Black holes and relativity

• 2 types of relativity:

  1. Special Theory of Relativity (SR)
  2. General Theory of Relativity(GR)
• Einstein’s Special Relativity showed that space and time are not absolute.

  • Instead, they are inextricably linked in a four-dimensional combination called spacetime.
• Key ideas of general relativity:

  • Gravity arises from distortions of spacetime.
  • Black holes can exist in spacetime.
  • The universe may have no boundaries and no center but may still have finite volume.
  • Rapid changes in the motion of large masses can cause gravitational waves.
  • Time runs slowly in gravitational fields.
• The Equivalence Principle:

  Einstein preserved the idea that all motion is relative by pointing out that the effects of acceleration are exactly equivalent to those of gravity.
• General Relativity says that spacetime can be curved.
• Gravity and Relative Motion:

  • Someone who feels a force may be hovering in a gravitational field.

  • Someone who feels weightless may be in free fall.
• Time in an Accelerating Spaceship:

  • Light pulses travel more quickly from front to back of an accelerating spaceship than in other direction.

  • Everyone on the ship agrees that time runs faster in front than in back.
• Time in a Gravitational Field:

  Time must run more quickly at higher altitudes in a gravitational field than at lower altitudes.
• Rules of Geometry in Flat Space:

  • A straight line is the shortest distance between two points.
  • Parallel lines stay the same distance apart.
  • Angles of a triangle add up to 180 °.
  • Circumference of a circle is 2 π r.
• • The straightest lines on a sphere are great circles sharing the same centre as the sphere.
• Great circles intersect, unlike parallel lines in flat space.
• • Straight lines are the shortest paths between two points in a flat space.
  • Great circles are the shortest paths between two points on a sphere/curved surface.
• What happens to the escape velocity of an object if you shrink it?

  It increases.
• Spacetime is so curved near a black hole that nothing can escape.

  • The “point of no return” is called the event horizon.
• Event horizon is a three-dimensional surface.
• No Escape: Nothing can escape from within the event horizon because nothing can go faster than light.
• As far as we know, gravity crushes all the matter into a single point known as a singularity.
• 2 types of black holes:

  Solar mass and supermassive black holes
• General relativity predicts that the movements of a massive object can produce gravitational waves.
• Black holes don’t suck
• sun's mass curves spacetime near its surface.
• Inside the event horizon, space is being pulled faster than the speed of light
• Beyond the neutron star limit, no known force can resist the crush of gravity.
• As far as we know, gravity crushes all the matter into a single point known as singularity.
• If the sun became a black hole, its gravity would be different only near the event horizon.
• Light waves take extra time to climb out of a deep hole in spacetime, leading to a gravitational redshift.
• LIGO measured the Mergers of 2 solar mass black holes.