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تسجيل مستخدم جديدRadiation enhancement and temperature in the collapse regime of gravitational scattering
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We generalize the semiclassical treatment of graviton radiation to gravitational scattering at very large energies $sqrt{s}gg m_P$ and finite scattering angles $Theta_s$, so as to approach the collapse regime of impact parameters $b simeq b_c sim Requiv 2Gsqrt{s}$. Our basic tool is the extension of the recently proposed, unified form of radiation to the ACV reduced-action model and to its resummed-eikonal exchange. By superimposing that radiation all-over eikonal scattering, we are able to derive the corresponding (unitary) coherent-state operator. The resulting graviton spectrum, tuned on the gravitational radius $R$, fully agrees with previous calculations for small angles $Theta_sll 1$ but, for sizeable angles $Theta_s(b)leq Theta_c = O(1)$ acquires an exponential cutoff of the large $omega R$ region, due to energy conservation, so as to emit a finite fraction of the total energy. In the approach-to-collapse regime of $bto b_c^+$ we find a radiation enhancement due to large tidal forces, so that the whole energy is radiated off, with a large multiplicity $langle N ranglesim Gs gg 1$ and a well-defined frequency cutoff of order $R^{-1}$. The latter corresponds to the Hawking temperature for a black hole of mass notably smaller than $sqrt{s}$.
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We generalize the semiclassical treatment of graviton radiation to gravitational scattering at very large energies $sqrt{s}gg m_P$ and finite scattering angles $Theta_s$, so as to approach the collapse regime of impact parameters $b simeq b_c sim Req
uiv 2Gsqrt{s}$. Our basic tool is the extension of the recently proposed, unified form of radiation to the ACV reduced-action model and to its resummed-eikonal exchange. By superimposing that radiation all-over eikonal scattering, we are able to derive the corresponding (unitary) coherent-state operator. The resulting graviton spectrum, tuned on the gravitational radius $R$, fully agrees with previous calculations for small angles $Theta_sll 1$ but, for sizeable angles $Theta_s(b)leq Theta_c = O(1)$ acquires an exponential cutoff of the large $omega R$ region, due to energy conservation, so as to emit a finite fraction of the total energy. In the approach-to-collapse regime of $bto b_c^+$ we find a radiation enhancement due to large tidal forces, so that the whole energy is radiated off, with a large multiplicity $langle N ranglesim Gs gg 1$ and a well-defined frequency cutoff of order $R^{-1}$. The latter corresponds to the Hawking temperature for a black hole of mass notably smaller than $sqrt{s}$.
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