General Relativity Year 3

What are the classical tests of general relativity?

• The gravitational red shift

• The perihelion shift of mercury

• The bending of light rays

• The Shapiro Delay

What is µ in the equation 2µ/c²R?

µ = GM, where G is the gravitational constant and M is the mass of the object.

Define a Geodesic in terms of general relativity

• A geodesic is the path a particle (or photon) would take through space time when no external forces EXCEPT GRAVITY are acting on it

• This is, in general, not the same as a World Line. A World Line is the actual path a particle or photon takes through space-time. In a Schwartzschild Universe though, both massive particles and photons will always follow geodesics: except for gravity there is nothing to affect their trajectory

What causes the perihelion shift of Mercury?

• This aperiodic orbital behaviour is due, in part, to the small aperiodic term that arises from relativistic gravity

• It is also partly due to the gravitational tugs of other planets

• And the Oblateness of the Sun

• The magnitude of the observed shift cannot be explained by classical physics

What are the effects that occur in a binary pulsar?

• The spacing of the pulses varies according to whether the pulsar is moving toward or away from us in accordance with the Relativistic Doppler Effect

• The spacing of the pulses gets longer as the two bodies get closer together, due to gravitational time dilation (a GR effect)

• The orbital period gradually decreases due to the loss of energy to gravitational waves (a GR effect)

• The pericentre of the binary shifts (a GR effect

What is a dark star?

It is a star so massive and so dense that the escape velocity predicted by Newtonian mechanics exceeds the speed of light.

State the principle of equivalence.

The effect on any system of a uniform gravitational field of strength g is the same as an acceleration -g of an identical system relative to an inertial frame in a zero-g field

What does a Metric equation describe?

The metric equation describes the geometry of space time of a particular universe

Write down the Schwarzschild Metric, explaining the terms in the expression.

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Briefly describe the Schwarzschild Universe.

• It’s a spherically symmetric universe that is empty apart from a point mass in its centre

• It is a curved space-time

Sketch and briefly explain what happens to the light cone as it approaches the event horizon of a black hole from infinity.

• The light cone closes up as it approaches the surface r = 2µ/c²

• At the surface the light cone collapse and therefore can only move in time