Extragalactic Astronomy & Cosmology Lecture GR Jane Turner Joint Center for Astrophysics UMBC & NASA/GSFC 2003 Spring [4246] Physics 316

Jane Turner [4246] PHY 316 (2003 Spring) Last Time… We have learned the special theory of relativity relates observations made in inertial frames to one another, because inertial frames are special, we call it the Special Theory Special Relativity showed us we had to discard the concepts of absolute space & time, space & time are inextricably linked Special Relativity brought mechanics and electromagnetics into consistency and provided a model for situations where velocities approached the speed of light

Jane Turner [4246] PHY 316 (2003 Spring) General Relativity Considering the special theory we have been assuming we have true inertial frames on earth However, this was an approximation, as Earths gravity is an acceleration Any object with mass produces a gravitational force

Jane Turner [4246] PHY 316 (2003 Spring) General Relativity The Universe is filled with masses - we need a theory which accommodates inertial & non-inertial frames & which can describe the effects of gravity

Jane Turner [4246] PHY 316 (2003 Spring) GR in a nutshell General Relativity is essentially a geometrical theory concerning the curvature of Spacetime. For this course, the two most important aspects of GR are needed: Gravity is the manifestation of the curvature of Spacetime Gravity is no longer described by a gravitational "field" /”force” but is a manifestation of the distortion of spacetime. Matter curves spacetime; the geometry of spacetime determines how matter moves. Energy and Mass are equivalent Any object with energy is affected by the curvature of spacetime.

Jane Turner [4246] PHY 316 (2003 Spring) Mass Curves spacetime e The greater the mass, the greater the distortion of spacetime

Jane Turner [4246] PHY 316 (2003 Spring) GR The General Theory of Relativity: - explains the 1/r 2 -law in Newton's law of gravitation as the "natural” consequence of curvature in spacetime. (other forms of gravity might be possible, but beyond the scope) - first confirmed in 1919 May by bending of starlight by Sun (during an eclipse). GR predicted twice the bending c.f. Newtonian mechanics. The Times headline: Lights all askew in the Heavens, Men of science more or less agog

Jane Turner [4246] PHY 316 (2003 Spring) GR Overview GR encompasses the following ideas:  Gravity arises from distortions of spacetime -not a force acting at a distance, mass causes the distortion and thus affects how objects move through spacetime  Time runs slow in gravitational fields, the stronger the gravity, the slower time runs  Black Holes can exist in spacetime  The universe has no boundaries and no center, but might still have a finite volume  Large masses that undergo rapid changes in motion or structure emit gravitational waves that travel at the speed of light

Jane Turner [4246] PHY 316 (2003 Spring) The Equivalence Principle SR shows there is no answer to the question “who is moving”, observers see speeds relative to them, and there is no absolute definition of who is at rest Situation may be different when acceleration is involved Suppose you and friend Jackie are floating freely in space, then your pilot fires your rocket engines Jackie sees you accelerate away

Jane Turner [4246] PHY 316 (2003 Spring) The Equivalence Principle From your perspective Jackie is receding and if you don’t know whose engines fired how do you know who is at rest and who is moving away If both were at constant velocity you could not tell However, your acceleration means you feel a force, instead of floating freely like Jackie you are held to the floor of your spaceship An acceleration of 1g=9.8 m/s 2 would feel like gravity of Earth

Jane Turner [4246] PHY 316 (2003 Spring) The Equivalence Principle Einstein did not like ideas like these as he was convinced all motion should be relative Then, in 1907, he hit upon the happiest thought of his life that the effects of gravity are exactly equivalent to the effects of acceleration

Jane Turner [4246] PHY 316 (2003 Spring) The Equivalence Principle the effects of gravity are exactly equivalent to the effects of acceleration thus you cannot tell the difference between being in a closed room on Earth and one accelerating through space at 1g any experiments performed (dropping balls of different weights etc) would produce the same results in both cases

Jane Turner [4246] PHY 316 (2003 Spring) Free Fall-a state where nothing is preventing you from falling Astronauts orbiting Earth feel weightless, yet gravity at orbital altitudes is ~89% of that on the Earths surface - so why do they feel weightless? Answer is, they are in free fall around the Earth, and this means the centrifugal force balances the gravitational one, so they feel as though no forces are acting on them, i.e. weightless -in fact, just ‘’falling’’ around the Earth under the influence of gravity

Jane Turner [4246] PHY 316 (2003 Spring) Free Fall Consider being in a elevator whose cable has broken… you feel weightless because as you and the elevator go into free fall down the shaft the floor of the elevator exerts no force on you A free-falling frame in a gravitational field is equivalent to an inertial frame free of any gravitational field

Jane Turner [4246] PHY 316 (2003 Spring) Accelerated situation When the elevator is working normally and accelerates upward the floor exerts a force upwards on you but it feels like you are pushing down on the floor,i.e you feel heavier

Jane Turner [4246] PHY 316 (2003 Spring) The Equivalence Principle …back to the two spaceships, is it possible for you to feel the acceleration but for Jackie to be the one moving away? …imagine the two under a gravitational force, your engines fire, keep your spaceship stationary against gravity Jackie is not resisting gravity and so is in free fall under that gravity You feel the sense of gravity as it acts on you, but you can be stationary,balancing engine power against g Jackie free falls, feels no acceleration, but is the one moving away from you

Jane Turner [4246] PHY 316 (2003 Spring) The Equivalence Principle So, all motion is relative - the concept of who is moving away from whom cannot be determined just be noting who feels a sensation of weight