A collapsing star when explode (supernova), due to the sudden ejection of massive mass around the central core, there is a disturbance in space-time leading to emission of gravitational waves. But what will happen if a collapsing goes on till black hole is formed, without any explosion? Will there be an emission of gravitational waves due to the continuous grow in curvature because of the growing mass?
Gravitational waves require a change in quadrupole or higher order terms in a spherical harmonic expansion of the gravitational field (i.e., an oscillating quadrupole moment). So, spherically symmetric collapsing dust, if it stays spherically symmetric, will not radiate gravitationally*.
* That is true for General Relativity. Other theories of gravity can have other polarizations for their gravitational radiation, and so might be able to support a scalar radiation term.
Thank You Marshall Eubanks, Could to send me any article related to this topic?
This is all in Misner Thorne and Wheeler or most other textbooks in General Relativity.
Radiation is an irreversible process; this fact emerges at once if absorption is taken into account and/or Sommerfeld type conditions, which eliminate inward traveling waves, are imposed. Therefore, it is obvious that an entropy generator factor should be present in the description of the source. But such a factor is absent in a perfect fluid and more so in a collisionless dust. In other words, the irreversibility of the process of emission of gravitational waves must be reflected in the equation of state through an entropy increasing (dissipative) factor. So, the answer to your question is negative.
In the Field Gravity theory there is scalar gravitational radiation via spherical pulsation (or acceleration in free fall) of a body, which relates to the kinetic energy changing of an accelerated matter of a collapsing star, see
http://arxiv.org/abs/gr-qc/9911081
Hawking, S. W. and Israel, W., General Relativity: An Einstein Centenary Survey, Cambridge University Press, Cambridge, 1979, 98, shows the emission of gravitational radiation from mutual orbits. Free fall, such as the gravitational collapse of material, would obey derivations describing relativistic orbital dynamics in the same way. Actually, the Wiki article is not bad and you should be able to work out the math from there: http://en.wikipedia.org/wiki/Gravitational_wave
Dear Bruce, it is well known to physicists that in a binary system (e.g. two neutron stars rotating each other) emits of gravitational wave. But what will happen if we have a freely falling collapsing dust? During the course of free fall collapse, the mass will confine in more and more smaller region of space and therefore the curvature of space-time will be more and more. Therefore during the collapsing stage the curvature of space time will be increasing, but whether this growing space time curvature leads to gravitational waves or not?
Hi Dr. Singh,
This is covered in the literature provided. Short answer: yes.
Yours,
Bruce
According to GR there is now GW from monopole spherically symmetric systems,
so the short answer is "no".
Thanks Dr. Yang, could you please send me a related article, I could not find any paper regarding the question.
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