Black Hole Perspectives

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A thought experiment provides insight into what it is like inside and outside of a black hole.

Transcript of Black Hole Perspectives

  • Black Hole Perspectives

    by John Michael Williams

    jmmwill@comcast.net

    2011-02-19

    A nonmathematical thought experiment provides insight into what it might be like inside and

    outside of a black hole.

    Copyright (c) 2011, John Michael Williams. All rights reserved.

  • J. M. Williams 2011-02-19 page 1

    Preface

    Everything in this essay is intended to be physically correct, although it represents the author's particular reasoning and is subject to criticism based on prevailing opinions, some of which, in turn, may be based on inconsistent applications of mathematics. Because no black hole can be observed except by its gravitational influence on other objects, some arguments and calculations in the literature must be accepted as much on mathematical faith as on evidence.

    Readers wanting some simplified mathematics to support the theory behind the discussion in this essay should read the excellent presentation on relativity by Christoph Schiller, Motion Mountain: The Adventure of Physics,Volume II, which is downloadable at http://www.motionmountain.net/mmdownload.php?f=motionmountain-volume2.pdf.

    Black holes remain a complex and sometimes controversial subject in astrophysics. This essay ignores quantum effects near the event horizon and just touches upon questions of whether time might be reversed, in some sense, inside a black hole. The idea of low-mass "little black holes", in which energy density alone could create a gravitational event horizon, is proposed solely to implement a thought-experiment neutrino detector.

    Basic Assumptions

    We assume here that the reader has some familiarity with the basics of relativity theory: The speed of light in vacuum is the maximum, limiting speed -- nothing can move at a speed faster than light. Also, the speed of light always is the same, constant value, c, no matter how or by what instrument that speed is measured.

    Along these same lines, it must be understood that accelerating an object to a very high velocity in a particular reference frame, adding energy to that object, causes it to experience time dilation and length contraction relative to other objects not accelerated in that reference frame. Time dilation means that time for the accelerated object passes more slowly than for unaccelerated objects, as measured from an unaccelerated object. Length contraction means that the length of the accelerated object becomes less in the direction of motion when measured from an unaccelerated object.

    These effects, time dilation and length contraction, are relativistic: In other words, they are relative to ones point of view. When measured within an accelerated object, time, which is to say proper time, passes at a normal rate and is not dilated; however, time is compressed, passes more rapidly, for unaccelerated objects when measured from the accelerated object. Likewise, unaccelerated lengths become greater, are expanded, when measured from the accelerated object.

    It has been confirmed again and again, by experiment, theory, and observation, that there is no possible vacuum frame of reference, no fixed structure or coordinate grid in space, except as shared locally by objects not (a) moving or (b) accelerating in any

  • J. M. Williams 2011-02-19 page 2

    significant way relative to one another and not (c) in significantly different gravitational fields.

    The Home Object

    We begin our thought experiment by imagining a very dense, very massive object in space which we shall call the Home Object. This object, perhaps something like a neutron star, is spherical, fairly small, say 10 kilometers (km) in radius, and extremely massive. The Home Object does not rotate, and it is almost homogeneous, with maybe some minor lumpiness and layering of structure from place to place within it.

    At the very center of the Home Object, there resides an observer. Because the mass of the Home Object is symmetrical about the observer, the pull of gravity at its center cancels out and is zero. However, the weight of the overlying matter creates an enormous pressure on the observer, a pressure which we shall ignore for now.

    The matter of which the Home Object is composed, whatever its nature, would make it opaque to light: Photons within such a dense medium would be scattered or absorbed completely. So, the observer could not see anything by light. However, like all matter, the Home Object would be much more transparent to neutrinos, tiny massive particles which travel almost at the speed of light. Neutrinos do not interact with anything except very rarely by the weak force. A neutrino could traverse a light-year of solid lead, and the likelihood that it would interact with a lead atom would be very small -- but not zero. Whatever the Home Object might be, we assume that it does not interact much with neutrinos -- specifically, we shall assume that a neutrino could pass through the Home Object with only about a 10% probability of an interaction.

    In addition to being very transparent to neutrinos, let us assume that all the matter in the Home Object also emits neutrinos, making it slightly luminous (in neutrinos). We do not specify the presumably nuclear source of these neutrinos.

    Our observer has a very special neutrino telescope which allows her to see: In our thought experiment, its sensitive surface is made of a grid of thousands of tiny, low-mass black holes. The black holes are held fixed rigidly and, like all black holes, absorb everything, even neutrinos, which intercept them. Every neutrino has momentum, and this momentum is transferred to any black hole which absorbs it. The resulting vibration of the black holes on their grid thus reports every neutrino reaching the telescope. Our observer can see by what, for brevity, we shall call "neutrino light".

    Neutrinos are produced by high-energy cosmic rays and also by the nuclear fusion reactions which power the Sun and stars. Stellar neutrinos typically have an energy in the range of 5 to 15 MeV (million electron volts). We shall not care exactly what this energy means, but it does correspond to a specific quantum wavelength or frequency of each neutrino: A neutrino of 5 MeV will have a longer wavelength, and a lower frequency, than one of 10 MeV. A neutrino of 10 MeV will travel at a speed a little closer to the speed of light than one of 5 MeV; the speed is what makes the energy, wavelength, and frequency, differ.

  • J. M. Williams 2011-02-19 page 3

    Gravity and Neutrino Light

    So, what can our observer see? Well, the Home Object itself will appear to be like a slightly tinted, luminous glass ball; she will see perhaps some of the lumpiness and layering and will be able to tell where the outer surface is. She also will be able to observe the external stars and galaxies beyond the Home Object. Whereas astronomy by light observes the hot surfaces of the stars, astronomy by neutrino light observes the hot neutrinos created in their cores.

    But, there is a factor which we have omitted: Gravity. The Home Object has an enormous gravitational field. To move anything from the observer's location toward the surface of the Home Object would reduce the gravitational energy it would have gained by falling to the center; equivalently, if an object located near the surface could fall freely to the center, its energy would be increased enormously by gravity. It is the latter which determines, by relativity theory, that our observer will see objects distant from the center to experience time compression and length expansion, just as though the observer were moving at a high speed or were being accelerated strongly. Features of the Home Object near its surface will be seen by our observer as increased in length; and, the frequency of their emitted neutrino light will be raised because of time compression, making them appear "bluer" in neutrino color (because blue light has a higher frequency than red light).

    So, our observer will see the radius of the Home Object as being more than 10 km, perhaps 50 km; and, more distant features of the Home Object will appear expanded away from one another -- increasingly expanded, the closer they are to the surface. As already mentioned, the neutrino light from the outer layers of the Home Object will be blue-shifted; the farther away, the bluer the shift.

    Because a blue shift in general can be interpreted as being caused by a positive Doppler shift, a velocity directed toward the observer, our observer in principle could interpret the neutrino-light blue shift as an ongoing contraction of the Home Object. Thus, our observer could interpret her observations as meaning that the Home Object was collapsing, with the rate of collapse being greater, the greater the distance away. Alternatively, our observer could interpret the blue shift as an expansion of the central regions of the Home Object, bringing herself and her telescope toward the outer regions of the Home Object at an increasingly high speed.

    Neutrino light from the stars also would be blue-shifted as it was accelerated and fell toward the surface of the Home Object, a process which would increase the speed of the neutrinos relative to the Home Object. After passing through the surface of the Home Object and reaching the telescope at its zero-gravity center, the acceleration from the Home Object would fall to zero, but a maximal s