![]() This is a sketch of a curved spacetime manifold, which has a time dimension and a spacial dimension. If you wish to understand the underlying ideas behind this, I recommend reading this introduction to general relativity. The effects of gravity are then modeled by the curvature of this spacetime manifold. ![]() Essentially, this means that both space and time are “combined” together into a 4-dimensional geometry known as a manifold. In general relativity, we model everything through a concept called spacetime. In case you’d want an ad-free PDF version of this article (an my other general relativity articles), you’ll find it here, available as part of my full General Relativity Bundle. We’ll also look at some concrete examples of how much time actually slows down near a black hole as well as how different properties of black holes affect this (such as electric charge and spin). In this article, we’ll be discussing all about this slowing down of time -thing in great detail (namely the interesting geometry behind it) as well as looking at some consequences of this phenomenon (such as how it affects aging). According to the theory of general relativity, this phenomenon is due to the gravity of the black hole curving spacetime in a way that affects all measurements of time and space near the black hole. Time slows down near a black hole due to the extremely strong gravitational field of the black hole. One of the more interesting predictions of the theory is that even time will slow down near a black hole. Calculate the duration of this unpleasant time interval! Does the size of the black hole matter? (4 p) (C) Suppose that x = 100 (m/s)/m (that is, 10 g per meter).Black holes are some of the most intriguing, yet not very well-understood objects in the universe, which are best described by Einstein’s theory of general relativity. Given this value x, at what radius does it start to hurt? (1 p) (d) So pain sets in at the radius in (c), and you are certainly dead at r=0. Suppose that the tidal stretching becomes painful as the tidal acceleration per meter exceeds a certain value x. (a) What is the tidal acceleration per meter along your body that you will experience the moment you pass the horizon of the black hole? Is it more or less painful if the black hole is large? (1 p) (b) What is the value in (a) for a black hole with the mass of the sun in standard units)? Would you be alive as you pass the event horizon of such a black hole? (1 p) (c) Now, return to the case with general black hole mass, and geometrized units. (21.31)) that the tidal stretching in the radial direction is 2M d7² where x is the radial component of the deviation vector as measured in your freely falling frame (defined by eqns. From the geodesic deviation equation with the relevant component of the Riemann tensor inserted, Hartle shows (eqn. You are diving into the black hole, head first, so that your body, from head to feet, is in the radial direction. Suppose that you are falling radially into a Schwarzschild black hole, with line element ds? = 2M Idi² + -11-20) (1-2 M 2M) *4r? + rºd = You start from rest far away from the black hole (for the calculations we can assume that you start infinitely far away), and then just fall freely.
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