# My Research Interests

Einstein's Theory of General Relativity and Cosmology

What is General Relativity?

General Relativity (GR) is the modern theory of gravity: it is an improvement over Newton's theory of gravity where gravity is strong, but agrees with it where gravity is weak. In GR, space and time are combined into a 4-dimensional space-time. The basic concept is that gravity is not a force, but rather it is the curvature of space. For example, the space (and space-time) near a `black-hole' are so strongly curved that light cannot escape. The Einstein field equations are

_{μν}= κ T

_{μν}

where

G_{μν } is a matrix (tensor) derived from the curvature of space-time |

T_{μν } is a matrix (tensor) describing the distribution of matter (density, pressure, etc) |

κ = 8πG/c^{4 is a constant.} |

A solution of these field equations is called a "metric", another tensor g_{αβ }, and it describes the geometry of the spacetime. This theory has now been tested in many ways, and has always agreed well with observations. (The ongoing attempt to reconcile General Relativity with Quantum Theory has not so far succeeded, though String Theory is the current favourite.)

What is Cosmology?

GR provides the basis for modern cosmology - the study of the Universe as a whole. (In Newtonian gravity, cosmology was not really possible as the maths does not work for an infinite distribution of matter.) GR has led to the standard `big bang' model of the cosmos. This states that the universe is expanding - observations do indeed show that all the galaxies are moving away from each other - and that about 14 billion years ago, there was something like a gigantic explosion - a `big bang' - that started the expansion. But, unlike a normal explosion, the space and the matter in it expand together. (Whether this big bang was really the beginning of spacetime itself is a more metaphysical question).

A more recent concept is the idea of `inflation', in which quantum fields caused a period of very rapid expansion that occurs very early on.

The latest observations seem to show that the matter content of the universe is about 70% "dark energy", %27% "dark matter", and 3% normal matter. There is much debate about the nature of "dark matter" and "dark energy", but as yet no certainty. It is quite worrying that we don't really know the physics behind 97% of the universe!

My Interests in Particular

My particular interests include:

- Inhomogeneous cosmology - standard cosmology assumes a smooth homogeneous universe, but the the real universe is very lumpy!
- Inhomogeneous cosmological models - their evolution, geometry and singularities
- Non-linear structure formation in the universe
- Extracting the geometry of the cosmos from observations
- The Lemaitre-Tolman model
- The Szekeres model
- Junction conditions in GR
- Dense black holes
- Local inhomogeneities and the swiss cheese model

I have also worked on

- The models of Vaidya, Schwarzschild-Kruskal-Szekeres & Kinnersley
- Classical signature change
- Cosmic strings
- Gravitational collapse