310
Index
Curvature, 38, 64, 66, 79, 100, 109, 121, 225,
230, 231, 235–237, 239, 240, 251,
254–256, 259, 262, 273, 293, 296
Curvature parameter, 208, 210, 211, 217,
220, 224–226, 237, 244, 245, 254,
257, 273
Curvature tensor, 100, 111, 157
D
D’Alembertian operator, 162, 182
Dark energy, 193, 198–201, 205, 206, 219,
225–227, 231, 234, 241–245, 248,
251, 253, 254, 259, 275, 290
Dark matter, 157, 201, 205, 206, 226, 227,
232, 238, 248, 250, 251, 254, 275,
278, 291, 292, 295, 299, 301
Deceleration parameter q, 216, 233, 247, 251
Decoupling, 251, 252, 266–271, 273, 278,
279, 281, 282
Deflection of light, 121, 134
De Sitter universe, 220, 259, 262
Determinant, metric, 36, 53–55, 57, 88, 91,
126, 140, 284, 297, 298
Divergence, 87, 88, 91, 92, 116–118, 120,
162, 163, 172, 173, 185, 187, 193–
198, 201
Doppler effect, 10
Dust, 118, 149, 150, 152, 153, 163, 193–196,
201, 227
Dust star, 143, 149, 150, 157
Dust tensor, 119, 120, 193, 196
E
Eddington parameters, 139, 140
Electromagnetism, 3, 4, 90, 106, 160, 161,
163, 182, 186, 189
Energy, 19, 21–23, 28, 29, 77–79, 96, 106,
116–118, 120, 141, 148, 151–156,
158, 164, 172, 176, 177, 179, 181,
189, 190, 193–201, 205, 206, 219,
223, 225–229, 241, 249–251, 253,
256, 257, 263–268, 272, 273, 275–
279, 282–287, 290, 292–296, 299–
302
Energy-momentum tensor, 117–120, 161,
163, 164, 172–174, 193–200, 223,
224, 285, 298, 299
Equivalence principle, 64, 98–102, 105, 121,
122, 134, 137, 138
Euclidian, 221
Euler-Lagrange equations, 70–72, 76, 77,
79, 129, 130, 168, 297
Event horizon, 153
Event Horizon Telescope (EHT), 153, 154
Expansion of the universe, 205, 227, 238,
243, 244, 249, 259, 264, 265, 269,
279
Exterior derivative, 90
Extremum curves, 68–71
F
Fictitious forces, 77, 78, 99, 100, 102, 104
Field theory, 77, 154, 155, 170, 200, 284,
290, 291, 296, 297, 302
Flat space, 36, 58, 69, 74, 83, 111, 116, 126,
127, 138, 139, 161, 194, 196, 197,
259, 302
FLRW metric, 207, 211, 212, 214, 216, 221,
223, 224, 231, 257–259, 261, 285
Four-velocity, 20–24, 119, 120, 194, 211,
224
Friedmann equation, 224, 234, 250, 296
G
Galaxy, 140, 153, 195, 201, 203–206, 211–
220, 226, 227, 232, 238, 242, 244,
245, 247, 248, 250, 258, 261, 263,
275–277, 286, 301
Galilean transformation, 3, 5, 18
Gauge transformation, 160, 161, 163, 166,
185, 186
Generalized Uncertainty Principle (GUP),
293–295, 300, 301
Geodesic, 59, 64, 66–69, 71, 72, 74, 75, 77–
79, 103, 106, 113, 114, 134, 135, 168,
169, 189, 211, 269
Geodesic system, 64, 75, 113, 114, 160
Geometric mass, 128, 131, 141, 151, 157
Gluons, 195, 265, 266, 276, 278, 279
Godel model universe, 244
Gravitational redshift, 101, 105, 106, 137,
141
Gravitational waves, 91, 138, 153, 159, 161,
166, 168–172, 175–177, 179, 180,
182, 184, 186–190, 206, 218, 219,
249–251, 276
Gravity, 55, 64, 78, 95–98, 100, 102, 106,
109, 110, 115–117, 119–121, 123,
125, 127, 137–139, 141, 148–150,
156, 159, 163, 166, 168, 186, 189,
195, 197, 198, 201, 206, 243, 245,
277, 279, 280, 292–294, 301
Index
Curvature, 38, 64, 66, 79, 100, 109, 121, 225,
230, 231, 235–237, 239, 240, 251,
254–256, 259, 262, 273, 293, 296
Curvature parameter, 208, 210, 211, 217,
220, 224–226, 237, 244, 245, 254,
257, 273
Curvature tensor, 100, 111, 157
D
D’Alembertian operator, 162, 182
Dark energy, 193, 198–201, 205, 206, 219,
225–227, 231, 234, 241–245, 248,
251, 253, 254, 259, 275, 290
Dark matter, 157, 201, 205, 206, 226, 227,
232, 238, 248, 250, 251, 254, 275,
278, 291, 292, 295, 299, 301
Deceleration parameter q, 216, 233, 247, 251
Decoupling, 251, 252, 266–271, 273, 278,
279, 281, 282
Deflection of light, 121, 134
De Sitter universe, 220, 259, 262
Determinant, metric, 36, 53–55, 57, 88, 91,
126, 140, 284, 297, 298
Divergence, 87, 88, 91, 92, 116–118, 120,
162, 163, 172, 173, 185, 187, 193–
198, 201
Doppler effect, 10
Dust, 118, 149, 150, 152, 153, 163, 193–196,
201, 227
Dust star, 143, 149, 150, 157
Dust tensor, 119, 120, 193, 196
E
Eddington parameters, 139, 140
Electromagnetism, 3, 4, 90, 106, 160, 161,
163, 182, 186, 189
Energy, 19, 21–23, 28, 29, 77–79, 96, 106,
116–118, 120, 141, 148, 151–156,
158, 164, 172, 176, 177, 179, 181,
189, 190, 193–201, 205, 206, 219,
223, 225–229, 241, 249–251, 253,
256, 257, 263–268, 272, 273, 275–
279, 282–287, 290, 292–296, 299–
302
Energy-momentum tensor, 117–120, 161,
163, 164, 172–174, 193–200, 223,
224, 285, 298, 299
Equivalence principle, 64, 98–102, 105, 121,
122, 134, 137, 138
Euclidian, 221
Euler-Lagrange equations, 70–72, 76, 77,
79, 129, 130, 168, 297
Event horizon, 153
Event Horizon Telescope (EHT), 153, 154
Expansion of the universe, 205, 227, 238,
243, 244, 249, 259, 264, 265, 269,
279
Exterior derivative, 90
Extremum curves, 68–71
F
Fictitious forces, 77, 78, 99, 100, 102, 104
Field theory, 77, 154, 155, 170, 200, 284,
290, 291, 296, 297, 302
Flat space, 36, 58, 69, 74, 83, 111, 116, 126,
127, 138, 139, 161, 194, 196, 197,
259, 302
FLRW metric, 207, 211, 212, 214, 216, 221,
223, 224, 231, 257–259, 261, 285
Four-velocity, 20–24, 119, 120, 194, 211,
224
Friedmann equation, 224, 234, 250, 296
G
Galaxy, 140, 153, 195, 201, 203–206, 211–
220, 226, 227, 232, 238, 242, 244,
245, 247, 248, 250, 258, 261, 263,
275–277, 286, 301
Galilean transformation, 3, 5, 18
Gauge transformation, 160, 161, 163, 166,
185, 186
Generalized Uncertainty Principle (GUP),
293–295, 300, 301
Geodesic, 59, 64, 66–69, 71, 72, 74, 75, 77–
79, 103, 106, 113, 114, 134, 135, 168,
169, 189, 211, 269
Geodesic system, 64, 75, 113, 114, 160
Geometric mass, 128, 131, 141, 151, 157
Gluons, 195, 265, 266, 276, 278, 279
Godel model universe, 244
Gravitational redshift, 101, 105, 106, 137,
141
Gravitational waves, 91, 138, 153, 159, 161,
166, 168–172, 175–177, 179, 180,
182, 184, 186–190, 206, 218, 219,
249–251, 276
Gravity, 55, 64, 78, 95–98, 100, 102, 106,
109, 110, 115–117, 119–121, 123,
125, 127, 137–139, 141, 148–150,
156, 159, 163, 166, 168, 186, 189,
195, 197, 198, 201, 206, 243, 245,
277, 279, 280, 292–294, 301