Homework 4

Note: since you all found the first three homeworks relatively easy, this one (and the last) will be a bit longer and a bit tougher…

New due date: Mon.31.Mar before 18:00 (6pm).

Question 1A Separated Dp-branes and an Op-plane

Z14.4

Question 1B More about orientifolds [*optional]

Z14.10

Question 2 Strings and the Kalb-Ramond field

Z15.6 and Z15.7

Question 3 String partition function and Hagedorn temperature

Z16.2 and Z16.5

Question 4 Hot strings, random walks, and black holes

A: Z16.9

B: Starting from the following metric

it can be shown that the Hawking temperature is inversely proportional to the horizon radius of the black hole

(a) Using the Stefan-Boltzmann law and the fact that a Schwarzschild black hole horizon is spherical, estimate the lifetime of the Schwarzschild black hole (in D dimensions) caused by emission of Hawking radiation.

(b) What is the physical endpoint of Hawking radiation for this type of black hole?

(c) What is the Black Hole Correspondence Principle and why is it relevant here?