Article
Scattering of Gravitational Radiation by a Schwarzschild Blackhole
Department of Physics, New York University, New York, NY 10012, USA.
Nature (Impact Factor: 41.46). 09/1970; 227(5261):9368. DOI: 10.1038/227936a0 Source: PubMed
ABSTRACT
THE discovery of pulsars and the general conviction that they are
neutron stars resulting from gravitational collapse have strengthened
the belief in the possible presence of Schwarzschild blackholesor
Schwarzschild horizonsin nature, the latter being the ultimate stage in
the progressive spherical collapse of a massive star. The stability of
these objects, which has been discussed in a recent report1,
ensures their continued existence after formation. Inasmuch as the
infinite redshift associated with it and its behaviour as a oneway
membrane make the Schwarzschild horizon at once elusive and intriguing,
it is important to explore theoretically all possible modes in which the
presence of such a blackhole manifests itself. In what follows, we
present a partial summary of some results obtained from an investigation
of the scattering of gravitational waves by a Schwarzschild horizon.
neutron stars resulting from gravitational collapse have strengthened
the belief in the possible presence of Schwarzschild blackholesor
Schwarzschild horizonsin nature, the latter being the ultimate stage in
the progressive spherical collapse of a massive star. The stability of
these objects, which has been discussed in a recent report1,
ensures their continued existence after formation. Inasmuch as the
infinite redshift associated with it and its behaviour as a oneway
membrane make the Schwarzschild horizon at once elusive and intriguing,
it is important to explore theoretically all possible modes in which the
presence of such a blackhole manifests itself. In what follows, we
present a partial summary of some results obtained from an investigation
of the scattering of gravitational waves by a Schwarzschild horizon.

 "Understanding classical physical phenomena that occurs with black holes is important. For instance, black hole quasinormal modes (QNMs), which appear when a black hole is naturally perturbed, can test black hole stability and should provide means to identifying black hole parameters like the mass M , the angular momentum J, and the charge Q, from the real ω R and imaginary ω I parts of the mode frequencies [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]. Powerlaw tails that rise at the end of the perturbation also give insight into the black hole features and parameters [14]. "
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ABSTRACT: The analogy between sound wave propagation and light waves led to the study of acoustic holes, the acoustic analogues of black holes. Many black hole features have their counterparts in acoustic holes. The Kerr metric, the rotating metric for black holes in general relativity, has as analogue the draining bathtub metric, a metric for a rotating acoustic hole. Here we report on the progress that has been made in the understanding of features, such as quasinormal modes and tails, superresonance, and instabilities when the hole is surrounded by a reflected mirror, in the draining bathtub metric. Given then the right settings one can build up from these instabilities an apparatus that stores energy in the form of amplified sound waves. This can be put to wicked purposes as in a bomb, or to good profit as in a sonic plant. 
 "In an influential study, Regge and Wheeler [41] showed that the Schwarzschild solution is stable. If a Schwarzschild black hole is perturbed slightly, then the perturbation will oscillate and die away, rather than grow, over time [50]. Some fraction of the initial perturbation is absorbed through the event horizon, and the remainder is radiated away to infinity. "
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ABSTRACT: We investigate the instability of the massive scalar field in the vicinity of a rotating black hole. The instability arises from amplification caused by the classical superradiance effect. The instability affects bound states: solutions to the massive KleinGordon equation which tend to zero at infinity. We calculate the spectrum of bound state frequencies on the Kerr background using a continued fraction method, adapted from studies of quasinormal modes. We demonstrate that the instability is most significant for the $l = 1$, $m = 1$ state, for $M \mu \lesssim 0.5$. For a fast rotating hole ($a = 0.99$) we find a maximum growth rate of $\tau^{1} \approx 1.5 \times 10^{7} (GM/c^3)^{1}$, at $M \mu \approx 0.42$. The physical implications are discussed. 
 "In the 4d limit the vector mode corresponds to the gravitational axial perturbation [15] "
Article: Emissivities for the various graviton modes in the background of the higherdimensional black hole
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ABSTRACT: The Hawking emissivities for the scalar, vector, and tensormode bulk gravitons are computed in the full range of the graviton's energy by adopting the analytic continuation numerically when the spacetime background is (4+n)dimensional nonrotating black hole. The total emissivity for the gravitons is only 5.16% of that for the spin0 field when there is no extra dimension. However, this ratio factor increases rapidly when the extra dimensions exist. For example, this factor becomes 147.7%, 595.2% and 3496% when the number of extra dimensions is 1, 2 and 6, respectively. This fact indicates that the Hawking radiation for the graviton modes becomes more and more significant and dominant with increasing the number of extra dimensions.
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