general relativity
........ 84
4.9
Recent developments on dark matter
....... 84
cosmological general relativity in flve
Dimensions
87
5.1
Introduction
..................... 87
5.1.1
Five-dimensional manifold of space,
time and velocity
.............. 87
5.2
Universe with gravitation
.............. 88
5.2.1
The
Bianchi
identities
........... 89
5.2.2
The gravitational field equations
...... 89
5.2.3
Velocity as an independent coordinate
. . 90
5.2.4
Effective mass density in cosmology
.... 90
5.3
The accelerating Universe
............. 91
5.3.1
Preliminaries
................ 91
5.3.2
Expanding Universe
............ 93
5.3.3
Decelerating, constant and accelerating
expansions
.................. 95
5.3.4
Accelerating Universe
............ 96
5.4
The Tully-Fisher formula: Nonexistence of halo
dark matter
..................... 97
5.4.1
The Geodesic Equation
........... 98
5.4.2
Equations of motion
............ 99
5.4.3
The Tully-Fisher law
............ 102
Contents xi
5.5 Cosmological redshift
analysis
...........104
5.5.1 The redshift
formula
............104
5.5.2
Particular cases
...............105
5.5.3
Conclusions
.................106
5.6
Verification of the classical general relativity
tests
.........................106
5.6.1
Comparison with general relativity
.... 106
5.6.2
Gravitational redshift
............109
5.6.3
Motion in a centrally symmetric
gravitational field
..............
Ill
5.6.4
Deflection of light in a gravitational
field
.....................117
5.7
Gravitational waves
.................120
A Mathematical Conventions
123
A.I Components of the
Ricci
tensor
..........124
В
Integration of the Universe Expansion
Equation
127
Index
129
___,
theory presented in this book is a combination of Einstein s original
^
-----
special and general relativity, but now the starting point is not the
propagation of light but the expansion of the Universe. The traditional
Hubble constant Ho (which is not constant) is called in this book the
Hubble parameter. Its value at low gravity is denoted by h, and its
reciprocal is denoted by
τ.
Thus
τ
is the Big Bang time (some authors
call it the Hubble-Carmeli constant). This is actually the only constant
that appears in this theory, just as
с
is the only constant that appears
in Einstein s theory. There is no
cosmologica!
constant but there is a
critical mass density. The theory presents general relativity in the
space-velocity (of the receding galaxies) which is later on extended
to include the time dimension. So far all experimental findings are
satisfied by this theory.
|
| adam_txt |
Contents
Preface
v
1
Introduction
1
1.1
Remarks on cosmological special relativity
. 1
2
Cosmological Special Relativity
3
2.1
The Galileo transformation and its
generalization
. 3
2.1.1
The Galileo transformation
. 3
2.1.2
Difficulties with light
. 5
2.1.3
Role of velocity in classical physics
. 5
2.2
Nonrelativistic cosmological transformation
. 6
2.2.1
Nonrelativistic transformation
. 6
2.2.2
Difficulties at the Big Bang
. 6
2.3
Extension to the
Lorentz
transformation
. 8
2.3.1
Invariance
of light propagation
. 8
2.3.2
The
Lorentz
transformation
. 8
2.4
Extension to the cosmological transformation
. . 9
2.4.1
Invariance
of the Big Bang time
. 9
2.4.2
The cosmological transformation
. 9
2.5
Temperature of the Universe
. 10
2.5.1
Conclusions
. 11
2.6
Line elements in Einstein's special relativity
and in cosmological special relativity
. 11
2.6.1
Line element in Einstein's relativity
. 11
VII
viii
Contents
2.6.2
Light propagation
. 12
2.6.3
Line element in cosmological special
relativity
. 12
2.6.4
Hubble's expansion
. 12
2.7
Inflation of the Universe
. 15
2.7.1
Matter density
. 15
2.7.2
Ratio of volumes
. 16
2.8
Minimal acceleration in Nature
. 16
2.8.1
Relation to Pioneer spacecrafts
. 17
2.9
Redshift and cosmic time
. 17
2.10
Field equations of a different kind
. 19
2.10.1
Examples
. 21
2.11
Cosmological special relativity in five
dimensions
. 22
2.11.1
Subtransformations
. 23
2.11.2
Electrodynamics in five dimensions
. 24
2.11.3
Field equations
. 25
2.12
Generalized Maxwell's equations
. 25
2.12.1
The mix-up
. 26
2.12.2
Does the Cabibbo angle describe a
rotation in the time-velocity plane?
. 28
3
Elements of General Relativity
29
3.1
Riemannian geometry
. 29
3.1.1
Transformation of coordinates
. 29
3.1.2
Contravariant
vectors
. 30
3.1.3
Invariants. Covariant vectors
. 31
3.1.4
Tensors
. 32
3.1.5
Metric tensor
. 32
3.1.6 Christoffel
symbols
. 33
3.1.7
Covariant differentiation
. 34
3.1.8
Riemann,
Ricci
and Einstein tensors
. 36
3.1.9
Geodesies
. 37
3.1.10
Bianchi
identities
. 38
3.2
Principle of equivalence
. 39
Contents
ix
3.2.1
Null experiments.
Eötvös
experiment
. 39
3.3
Principle of general covariance
. 41
3.4
Gravitational field equations
. 42
3.4.1
Einstein's field equations
. 43
3.4.2
Deduction of Einstein's equations from
variational principle
. 44
3.4.3
The electromagnetic energy-momentum
tensor
. 45
3.5
The
Schwarzschild
metric
. 46
3.6
Experimental tests of general relativity
. 51
3.6.1
Gravitational red shift
. 51
3.6.2
Effects on planetary motion
. 52
3.6.3
Deflection of light
. 56
3.6.4
Gravitational radiation experiments
. 59
3.6.5
Radar experiment
. 59
3.6.6
Low-temperature experiments
. 60
3.7
Equations of motion
. 61
3.7.1
Geodesic postulate
. 61
3.7.2
Equations of motion as a consequence of
field equations
. 61
3.7.3
Self-action terms
. 63
3.7.4
Einstein-Infeld-Hoffmann method
. 67
3.7.5
Newtonian equation of motion
. 69
3.7.6
Einstein-Infeld-Hoffmann equation
. 70
3.8
Decomposition of the Riemann tensor
. 71
4
COSMOLOGICAL GENERAL RELATIVITY
73
4.1
Introduction
. 73
4.2
Space and velocity
. 74
4.3
Gravitational field equations
. 74
4.3.1
Universe expansion
. 75
4.3.2
Energy-momentum tensor
. 75
4.3.3
Independent field equations
. 76
4.4
Solution of the field equations
. 76
4.4.1
Simple solution
. 76
Contents
4.4.2
Pressure
. 77
4.4.3 Line
element
. 77
4.5
Physical meaning
. 77
4.5.1
Пт
> 1:. 78
4.5.2
Пт
< 1:. 78
4.5.3
Qm
= 1:. 78
4.6
The accelerating Universe
. 78
4.6.1
Tri-phase expansion
. 79
4.7
Theory versus experiment
. 80
4.7.1
Value of the Big Bang time
r
. 80
4.7.2
Value of
Ω£η
. 82
4.8
Comparison with general relativity
. 84
4.9
Recent developments on dark matter
. 84
cosmological general relativity in flve
Dimensions
87
5.1
Introduction
. 87
5.1.1
Five-dimensional manifold of space,
time and velocity
. 87
5.2
Universe with gravitation
. 88
5.2.1
The
Bianchi
identities
. 89
5.2.2
The gravitational field equations
. 89
5.2.3
Velocity as an independent coordinate
. . 90
5.2.4
Effective mass density in cosmology
. 90
5.3
The accelerating Universe
. 91
5.3.1
Preliminaries
. 91
5.3.2
Expanding Universe
. 93
5.3.3
Decelerating, constant and accelerating
expansions
. 95
5.3.4
Accelerating Universe
. 96
5.4
The Tully-Fisher formula: Nonexistence of halo
dark matter
. 97
5.4.1
The Geodesic Equation
. 98
5.4.2
Equations of motion
. 99
5.4.3
The Tully-Fisher law
. 102
Contents xi
5.5 Cosmological redshift
analysis
.104
5.5.1 The redshift
formula
.104
5.5.2
Particular cases
.105
5.5.3
Conclusions
.106
5.6
Verification of the classical general relativity
tests
.106
5.6.1
Comparison with general relativity
. 106
5.6.2
Gravitational redshift
.109
5.6.3
Motion in a centrally symmetric
gravitational field
.
Ill
5.6.4
Deflection of light in a gravitational
field
.117
5.7
Gravitational waves
.120
A Mathematical Conventions
123
A.I Components of the
Ricci
tensor
.124
В
Integration of the Universe Expansion
Equation
127
Index
129
_,
theory presented in this book is a combination of Einstein's original
^
-----
"special and general relativity, but now the starting point is not the
propagation of light but the expansion of the Universe. The traditional
Hubble constant Ho (which is not constant) is called in this book the
Hubble parameter. Its value at low gravity is denoted by h, and its
reciprocal is denoted by
τ.
Thus
τ
is the Big Bang time (some authors
call it the Hubble-Carmeli constant). This is actually the only constant
that appears in this theory, just as
с
is the only constant that appears
in Einstein's theory. There is no
cosmologica!
constant but there is a
critical mass density. The theory presents general relativity in the
space-velocity (of the receding galaxies) which is later on extended
to include the time dimension. So far all experimental findings are
satisfied by this theory. |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Carmeli, Moshe 1933-2007 |
| author_GND | (DE-588)128455624 |
| author_facet | Carmeli, Moshe 1933-2007 |
| author_role | aut |
| author_sort | Carmeli, Moshe 1933-2007 |
| author_variant | m c mc |
| building | Verbundindex |
| bvnumber | BV035127641 |
| callnumber-first | Q - Science |
| callnumber-label | QB981 |
| callnumber-raw | QB981 |
| callnumber-search | QB981 |
| callnumber-sort | QB 3981 |
| callnumber-subject | QB - Astronomy |
| classification_rvk | UH 8000 US 2000 |
| ctrlnum | (OCoLC)122702267 (DE-599)DNB 2007272376 |
| dewey-full | 523.1 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 523 - Specific celestial bodies and phenomena |
| dewey-raw | 523.1 |
| dewey-search | 523.1 |
| dewey-sort | 3523.1 |
| dewey-tens | 520 - Astronomy and allied sciences |
| discipline | Physik |
| discipline_str_mv | Physik |
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| id | DE-604.BV035127641 |
| illustrated | Illustrated |
| index_date | 2024-07-02T22:23:30Z |
| indexdate | 2024-07-09T21:22:57Z |
| institution | BVB |
| isbn | 9812700757 9789812700759 |
| language | English |
| lccn | 2007272376 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016795196 |
| oclc_num | 122702267 |
| open_access_boolean | |
| owner | DE-703 DE-11 |
| owner_facet | DE-703 DE-11 |
| physical | XI, 138 S. graph. Darst. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Carmeli, Moshe 1933-2007 Verfasser (DE-588)128455624 aut Cosmological relativity the special and general theories for the structure of the universe Moshe Carmeli Singapore [u.a.] World Scientific 2006 XI, 138 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Cosmology Special relativity (Physics) Space and time Kosmologie (DE-588)4114294-9 gnd rswk-swf Relativitätstheorie (DE-588)4049363-5 gnd rswk-swf Relativitätstheorie (DE-588)4049363-5 s Kosmologie (DE-588)4114294-9 s DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016795196&sequence=000005&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016795196&sequence=000006&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Carmeli, Moshe 1933-2007 Cosmological relativity the special and general theories for the structure of the universe Cosmology Special relativity (Physics) Space and time Kosmologie (DE-588)4114294-9 gnd Relativitätstheorie (DE-588)4049363-5 gnd |
| subject_GND | (DE-588)4114294-9 (DE-588)4049363-5 |
| title | Cosmological relativity the special and general theories for the structure of the universe |
| title_auth | Cosmological relativity the special and general theories for the structure of the universe |
| title_exact_search | Cosmological relativity the special and general theories for the structure of the universe |
| title_exact_search_txtP | Cosmological relativity the special and general theories for the structure of the universe |
| title_full | Cosmological relativity the special and general theories for the structure of the universe Moshe Carmeli |
| title_fullStr | Cosmological relativity the special and general theories for the structure of the universe Moshe Carmeli |
| title_full_unstemmed | Cosmological relativity the special and general theories for the structure of the universe Moshe Carmeli |
| title_short | Cosmological relativity |
| title_sort | cosmological relativity the special and general theories for the structure of the universe |
| title_sub | the special and general theories for the structure of the universe |
| topic | Cosmology Special relativity (Physics) Space and time Kosmologie (DE-588)4114294-9 gnd Relativitätstheorie (DE-588)4049363-5 gnd |
| topic_facet | Cosmology Special relativity (Physics) Space and time Kosmologie Relativitätstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016795196&sequence=000005&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016795196&sequence=000006&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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