Module 10 Black Holes

Module 10: Black Holes

Formation of Black Holes

• Neutron Stars:
  • Made of tightly packed neutrons that prevent further collapse.
  • Counteracts gravity, allowing the star to remain stable.
  • Upper mass limit ~ 3 imes ext{mass of the Sun}.
• When a star exceeds this mass, neutron degeneracy pressure fails, leading to further collapse.
• This happens in stars that are approximately 25 times more massive than the Sun.
• The core compresses to form a black hole.
• Black holes are studied using infrared and X-ray wavelengths.

Characteristics of Black Holes

• Gravity: Supermassive core with tremendous gravitational pull.
• Inescapable: Gravity pulls in all nearby matter, including light and radiation.
• Physical Properties: Very dense and typically spherical in shape.

Escape Speed of Black Holes

• Definition: Escape speed is how fast an object must travel to counteract the gravitational pull of another body.
• It increases with larger mass or smaller radius.
• Escape speed formula: V_{escape} = ext{Escape speed} imes rac{ ext{√(mass of body)}}{ ext{√(radius of body)}}
• Examples:
  • Earth's escape speed: 11 km/s.
  • If Earth shrinks to ¼ of its size, escape speed doubles: 22 km/s.
  • Shrinking Earth to 1 km results in an escape speed of 700 km/s.
  • If compressed to 2 cm, escape speed reaches 300,000 km/s, close to the speed of light.
• No object can escape if the escape speed exceeds the speed of light (c).
• This is why they are called black holes as no forms of electromagnetic radiation can escape.

Event Horizon

• Schwarzschild radius: The critical radius where the escape velocity equals the speed of light.
  • Objects below this radius cannot allow light to escape.
  • Example values:
  • Earth: 1 cm
  • Jupiter: 3 m
  • Sun: 3 km
• Black holes are objects with mass smaller than their Schwarzschild radius, leading to total collapse.
• The event horizon is a surface marking the boundary from which nothing can escape the black hole.

Two Types of Black Holes

• Non-rotating Black Holes:
  • Do not exhibit any rotation.
  • Known as Schwarzschild black holes.
• Rotating Black Holes:
  • Original mass retained angular momentum.
  • Matter spirals inward around them, forming a ring at the center.
  • Known as Kerr black holes, with speeds up to 1000 times/sec.

Space Travel Near Black Holes

• Proximity to a black hole poses serious risks for astronauts.
• Spaghettification:
  • Astronauts would experience extreme tidal forces, causing differing gravitational pulls on their feet and head (stretching effect).
  • Nearer to the black hole, gravitational tug increases, resulting in heating and emission of radiation.

Binary Star System with Black Holes

• Binary system consists of one star and one black hole.
• Material from the star does not fall directly in but instead forms an accretion disk, spiraling around the black hole and heating up before crossing the event horizon.
• Astronomers detect these systems by identifying stars emitting X-rays within their vicinity.
• Ten stellar-remnant black holes identified so far.

Supermassive Black Holes

• Formed through collisions in the early universe.
• Ranges from 1 million to 20 million solar masses.
• The most massive known black hole is 66 billion solar masses.
• These black holes can be the size of solar systems and several dozen have been found; most galaxies harbor at least one supermassive black hole.

Intermediate Mass and Primordial Black Holes

• Intermediate Mass Black Holes:
  • Formed from star collisions in globular clusters.
  • Mass ranges from hundreds to millions of solar masses and are thought to reside in galaxy centers.
  • Example: the Milky Way's black hole is approximately 4.3 million solar masses, situated 26,000 light-years from Earth.
• Primordial Black Holes:
  • Formed from conditions present at the universe's inception, compressing significant mass.
  • Despite their theorization, none found as of now.

Black Holes Evaporate

• Energy-Mass Relation: Energy can convert to mass and vice versa.
• Virtual Particle Production:
  • Particle pairs (e.g., electron and positron) form and annihilate. Under extreme gravitational conditions, one may escape, resulting in the production of energy from the black hole's mass.
  • Hawking radiation: A phenomenon where black holes lose mass over time.
  • Smaller black holes produce these particles faster, leading to a quicker evaporation rate than larger ones.