Definitions Flashcards
What are the foundations of general relativity?
Spacetime tells matter how to move, and matter tells spacetime how to curve.
What is general relativity?
GR is a generalisation of special relativity in which the laws of physics are valid in all inertial reference frames.
What are the postulates of relativity?
The speed of light in the vacuum will be the same for every inertial observer.
How are observers motion related?
Through lorentz transformations
Describe the spacetime interval between events.
It is independent of the observers reference frame.
What are the two forms of the equivalence principle?
The weak equivalence principle and the strong equivalence principle.
Describe inertial mass in Newtonian physics.
The inertial mass of a body is a measure of its resistance to acceleration.
What is the weak equivalence principle (WEP)?
The inertial mass and the gravitational mass are identically equal. Such that freely falling objects inhabits an inertial frame in which all gravitational forces have disappeared.
What is the local inertial frame (LIF)?
It is the reference frame inhabited by our freely falling object.
What is the strong equivalence principle (SEP)?
Locally all the laws of physics have their usual special relativistic form apart from gravity which disappears. Where there is no experiment that can distinguish between a LIF which is freely falling in a uniform gravitational field and an inertial frame which is in a region of the universe far from any gravitating mass.
What are the consequences of the equivalence principles?
- The empirically observed equality of gravitational and inertial mass is explained.
- The acceleration of a test mass in a gravitational field is entirely independent of its nature, mass and composition.
- The path of a light ray will be bent by the gravitational field of a massive body.
- A light ray emitted from the surface of a massive body will be redshifted - gravitational redshift - when its wavelength is measured by a distant observer
How can we describe space time rigorously?
Using physical quantities in terms of scalars and vectors to tensors.
What are geodesics?
The trajectories of freely falling particles in GR generalised to curved paths. They parallel transport their own tangent vectors.
What can geodesics not distinguish between?
Zero gravitational fields and a uniform gravitational field.
When do geodesic deviations accelerate?
They only accelerate for a non uniform or tidal gravitational field.
What are manifolds?
A manifold is a continuous space which is locally flat. They can be continuously parametrised.
What is a Riemannian manifold?
A differential manifold on which a distance, or metric has been defined.
What is a tensor?
A tensor of type (l,m) defined on an n dimensional manifold, is a linear operator which maps l one-forms and m vectors into a real number.
What is the covariant derivative?
A derivative which transforms covariently under a general coordinate transformation.
What do Christoffel symbols describe?
They describe how the basis vectors at different points in the manifold change as one moves across the manifold.
What does the Riemann Christoffel tensor or Riemann tensor describe?
The curvature of space time.
How can one derive the Riemann Christoffel tensor?
- by parallel transporting of a vector around a closed loop in our manifold
- by computing the deviation of two neighbouring geodesics in our manifold
What is the energy momentum tensor?
It is the source of space time curvature. Describing the presence and motion of gravitating matter.
What is a perfect fluid?
A mathematical idealisation but one which is a good approximate description of the gravitating matter in many astrophysical situations.