Problem 10 Life expectancy of black holes. Consider a black hole, mass M (A) Find the equation of Schwarzschild radius (B) Stephen Hawking predicted that a black hole is a black object which the temperature of the black hole( Hawking Temperature) With values according to the equation T = he 8kBGM From the information provided, we can find the relationship of the black hole life expectancy tx MB Find Problem 2 You short 200 contracts of a call option on Stock XYZ. The contract multiplier is 100, i.e. each contract is on 100 shares of the stock. Strike price is $50, and the option is currently at the money, i.e. the stock price is $50 right now. Option has 0.08 years to expiration, risk-free interest rate is zero, and volatility of stock returns is 15% per year. a. Using Black Sholes option pricing model, calculate the delta of the call position and determine the number of shares of the underlying stock that you need to buy to hedge the option position initially. b. Suppose that price of the stock increases to $51. Time to expiration is now 0.07 years. The other parameters are unchanged. Recalculate delta and determine the number of shares you need to buy (sell) to trade to maintain the hedge. Initials: 13 of 13 D) The result of (C) suggests that the pressure of a black hole must be zero (since no work is done as its radius contracts). We can therefore take the pressure to be constant. Please calculate the heat capacity of a black hole at constant pressure. Is CP positive or negative? What is the significance of the sign? E) The title of Stephen Hawking's original paper on black hole radiation was "Black Hole Explosions?". Use your calculations to justify his use of the word "explosion"