Summary and overview of the main ideas in Erik Verlinde’s paper on emergent gravity.
My apologies to everyone who is following me on my blog here – I realise I have not done and written much at all this year. The reason for this is simply that I had a lot to deal with in my personal life, and just didn’t find it in me to vocalise these things. […]
A brief and very basic introduction is given to Kerr spacetime. The metric is presented, and the various horizon surfaces and their physical meanings are discussed. An overview of the geometric and topological structure of maximally extended Kerr spacetime is given, using the waterfall analogy. Frame dragging, closed time-like curves, naked singularities, and the cosmic censorship hypothesis are introduced.
We take a closer look at the maximally extended version of Schwarzschild spacetime, and investigate the geometry and topology beyond the event horizon, leading us to the notion of “white holes”. We discuss the concept of wormhole, its implications, and choices of coordinate system which allow us to quantify them. We then consider the laws of thermodynamics in the presence of event horizons, and find that Schwarzschild black holes have entropy and temperature, and undergo an evaporation process through the emission of thermal radiation. We introduce the holographic principle, and briefly discuss the implications it has for our understanding of the interior region enclosed by the horizon surface.
Just to keep all my followers here in the loop – I am currently very busy in my real life job, and quite simply do not have the time to compose any articles on here. I expect this will still be the case for another week or so, after which I should be able to […]
Are time dilation and frequency shift really infinite at the event horizon of a Schwarzschild black hole ?
We introduce and discuss the Schwarzschild metric, at a level suitable for beginners with basic calculus knowledge. First, the exterior vacuum metric is examined, and several techniques about how to work with metrics are demonstrated, and their physical significance explained. A geometric understanding of the various terms in the metric is developed, and some fully worked examples are given. We then progress on to the interior metric, and present its peculiarities and physical consequences. This leads on to a discussion of Schwarzschild black holes, the meaning of event horizons, and what physically happens if we allow a test particle to freely fall into such black holes, from the points of view of different observers. Animations and a video are presented that help visualise these principles.