arXiv subjects

Vitor Cardoso

Publications and source records attributed to Vitor Cardoso.

340 records · Page 19Linked to original sources

arXiv2003

Quasinormal modes of Schwarzschild black holes in four and higher dimensions

We make a thorough investigation of the asymptotic quasinormal modes of the four and five-dimensional Schwarzschild black hole for scalar, electromagnetic and gravitational perturbations. Our numerical results give full support to all the analytical predictions by Motl and Neitzke, for the leading term. We also compute the first order corrections analytically, by extending to higher dimensions, previous work of Musiri and Siopsis, and find excellent agreement with the numerical results. For generic spacetime dimension number D the first-order corrections go as $\frac{1}{n^{(D-3)/(D-2)}}$. This means that there is a more rapid convergence to the asymptotic value for the five dimensional case than for the four dimensional case, as we also show numerically.

gr-qc↗

arXiv2003

Late-Time Tails of Wave Propagation in Higher Dimensional Spacetimes

We study the late-time tails appearing in the propagation of massless fields (scalar, electromagnetic and gravitational) in the vicinities of a D-dimensional Schwarzschild black hole. We find that at late times the fields always exhibit a power-law falloff, but the power-law is highly sensitive to the dimensionality of the spacetime. Accordingly, for odd D>3 we find that the field behaves as t^[-(2l+D-2)] at late times, where l is the angular index determining the angular dependence of the field. This behavior is entirely due to D being odd, it does not depend on the presence of a black hole in the spacetime. Indeed this tails is already present in the flat space Green's function. On the other hand, for even D>4 the field decays as t^[-(2l+3D-8)], and this time there is no contribution from the flat background. This power-law is entirely due to the presence of the black hole. The D=4 case is special and exhibits, as is well known, the t^[-(2l+3)] behavior. In the extra dimensional scenario for our Universe, our results are strictly correct if the extra dimensions are infinite, but also give a good description of the late time behaviour of any field if the large extra dimensions are large enough.

hep-th↗

arXiv2003

Quasinormal frequencies of Schwarzschild black holes in anti-de Sitter spacetimes: A complete study on the asymptotic behavior

We present a thorough analysis for the quasinormal (QN) behavior, associated with the decay of scalar, electromagnetic and gravitational perturbations, of Schwarzschild-anti-de Sitter black holes. As it is known the anti-de Sitter (AdS) QN spectrum crucially depends on the relative size of the black hole to the AdS radius. There are three different types of behavior depending on whether the black hole is large, intermediate, or small. The results of previous works, concerning lower overtones for large black holes, are completed here by obtaining higher overtones for all the three black hole regimes. There are two major conclusions that one can draw from this work: First, asymptotically for high overtones, all the modes are evenly spaced, and this holds for all three types of regime, large, intermediate and small black holes, independently of l, where l is the quantum number characterizing the angular distribution; Second, the spacing between modes is apparently universal, in that it does not depend on the field, i.e., scalar, electromagnetic and gravitational QN modes all have the same spacing for high overtones. We are also able to prove why scalar and gravitational perturbations are isospectral, asymptotically for high overtones, by introducing appropriate superpartner potentials.

gr-qc↗

arXiv2003

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.

gr-qc↗

arXiv2003

Gravitational Radiation in D-dimensional Spacetimes

Gravitational wave solutions to Einstein's equations and their generation are examined in D-dimensional flat spacetimes. First the plane wave solutions are analyzed; then the wave generation is studied with the solution for the metric tensor being obtained with the help of retarded D-dimensional Green's function. Due to the difficulties in handling the wave tails in odd dimensions we concentrate our study in even dimensions. We compute the metric quantities in the wave zone in terms of the energy momentum tensor at retarded time. Some special cases of interest are studied: first the slow motion approximation, where the $D$-dimensional quadrupole formula is deduced. Within the quadrupole approximation, we consider two cases of interest, a particle in circular orbit and a particle falling radially into a higher dimensional Schwarzschild black hole. Then we turn our attention to the gravitational radiation emitted during collisions lasting zero seconds, i.e., hard collisions. We compute the gravitational energy radiated during the collision of two point particles, in terms of a cutoff frequency. In the case in which at least one of the particles is a black hole, we argue this cutoff frequency should be close to the lowest gravitational quasinormal frequency. In this context, we compute the scalar quasinormal frequencies of higher dimensional Schwarzschild black holes. Finally, as an interesting new application of this formalism, we compute the gravitational energy release during the quantum process of black hole pair creation. These results might be important in light of the recent proposal that there may exist extra dimensions in the Universe, one consequence of which may be black hole creation at the Large Hadron Collider at CERN.

hep-th↗

arXiv2003

Quasinormal modes of the near extremal Schwarzschild-de Sitter black hole

We present an exact expression for the quasinormal modes of scalar, electromagnetic and gravitational perturbations of a near extremal Scwarzschild-de Sitter black hole and we show why a previous approximation holds exactly in this near extremal regime. In particular, our results give the asymptotic behavior of the quasinormal frequencies for highly damped modes, which as recently attracted much attention due to the proposed identification of its real part with the Barbero-Immirzi parameter.

gr-qc↗

arXiv2003

Gravitational Radiation from the radial infall of highly relativistic point particles into Kerr black holes

In this paper, we consider the gravitational radiation generated by the collision of highly relativistic particles with rotating Kerr black holes. We use the Sasaki-Nakamura formalism to compute the waveform, energy spectra and total energy radiated during this process. We show that the gravitational spectrum for high-energy collisions has definite characteristic universal features, which are independent of the spin of the colliding objects. We also discuss possible connections between these results and the black hole-black hole collision at the speed of light process. With these results at hand, we predict that during the high speed collision of a non-rotating hole with a rotating one, about 35% of the total energy can get converted into gravitational waves. Thus, if one is able to produce black holes at the Large Hadron Collider, as much as 35% of the partons' energy should be emitted during the so called balding phase. This energy will be missing, since we don't have gravitational wave detectors able to measure such amplitudes. The collision at the speed of light between one rotating black hole and a non-rotating one or two rotating black holes turns out to be the most efficient gravitational wave generator in the Universe.

gr-qc↗

arXiv2002

Gravitational Optics: Self-phase modulation and harmonic cascades

Nonlinear wave interaction of low amplitude gravitational waves in flat space-time is considered. Analogy with optics is established. It is shown that the flat metric space-time is equivalent to a centro-symmetric optical medium, with no second order susceptibility. The lowest order nonlinear effects are those due to the third order nonlinearity and include self-phase modulation and high harmonic generation. These processes lead to an efficient energy dilution of the gravitational wave energy over an increasingly large spectral range.

gr-qc↗

arXiv2002

Black hole collision with a scalar particle in four, five and seven dimensional anti-de Sitter spacetimes: ringing and radiation

In this work we compute the spectra, waveforms and total scalar energy radiated during the radial infall of a small test particle coupled to a scalar field into a $d$-dimensional Schwarzschild-anti-de Sitter black hole. We focus on $d=4, 5$ and 7, extending the analysis we have done for $d=3$. For small black holes, the spectra peaks strongly at a frequency $ω\sim d-1$, which is the lowest pure anti-de Sitter (AdS) mode. The waveform vanishes exponentially as $t \to \infty$, and this exponential decay is governed entirely by the lowest quasinormal frequency. This collision process is interesting from the point of view of the dynamics itself in relation to the possibility of manufacturing black holes at LHC within the brane world scenario, and from the point of view of the AdS/CFT conjecture, since the scalar field can represent the string theory dilaton, and 4, 5, 7 are dimensions of interest for the AdS/CFT correspondence.

hep-th↗

arXiv2002

The radial infall of a highly relativistic point particle into a Kerr black hole along the symmetry axis

In this Letter we consider the radial infall along the symmetry axis of an ultra-relativistic point particle into a rotating Kerr black hole. We use the Sasaki-Nakamura formalism to compute the waveform, energy spectra and total energy radiated during this process. We discuss possible connections between these results and the black hole-black hole collision at the speed of light process.

gr-qc↗

arXiv2002

Gravitational radiation from collisions at the speed of light: a massless particle falling into a Schwarzschild black hole

We compute spectra, waveforms, angular distribution and total gravitational energy of the gravitiational radiation emitted during the radial infall of a massless particle into a Schwarzschild black hole. Our fully relativistic approach shows that (i) less than 50% of the total energy radiated to infinity is carried by quadrupole waves, (ii) the spectra is flat, and (iii) the zero frequency limit agrees extremely well with a prediction by Smarr. This process may be looked at as the limiting case of collisions between massive particles traveling at nearly the speed of light, by identifying the energy $E$ of the massless particle with $m_0 γ$, $m_0$ being the mass of the test particle and $γ$ the Lorentz boost parameter. We comment on the implications for the two black hole collision at nearly the speed of light process, where we obtain a 13.3% wave generation efficiency, and compare our results with previous results by D'Eath and Payne.

gr-qc↗

arXiv2002

Scalar Synchrotron Radiation in the Schwarzschild-anti-de Sitter Geometry

We present a complete relativistic analysis for the scalar radiation emitted by a particle in circular orbit around a Schwarzschild-anti-de Sitter black hole. If the black hole is large, then the radiation is concentrated in narrow angles- high multipolar distribution- i.e., the radiation is synchrotronic. However, small black holes exhibit a totally different behavior: in the small black hole regime, the radiation is concentrated in low multipoles. There is a transition mass at $M=0.427 R$, where $R$ is the AdS radius. This behavior is new, it is not present in asymptotically flat spacetimes.

hep-th↗

arXiv2002

Black hole collision with a scalar particle in three dimensional anti-de Sitter spacetime

We study the collision between a BTZ black hole and a test particle coupled to a scalar field. We compute the power spectrum, the energy radiated and the plunging waveforms for this process. We show that for late times the signal is dominated by the quasinormal ringing. In terms of the AdS/CFT correspondence the bulk gravity process maps into a thermal state, an expanding bubble and gauge particles decaying into bosons of the associated operator. These latter thermalize in a timescale predicted by the bulk theory.

hep-th↗

arXiv2001

Quasi-normal modes of toroidal, cylindrical and planar black holes in anti-de Sitter spacetimes: scalar, electromagnetic and gravitational perturbations

We study the quasi-normal modes (QNM) of scalar, electromagnetic and gravitational perturbations of black holes in general relativity whose horizons have toroidal, cylindrical or planar topology in an asymptotically anti-de Sitter (AdS) spacetime. The associated quasinormal frequencies describe the decay in time of the corresponding test field in the vicinities of the black hole. In terms of the AdS/CFT conjecture, the inverse of the frequency is a measure of the dynamical timescale of approach to thermal equilibrium of the corresponding conformal field theory.

gr-qc↗

arXiv2001

Quasi-Normal Modes of Schwarzschild Anti-De Sitter Black Holes: Electromagnetic and Gravitational Perturbations

We study the quasi-normal modes (QNM) of electromagnetic and gravitational perturbations of a Schwarzschild black hole in an asymptotically Anti-de Sitter (AdS) spacetime. Some of the electromagnetic modes do not oscillate, they only decay, since they have pure imaginary frequencies. The gravitational modes show peculiar features: the odd and even gravitational perturbations no longer have the same characteristic quasinormal frequencies. There is a special mode for odd perturbations whose behavior differs completely from the usual one in scalar and electromagnetic perturbation in an AdS spacetime, but has a similar behavior to the Schwarzschild black hole in an asymptotically flat spacetime: the imaginary part of the frequency goes as 1/r+, where r+ is the horizon radius. We also investigate the small black hole limit showing that the imaginary part of the frequency goes as r+^2. These results are important to the AdS/CFT conjecture since according to it the QNMs describe the approach to equilibrium in the conformal field theory.

gr-qc↗

arXiv2001

Scalar, electromagnetic and Weyl perturbations of BTZ black holes: quasi normal modes

We calculate the quasinormal modes and associated frequencies of the Banados, Zanelli and Teitelboim (BTZ) non-rotating black hole. This black hole lives in 2+1-dimensions in an asymptotically anti-de Sitter spacetime. We obtain exact results for the wavefunction and quasi normal frequencies of scalar, electromagnetic and Weyl (neutrino) perturbations.

gr-qc↗