High-energy head-on collisions of particles and hoop conjecture

We investigate the apparent horizon formation for high-energy head-on collisions of particles in multi-dimensional spacetime. The apparent horizons formed before the instance of particle collision are obtained analytically. Using these solutions, we discuss the feature of the apparent horizon formation in the multi-dimensional spacetime from the viewpoint of the hoop conjecture.Comment: 4pages, 4figure

How Black Holes Form in High Energy Collisions

We elucidate how black holes form in trans-Planckian collisions. In the rest frame of one of the incident particles, the gravitational field of the other, which is rapidly moving, looks like a gravitational shock wave. The shock wave focuses the target particle down to a much smaller impact parameter. In turn, the gravitational field of the target particle captures the projectile when the resultant impact parameter is smaller than its own Schwarzschild radius, forming a black hole. One can deduce this by referring to the original argument of escape velocities exceeding the speed of light, which Michell and Laplace used to discover the existence of black holes.Comment: 8 pages, 3 .eps figures, essa

Quantum amplitudes in black-hole evaporation: Spins 1 and 2

Quantum amplitudes for $s=1$ at Maxwell fields and for $s=2$ linearised gravitational wave perturbations of a spherically symmetric Einstein/massless scalar background, describing gravitational collapse to a black hole, are treated by analogy with a previous treatment of $s=0$ scalar-field perturbations of gravitational collapse at late times. In both the $s=1$ and $s=2$ cases, we isolate suitable 'co-ordinate' variables which can be taken as boundary data on a final space-like hypersurface $\Sigma_F$. For simplicity, we take the data on an initial pre-collapse surface $\Sigma_I$ to be exactly spherically symmetric. The (large) Lorentzian proper-time interval between $\Sigma_{I}, \Sigma_{F}$, measured at spatial infinity, is denoted by $T$. The complexified classical boundary-value problem is expected to be well-posed, provide that the time interval $T$ has been rotated into the complex: $T\to{\mid}T{\mid}\exp(-i\theta)$, for $0<\theta\leq{\pi}/2$. We calculate the second-variation classical Lorenztian action $S ^{(2)}_{\rm class}$. Following Feynman, we recover the Lorentzian quantum amplitude by taking the limit as $\theta\to 0_+$ of the semi-classical amplitude $\exp(iS^{(2)}_{\rm class})$. The boundary data for $s=1$ involve the Maxwell magnetic field; the data for $s=2$ involve the magnetic part of the Weyl curvature tensor. The magnetic boundary conditions are related to each other and to the natural $s={1 \over 2}$ boundary conditions by supersymmetry

Electromagnetic radiation from collisions at almost the speed of light: an extremely relativistic charged particle falling into a Schwarzschild black hole

We investigate the electromagnetic radiation released during the high energy collision of a charged point particle with a four-dimensional Schwarzschild black hole. We show that the spectra is flat, and well described by a classical calculation. We also compare the total electromagnetic and gravitational energies emitted, and find that the former is supressed in relation to the latter for very high energies. These results could apply to the astrophysical world in the case charged stars and small charged black holes are out there colliding into large black holes, and to a very high energy collision experiment in a four-dimensional world. In this latter scenario the calculation is to be used for the moments just after the black hole formation, when the collision of charged debris with the newly formed black hole is certainly expected. Since the calculation is four-dimensional, it does not directly apply to Tev-scale gravity black holes, as these inhabit a world of six to eleven dimensions, although our results should qualitatively hold when extrapolated with some care to higher dimensions.Comment: 6 pages, 2 figure

Exact Gravitational Shockwaves and Planckian Scattering on Branes

We obtain a solution describing a gravitational shockwave propagating along a Randall-Sundrum brane. The interest of such a solution is twofold: on the one hand, it is the first exact solution for a localized source on a Randall-Sundrum three-brane. On the other hand, one can use it to study forward scattering at Planckian energies, including the effects of the continuum of Kaluza-Klein modes. We map out the different regimes for the scattering obtained by varying the center-of-mass energy and the impact parameter. We also discuss exact shockwaves in ADD scenarios with compact extra dimensions.Comment: 19 pages, 3 figures. v2: references added, minor improvements and small errors correcte

Minimum black hole mass from colliding Gaussian packets

We study the formation of a black hole in the collision of two Gaussian packets. Rather than following their dynamical evolution in details, we assume a horizon forms when the mass function for the two packets becomes larger than half the flat areal radius, as it would occur in a spherically symmetric geometry. This simple approximation allows us to determine the existence of a minimum black hole mass solely related to the width of the packets. We then comment on the possible physical implications, both in classical and quantum physics, and models with extra spatial dimensions.Comment: 11 pages, 4 figure

Equation of motion for relativistic compact binaries with the strong field point particle limit : Formulation, the first post-Newtonian and multipole terms

We derive the equation of motion for the relativistic compact binaries in the post-Newtonian approximation taking explicitly their strong internal gravity into account. For this purpose we adopt the method of the point particle limit where the equation of motion is expressed in terms of the surface integrals. We examine carefully the behavior of the surface integrals in the derivation. As a result, we obtain the Einstein-Infeld-Hoffman equation of motion at the first post-Newtonian (1PN) order, and a part of the 2PN order which depends on the quadrupole moments and the spins of component stars. Hence, it is found that the equation of motion in the post-Newtonian approximation is valid for the compact binaries by a suitable definition of the mass, spin and quadrupole moment.Comment: revised version. 27pages, three tables, revtex. Some errors have been corrected and some explanations have been adde

Detecting Microscopic Black Holes with Neutrino Telescopes

If spacetime has more than four dimensions, ultra-high energy cosmic rays may create microscopic black holes. Black holes created by cosmic neutrinos in the Earth will evaporate, and the resulting hadronic showers, muons, and taus may be detected in neutrino telescopes below the Earth's surface. We simulate such events in detail and consider black hole cross sections with and without an exponential suppression factor. We find observable rates in both cases: for conservative cosmogenic neutrino fluxes, several black hole events per year are observable at the IceCube detector; for fluxes at the Waxman-Bahcall bound, tens of events per year are possible. We also present zenith angle and energy distributions for all three channels. The ability of neutrino telescopes to differentiate hadrons, muons, and possibly taus, and to measure these distributions provides a unique opportunity to identify black holes, to experimentally constrain the form of black hole production cross sections, and to study Hawking evaporation.Comment: 20 pages, 9 figure

Generalized Lagrangian of N = 1 supergravity and its canonical constraints with the real Ashtekar variable

We generalize the Lagrangian of N = 1 supergravity (SUGRA) by using an arbitrary parameter $\xi$, which corresponds to the inverse of Barbero's parameter $\beta$. This generalized Lagrangian involves the chiral one as a special case of the value $\xi = \pm i$. We show that the generalized Lagrangian gives the canonical formulation of N = 1 SUGRA with the real Ashtekar variable after the 3+1 decomposition of spacetime. This canonical formulation is also derived from those of the usual N = 1 SUGRA by performing Barbero's type canonical transformation with an arbitrary parameter $\beta (=\xi^{-1})$. We give some comments on the canonical formulation of the theory.Comment: 17 pages, LATE

Evolution of high-frequency gravitational waves in some cosmological models

We investigate Isaacson's high-frequency gravitational waves which propagate in some relevant cosmological models, in particular the FRW spacetimes. Their time evolution in Fourier space is explicitly obtained for various metric forms of (anti--)de Sitter universe. Behaviour of high-frequency waves in the anisotropic Kasner spacetime is also described.Comment: 14 pages, 8 figures, to appear in Czech. J. Phy