Reference no: EM13937942
Consider a comoving observer sitting at constant spatial coordinates (r*, e*, a Schwarzschild black hole of mass M. The observer drops a beacon into the black hole (straight down, along a radial trajectory). The beacon emits radiation at a constant wavelength Aem (in the beacon rest frame).
(a) Calculate the coordinate speed dr / dt of the beacon, as a function of r.
(b) Calculate the proper speed of the beacon. That is, imagine there is a comoving obseryer at fixed r, with a locally inertial coordinate system set up as the beacon passes by, and calculate the speed as measured by the comoving observer. What is itatr=2GM?
(c) Calculate the wavelength Aabs, measured by the observer at r*, as a function of the radius rem at which the radiation was emitted.
(d) Calculate the time tabs at which a beam emitted by the beacon at radius rem will be observed at r*.
(e) Show that at late times, the redshift grows exponentially: Aabs/Aem ex etobs/T. Give an expression for the time constant T in tenns of the black hole mass M.
Create a cost benefit analysis
: Create a cost benefit analysis that illustrates the retun on investment that you would receive from purchasing a computer. Project the computer at $1,070
|
Foundation for classical mechanics
: Newton's laws of motion are the three physical laws that provide a foundation for classical mechanics. They are used to describe the reaction of a body of mass m to a force F applied to it. The three laws (in order) are:
|
What is the strength of the magnetic field in the nebula
: An astronomer detects a signal of 2480 MHz from an electron travelling in a distant nebula. What is the strength of the magnetic field in the nebula?
|
Stock value is attributable to growth opportunities
: Colins Company current return on equity (ROE) is 16%. It pays out one-quarter of earnings as cash dividends. Current book value per share is $35. The company has 5 million shares outstanding. What is the terminal value? What is the current value of C..
|
Calculate the proper speed of the beacon
: Calculate the proper speed of the beacon. That is, imagine there is a comoving obseryer at fixed r, with a locally inertial coordinate system set up as the beacon passes by, and calculate the speed as measured by the comoving observer. What is ita..
|
Characteristics of self-reliance and leadership
: Effective problem-solving, capacity for life-long learning, the ability to work independently and collaboratively, social and ethical responsibility and an understanding of international perspectives, and characteristics of self-reliance and leade..
|
What is the bonds nominal coupon interest rate
: O'Brien Ltd.'s outstanding bonds have a $1,000 par value, and they mature in 25 years. Their nominal yield to maturity is 9.25%, they pay interest semiannually, and they sell at a price of $975. What is the bond's nominal coupon interest rate?
|
Compute the standard trigonometric function
: Suppose you need to implement a routine to compute the standard trigonometric function sin(x) on an embedded microprocessor that does not have a built-in sine function. For example you would need this when writing the firmware on a simple mobile p..
|
The quoted price of a bond with an actual
: It is May 1, and the quoted price of a bond with an Actual/365 day count and 9% per annum coupon in the United States is 106. It has a face value of 100 and pays coupons on April 1 and October 1. What is the cash price rounded to the nearest whole nu..
|