265 research outputs found
Scalar, Electromagnetic and Gravitational Perturbations of Kerr-Newman Black Holes in the Slow-Rotation Limit
In Einstein-Maxwell theory, according to classic uniqueness theorems, the
most general stationary black-hole solution is the axisymmetric Kerr-Newman
metric, which is defined by three parameters: mass, spin and electric charge.
The radial and angular dependence of gravitational and electromagnetic
perturbations in the Kerr-Newman geometry do not seem to be separable. In this
paper we circumvent this problem by studying scalar, electromagnetic and
gravitational perturbations of Kerr-Newman black holes in the slow-rotation
limit. We extend (and provide details of) the analysis presented in a recent
Letter [arXiv:1304.1160]. Working at linear order in the spin, we present the
first detailed derivation of the axial and polar perturbation equations in the
gravito-electromagnetic case, and we compute the corresponding quasinormal
modes for any value of the electric charge. Our study is the first
self-consistent stability analysis of the Kerr-Newman metric, and in principle
it can be extended to any order in the small rotation parameter. We find
numerical evidence that the axial and polar sectors are isospectral at first
order in the spin, and speculate on the possible implications of this result.Comment: 15 pages, 3 figures. Mathematica notebook with derivation of the
axial and polar equations available at
http://blackholes.ist.utl.pt/?page=Files and at
http://www.phy.olemiss.edu/~berti/qnms.htm
Tidal Love numbers of a slowly spinning neutron star
By extending our recent framework to describe the tidal deformations of a
spinning compact object, we compute for the first time the tidal Love numbers
of a spinning neutron star to linear order in the angular momentum. The spin of
the object introduces couplings between electric and magnetic distortions and
new classes of spin-induced ("rotational") tidal Love numbers emerge. We focus
on stationary tidal fields, which induce axisymmetric perturbations. We present
the perturbation equations for both electric-led and magnetic-led rotational
Love numbers for generic multipoles and explicitly solve them for various
tabulated equations of state and for a tidal field with an electric (even
parity) and magnetic (odd parity) component with . For a binary
system close to the merger, various components of the tidal field become
relevant. In this case we find that an octupolar magnetic tidal field can
significantly modify the mass quadrupole moment of a neutron star. Preliminary
estimates, assuming a spin parameter , show modifications
relative to the static case, at an orbital distance of five
stellar radii. Furthermore, the rotational Love numbers as functions of the
moment of inertia are much more sensitive to the equation of state than in the
static case, where approximate universal relations at the percent level exist.
For a neutron-star binary approaching the merger, we estimate that the
approximate universality of the induced mass quadrupole moment deteriorates
from in the static case to roughly when . Our
results suggest that spin-tidal couplings can introduce important corrections
to the gravitational waveforms of spinning neutron-star binaries approaching
the merger.Comment: v1: 16+11 pages, 6 appendices, 11 figures. v2: improved estimates of
the tidal-spin corrections to the quadrupole moment of spinning neutron-star
binaries approaching the merger. v3: version published in PR
Tidal deformations of a spinning compact object
The deformability of a compact object induced by a perturbing tidal field is
encoded in the tidal Love numbers, which depend sensibly on the object's
internal structure. These numbers are known only for static,
spherically-symmetric objects. As a first step to compute the tidal Love
numbers of a spinning compact star, here we extend powerful perturbative
techniques to compute the exterior geometry of a spinning object distorted by
an axisymmetric tidal field to second order in the angular momentum. The spin
of the object introduces couplings between electric and magnetic deformations
and new classes of induced Love numbers emerge. For example, a spinning object
immersed in a quadrupolar, electric tidal field can acquire some induced mass,
spin, quadrupole, octupole and hexadecapole moments to second order in the
spin. The deformations are encoded in a set of inhomogeneous differential
equations which, remarkably, can be solved analytically in vacuum. We discuss
certain subtleties in defining the multipole moments of the central object,
which are due to the difficulty in separating the tidal field from the linear
response of the object in the solution. By extending the standard procedure to
identify the linear response in the static case, we prove analytically that the
Love numbers of a Kerr black hole remain zero to second order in the spin. As a
by-product, we provide the explicit form for a slowly-rotating,
tidally-deformed Kerr black hole to quadratic order in the spin, and discuss
its geodesic and geometrical properties.Comment: 27 pages, 1 figure, 6 appendices; v2: improvements and
clarifications, version to appear in PR
Superradiant instability of the Kerr brane
We consider linear gravitational perturbations of the Kerr brane, an exact
solution of vacuum Einstein's equations in dimensions higher than four and a
low-energy solution of string theory. Decomposing the perturbations in tensor
harmonics of the transverse Ricci-flat space, we show that tensor- and
vector-type metric perturbations of the Kerr brane satisfy respectively a
massive Klein-Gordon equation and a Proca equation on the four-dimensional Kerr
space, where the mass term is proportional to the eigenvalue of the harmonics.
Massive bosonic fields trigger a well-known superradiant instability on a Kerr
black hole. We thus establish that Kerr branes in dimensions are
gravitationally unstable due to superradiance. These solutions are also
unstable against the Gregory-Laflamme instability and we discuss the conditions
for either instability to occur and their rather different nature. When the
transverse dimensions are compactified and much smaller than the Kerr horizon,
only the superradiant instability is present, with a time scale much longer
than the dynamical time scale. Our formalism can be also used to discuss other
types of higher-dimensional black objects, taking advantage of recent progress
in studying linear perturbations of four-dimensional black holes.Comment: 1+15 pages, no figure
Gravitational signature of Schwarzschild black holes in dynamical Chern-Simons gravity
Dynamical Chern-Simons gravity is an extension of General Relativity in which
the gravitational field is coupled to a scalar field through a parity-violating
Chern-Simons term. In this framework, we study perturbations of spherically
symmetric black hole spacetimes, assuming that the background scalar field
vanishes. Our results suggest that these spacetimes are stable, and small
perturbations die away as a ringdown. However, in contrast to standard General
Relativity, the gravitational waveforms are also driven by the scalar field.
Thus, the gravitational oscillation modes of black holes carry imprints of the
coupling to the scalar field. This is a smoking gun for Chern-Simons theory and
could be tested with gravitational-wave detectors, such as LIGO or LISA. For
negative values of the coupling constant, ghosts are known to arise, and we
explicitly verify their appearance numerically. Our results are validated using
both time evolution and frequency domain methods.Comment: RevTex4, 12 pages, 8 figures, 3 Tables. v2: minor typos corrected and
references added. Published versio
Magnetic tidal Love numbers clarified
In this brief note, we clarify certain aspects related to the magnetic (i.e.,
odd parity or axial) tidal Love numbers of a star in general relativity.
Magnetic tidal deformations of a compact star had been computed in 2009
independently by Damour and Nagar and by Binnington and Poisson. More recently,
Landry and Poisson showed that the magnetic tidal Love numbers depend on the
assumptions made on the fluid, in particular they are different (and of
opposite sign) if the fluid is assumed to be in static equilibrium or if it is
irrotational. We show that the zero-frequency limit of the Regge-Wheeler
equation forces the fluid to be irrotational. For this reason, the results of
Damour and Nagar are equivalent to those of Landry and Poisson for an
irrotational fluid, and are expected to be the most appropriate to describe
realistic configurations.Comment: v2: 4 pages, one extra equation. Matches the PRD versio
Direct Numerical Simulations of Turbulence Subjected to a Straining and De-Straining Cycle
In many turbulent flows, significant interactions between fluctuations and mean velocity gradients occur in nonequilibrium conditions, i.e., the turbulence does not have sufficient time to adjust to changes in the velocity gradients applied by the large scales. The simplest flow that retains such physics is the time dependent homogeneous strain flow. A detailed experimental study of initially isotropic turbulence subjected to a straining and destraining cycle was reported by Chen et al. [“Scale interactions of turbulence subjected to a straining-relaxation-destraining cycle,” J. Fluid Mech. 562, 123 (2006)] . Direct numerical simulation (DNS) of the experiment of Chen et al. [“Scale interactions of turbulence subjected to a straining-relaxation-destraining cycle,” J. Fluid Mech. 562, 123 (2006)] is undertaken, applying the measured straining and destraining cycle in the DNS. By necessity, the Reynolds number in the DNS is lower. The DNS study provides a complement to the experimental one including time evolution of small-scale gradients and pressure terms that could not be measured in the experiments. The turbulence response is characterized in terms of velocity variances, and similarities and differences between the experimental data and the DNS results are discussed. Most of the differences can be attributed to the response of the largest eddies, which, even if are subjected to the same straining cycle, evolve under different conditions in the simulations and experiment. To explore this issue, the time evolution of different initial conditions parametrized in terms of the integral scale is analyzed in computational domains with different aspect ratios. This systematic analysis is necessary to minimize artifacts due to unphysical confinement effects of the flow. The evolution of turbulent kinetic energy production predicted by DNS, in agreement with experimental data, provides a significant backscatter of kinetic energy during the destraining phase. This behavior is explained in terms of Reynolds stress anisotropy and nonequilibrium conditions. From the DNS, a substantial persistency of anisotropy is observed up to small scales, i.e., at the level of velocity gradients. Due to the time dependent deformation, we find that the major contribution in the Reynolds stresses budget is provided by the production term and by the pressure/strain correlation, resulting in large time variation of velocity intensities. The DNS data are compared with predictions from the classical Launder–Reece–Rodi isoptropic production [ B. E. Launder et al., “Progress in the development of a Reynolds stress turbulence closure,” J. Fluid Mech. 68, 537 (1975) ] Reynolds stress model, showing good agreement with some differences for the redistribution term
Energy fluxes in turbulent separated flows
Turbulent separation in channel flow containing a curved wall is studied using a generalised form of Kolmogorov equation. The equation successfully accounts for inhomogeneous effects in both the physical and separation spaces. We investigate the scale-by-scale energy dynamics in turbulent separated flow induced by a curved wall. The scale and spatial fluxes are highly dependent on the shear layer dynamics and the recirculation bubble forming behind the lower curved wall. The intense energy produced in the shear layer is transferred to the recirculation region, sustaining the turbulent velocity fluctuations. The energy dynamics radically changes depending on the physical position inside the domain, resembling planar turbulent channel dynamics downstream
- …