Undergraduate
  1. Classical mechanics  1.1. dynamics  1.1.1. Motion in one dimension  1.1.2. Motion in two dimensions  1.1.3. projectile motion  1.1.4. Relative speed  1.1.5. Uniform circular motion  1.1.6. Non-uniform circular motion  1.1.7. Reference frames and transformations  1.2. Newton's Laws of Motion  1.2.1. First law of motion  1.2.2. Second law of motion  1.2.3. Third Law of Motion  1.2.4. Applications of Newton's Laws  1.2.5. Friction and its types  1.2.6. Free Body Diagram  1.2.7. Constraints and pseudo-forces  1.3. Work and Energy  1.3.1. work done by the force  1.3.2. Work–energy theorem  1.3.3. Kinetic energy  1.3.4. Potential energy in classical mechanics  1.3.5. Conservative and non-conservative forces  1.3.6. Energy Conservation  1.3.7. Power and efficiency  1.4. Speed and collisions  1.4.1. Linear momentum  1.4.2. Conservation of momentum  1.4.3. Impulse and impact force  1.4.4. Elastic and inelastic collision  1.4.5. Center of mass and speed  1.4.6. Rocket Propulsion  1.5. Rotational motion  1.5.1. Torque and Angular Momentum  1.5.2. Moment of inertia  1.5.3. Rotational Kinematics  1.5.4. Rotational Energy  1.5.5. Rolling Motion  1.5.6. Precession and gyroscopic motion  1.6. Gravitational force  1.6.1. Newton's law of universal gravitation  1.6.2. Gravitational potential energy  1.6.3. Orbital mechanics  1.6.4. Kepler's laws of planetary motion  1.6.5. Gravitational field and potential  1.7. Fluid mechanics  1.7.1. Pressure and Pascal's Principle  1.7.2. Buoyancy and Archimedes' principle  1.7.3. Fluid Dynamics and Bernoulli's Principle  1.7.4. Viscosity and Poiseuille's law  1.7.5. Surface tension and capillarity  1.8. Oscillations and waves  1.8.1. Simple Harmonic Motion  1.8.2. Damped and driven oscillations  1.8.3. Coupled oscillations and common modes  1.8.4. Wave properties and types  1.8.5. Sound Waves and the Doppler Effect  1.8.6. Wave interference and superposition
  2. Electromagnetism  2.1. Electrostatics  2.1.1. Electric charge and properties  2.1.2. Coulomb's law  2.1.3. Electric field and electric potential  2.1.4. Gauss's Law  2.1.5. Capacitance and Dielectric  2.1.6. Electric dipole and potential energy  2.2. Electric circuits  2.2.1. Current and Resistance  2.2.2. Ohm's law  2.2.3. Kirchhoff's Laws  2.2.4. RC Circuit  2.2.5. AC Circuits and Reactance  2.2.6. Electric power and energy  2.3. Magnetism  2.3.1. Magnetic Fields and Forces  2.3.2. Ampere's Law  2.3.3. Magnetic dipole moment  2.3.4. Biot-Savart law  2.3.5. Magnetic Materials and Hysteresis  2.4. Electromagnetic induction  2.4.1. Faraday's Law  2.4.2. Lenz's law  2.4.3. Self and mutual induction  2.4.4. Transformers and Inductive Circuits  2.5. Maxwell's equations  2.5.1. Gauss's law for electricity  2.5.2. Gauss's law for magnetism  2.5.3. Faraday's law of induction  2.5.4. Ampere-Maxwell law  2.5.5. Electromagnetic waves
  3. Thermodynamics  3.1. Laws of Thermodynamics  3.1.1. Zeroth law of thermodynamics  3.1.2. First law of thermodynamics  3.1.3. Second Law  3.1.4. Third Law  3.2. Heat and work  3.2.1. Heat transfer (conduction, convection, radiation)  3.2.2. Thermal expansion  3.2.3. Heat engines and refrigerators  3.2.4. Carnot cycle and efficiency  3.3. Statistical mechanics  3.3.1. Maxwell–Boltzmann distribution  3.3.2. Entropy and Probability  3.3.3. Partition function  3.3.4. Fermi–Dirac and Bose–Einstein statistics
  4. Optics  4.1. Geometrical Optics  4.1.1. Reflection and Refraction  4.1.2. Mirrors and lenses  4.1.3. Optical Instruments  4.1.4. Fermat's principle  4.2. Wave optics  4.2.1. Interference in wave optics  4.2.2. Diffraction  4.2.3. Polarization  4.2.4. Coherence and holography
  5. Quantum mechanics  5.1. Wave–particle duality  5.1.1. Blackbody radiation in wave–particle duality in quantum mechanics  5.1.2. Photoelectric effect  5.1.3. Compton scattering  5.1.4. De Broglie wavelength  5.2. Schrödinger Equation  5.2.1. Time-independent Schrödinger equation  5.2.2. Particle in a box  5.2.3. Quantum Tunneling  5.2.4. Potential wells and obstacles  5.3. Quantum States  5.3.1. Wave function  5.3.2. Quantum operators  5.3.3. Heisenberg uncertainty principle  5.3.4. Angular momentum and spin
  6. Relativity  6.1. Special relativity  6.1.1. Lorentz transformations  6.1.2. Time expansion and length contraction  6.1.3. Relativistic energy and momentum  6.2. General relativity  6.2.1. Principle of Equivalence  6.2.2. Schwarzschild metric  6.2.3. Gravitational waves  6.2.4. Black holes and event horizons
  7. Solid state physics  7.1. Crystal structure  7.1.1. Bravais lattices  7.1.2. X-ray diffraction  7.1.3. Band theory  7.1.4. Phonons and lattice vibrations  7.2. Electrical and Magnetic Properties  7.2.1. Conductors, Semiconductors and Insulators  7.2.2. Superconductivity  7.2.3. Hall effect
  8. Nuclear and particle physics  8.1. Atomic Structure  8.1.1. Atomic Model  8.1.2. Nuclear binding energy  8.2. Radioactivity  8.2.1. Alpha, beta, gamma decay  8.2.2. Half life  8.2.3. Nuclear Fission and Fusion  8.3. Particle physics  8.3.1. Standard Model  8.3.2. Quarks and Leptons  8.3.3. antimatter  8.3.4. Fundamental interactions
  9. Astrophysics and cosmology  9.1. Stellar evolution  9.1.1. Star formation  9.1.2. Black holes and neutron stars  9.1.3. White dwarfs and supernovae  9.2. Cosmology  9.2.1. The Big Bang Theory  9.2.2. Dark matter and dark energy  9.2.3. Cosmic microwave background

Undergraduate → Astrophysics and cosmology → Stellar evolution ↓


Black holes and neutron stars


In the fascinating journey of stellar evolution, black holes and neutron stars represent some of the most fascinating endpoints. These celestial bodies form from the remains of massive stars that have exhausted their nuclear fuel and undergo dramatic changes. Although their underlying physics is complex, graduate-level exploration can help us appreciate their unique features and the dramatic processes that give rise to them.

Life cycle of a massive star

Stars begin their life cycles as clouds of gas and dust in the universe. Through a process called nuclear fusion, they generate energy by converting hydrogen into helium in their cores. The outward pressure from the fusion reactions balances the inward pull of gravity, keeping the star stable. However, when a star exhausts its nuclear fuel, this balance is disrupted, and the star's core begins to collapse under its own gravity.

Formation of a neutron star

When stars with masses of about 8 to 25 times the mass of our Sun reach the end of their life cycles, they undergo a spectacular explosion known as a supernova. The remnant core left behind can become a neutron star.

Characteristics of neutron stars

  • Neutron stars are incredibly dense; a sugar-cube-sized chunk of material from a neutron star weighs roughly the same as the weight of the entire human race.
  • They have strong magnetic fields and can often be observed as pulsars, which emit beams of radiation.
  • Despite their small size, about 20 kilometers in diameter, they are capable of condensing more mass than the Sun.

Physics of neutron stars

During core collapse, electrons and protons combine to form neutrons via inverse beta decay:

p + e⁻ → n + νₑ

This creates a neutron-rich structure, which gives the neutron star its name. The degeneracy pressure of the neutrons prevents further collapse, leading to a stable (albeit dense) body.

Neutron star scene

Neutron star

Formation of black holes

Stars with masses greater than 25 solar masses have a different fate. When their nuclear fuel is exhausted, their core collapses without returning to equilibrium, forming a black hole.

Characteristics of black holes

  • Defined by an event horizon, beyond which nothing (not even light) can escape.
  • Extremely dense, and with gravitational pulls so strong that they distort space-time significantly.
  • Although black holes are invisible, their effects can be seen through their gravitational effect on nearby objects.

Physics of black holes

The concept of the Schwarzschild radius helps us understand the size of the event horizon:

R_s = (frac{2GM}{c^2})

Here, (G) is the gravitational constant, (M) is the mass of the object, and (c) is the speed of light. When the center of a star shrinks to this radius, a black hole is formed.

Black hole visualization

Black holes

Comparison of neutron stars and black holes

Neutron stars and black holes are both fascinating products of stellar evolution, exhibiting extreme states of matter and gravity. Comparing the two gives insight into the wonders of astrophysics:

Speciality Neutron stars Black holes
Physical state Dense core of neutrons Singularity with event horizon
Size About 20 km in diameter Defined by the event horizon
Density Very dense but finite Potentially infinite at the origin
Detectability Appear as pulsars or X-ray binaries Detected by gravitational effects

Conclusion

The evolution of stars into neutron stars and black holes underscores the balance of forces that govern our universe. Understanding how these celestial bodies form and what their properties are advances our knowledge of gravity, nuclear physics and relativistic physics. They provide a glimpse into areas where our standard laws of physics come under strain and demonstrate the extraordinary scale and forces that exist in the universe.

Further exploration

Research and observations continue to yield new insights about black holes and neutron stars. As technology advances, we can expect even greater discoveries that will further unravel the mysteries of these mysterious celestial giants.


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Black holes and neutron stars

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