Mathematical Principles of Theoretical Physics

7.2. STARS 427 To derive an explicit expression of (7.2.46), we need to compute the covariant derivatives of the dual gravitatio ...

428 CHAPTER 7. ASTROPHYSICS AND COSMOLOGY 2.Fluid dynamic model.The fluid dynamic model takes the momentum representation equati ...

7.2. STARS 429 and (7.2.55) follows. 5.Shock wave.As the total energyERof the star is invariant, we have d dt ER= 0. It follows ...

430 CHAPTER 7. ASTROPHYSICS AND COSMOLOGY When a very massive red giant completely consumes its central supply of nuclear fuels ...

7.2. STARS 431 core Figure 7.2: Circulation in a shell layer causing blast. In particular, the huge explosion has no imploding f ...

432 CHAPTER 7. ASTROPHYSICS AND COSMOLOGY 7.3 Black Holes 7.3.1 Geometric realization of black holes The concept of black holes ...

7.3. BLACK HOLES 433 The coordinate system(t,x)withx= (r,θ,φ)represents the projection of the real world to the coordinate space ...

434 CHAPTER 7. ASTROPHYSICS AND COSMOLOGY and case (b) is the embedding ~r−= { ~rext forr>Rs, ~r−int forr<Rs. The base spa ...

7.3. BLACK HOLES 435 2) black holes are innate: they are neither born to explosion ofcosmic objects, nor born to gravitational c ...

436 CHAPTER 7. ASTROPHYSICS AND COSMOLOGY In other words, there is no energy fluxPron the Schwarzschild surface, and we have sho ...

7.3. BLACK HOLES 437 it is regarded as a black hole. Hence the neutron pressure gradient is thought to be a final defense to pre ...

438 CHAPTER 7. ASTROPHYSICS AND COSMOLOGY andt=r/v, wherevis the particle velocity. Replacingvby the speed of lightc, we have ε ...

7.3. BLACK HOLES 439 If theδ-factor satisfies that (7.3.26) 4 π g^2 n ̄hc ≤δ< 4 π g^2 q ̄hc , then the neutrons will be crush ...

440 CHAPTER 7. ASTROPHYSICS AND COSMOLOGY Due to the closedness of black holes, planets, stars and galaxy nuclei are stable, whi ...

7.3. BLACK HOLES 441 whereRis the object radius,Rsis the radius of the black hole,ρis the mass density outside the core, and (7. ...

442 CHAPTER 7. ASTROPHYSICS AND COSMOLOGY Table 7.1: Levels of Cosmic Structure levels Sun star clusters (globular) galaxies (sp ...

7.4. GALAXIES 443 Table 7.2: Galaxy distribution Types E S 0 S+SB Irr Undetermined % 13.0 21.5 61.1 3.1 0.9 radius andbis the mi ...

444 CHAPTER 7. ASTROPHYSICS AND COSMOLOGY Table 7.3: Average physical quantities Types E Sa Sb Sc Irr mass (M⊙) 2. 0 × 1011 1. 6 ...

7.4. GALAXIES 445 rotating around the center of the galaxy. The Sun is 3× 104 ly from the nucleus, it moves at 300km/s and has a ...

446 CHAPTER 7. ASTROPHYSICS AND COSMOLOGY galaxy nucleus galaxy disk Figure 7.6: A schematic diagram of spiral galaxy. for which ...