59 research outputs found
The fastest way to circle a black hole
Black-hole spacetimes with a "photonsphere", a hypersurface on which massless
particles can orbit the black hole on circular null geodesics, are studied. We
prove that among all possible trajectories (both geodesic and non-geodesic)
which circle the central black hole, the null circular geodesic is
characterized by the {\it shortest} possible orbital period as measured by
asymptotic observers. Thus, null circular geodesics provide the fastest way to
circle black holes. In addition, we conjecture the existence of a universal
lower bound for orbital periods around compact objects (as measured by
flat-space asymptotic observers): , where is the
mass of the central object. This bound is saturated by the null circular
geodesic of the maximally rotating Kerr black hole.Comment: 5 page
Geodesic stability, Lyapunov exponents and quasinormal modes
Geodesic motion determines important features of spacetimes. Null unstable
geodesics are closely related to the appearance of compact objects to external
observers and have been associated with the characteristic modes of black
holes. By computing the Lyapunov exponent, which is the inverse of the
instability timescale associated with this geodesic motion, we show that, in
the eikonal limit, quasinormal modes of black holes in any dimensions are
determined by the parameters of the circular null geodesics. This result is
independent of the field equations and only assumes a stationary, spherically
symmetric and asymptotically flat line element, but it does not seem to be
easily extendable to anti-de Sitter spacetimes. We further show that (i) in
spacetime dimensions greater than four, equatorial circular timelike geodesics
in a Myers-Perry black hole background are unstable, and (ii) the instability
timescale of equatorial null geodesics in Myers-Perry spacetimes has a local
minimum for spacetimes of dimension d > 5.Comment: 13 pages, 2 Figs, RevTex4. v2: Minor corrections. v3: more minor
correction
Dark matter annihilation in the gravitational field of a black hole
In this paper we consider dark matter particle annihilation in the
gravitational field of black holes. We obtain exact distribution function of
the infalling dark matter particles, and compute the resulting flux and spectra
of gamma rays coming from the objects. It is shown that the dark matter density
significantly increases near a black hole. Particle collision energy becomes
very high affecting relative cross-sections of various annihilation channels.
We also discuss possible experimental consequences of these effects.Comment: 9 pages, 1 figur
Visualizing Spacetime Curvature via Gradient Flows I: Introduction
Traditional approaches to the study of the dynamics of spacetime curvature in
a very real sense hide the intricacies of the nonlinear regime. Whether it be
huge formulae, or mountains of numerical data, standard methods of presentation
make little use of our remarkable skill, as humans, at pattern recognition.
Here we introduce a new approach to the visualization of spacetime curvature.
We examine the flows associated with the gradient fields of invariants derived
from the spacetime. These flows reveal a remarkably rich structure, and offer
fresh insights even for well known analytical solutions to Einstein's
equations. This paper serves as an overview and as an introduction to this
approach.Comment: 10 pages twocolumn revtex 4-1 two figures. Final form to appear in
Phys Rev
Classical model of elementary particle with Bertotti-Robinson core and extremal black holes
We discuss the question, whether the Reissner-Nordstr\"{o}m RN) metric can be
glued to another solutions of Einstein-Maxwell equations in such a way that (i)
the singularity at r=0 typical of the RN metric is removed (ii), matching is
smooth. Such a construction could be viewed as a classical model of an
elementary particle balanced by its own forces without support by an external
agent. One choice is the Minkowski interior that goes back to the old Vilenkin
and Fomin's idea who claimed that in this case the bare delta-like stresses at
the horizon vanish if the RN metric is extremal. However, the relevant entity
here is the integral of these stresses over the proper distance which is
infinite in the extremal case. As a result of the competition of these two
factors, the Lanczos tensor does not vanish and the extremal RN cannot be glued
to the Minkowski metric smoothly, so the elementary-particle model as a ball
empty inside fails. We examine the alternative possibility for the extremal RN
metric - gluing to the Bertotti-Robinson (BR) metric. For a surface placed
outside the horizon there always exist bare stresses but their amplitude goes
to zero as the radius of the shell approaches that of the horizon. This limit
realizes the Wheeler idea of "mass without mass" and "charge without charge".
We generalize the model to the extremal Kerr-Newman metric glued to the
rotating analog of the BR metric.Comment: 23 pages. Misprints correcte
Observable form of pulses emitted from relativistic collapsing objects
In this work, we discuss observable characteristics of the radiation emitted
from a surface of a collapsing object. We study a simplified model in which a
radiation of massless particles has a sharp in time profile and it happens at
the surface at the same moment of comoving time. Since the radiating surface
has finite size the observed radiation will occur during some finite time. Its
redshift and bending angle are affected by the strong gravitational field. We
obtain a simple expression for the observed flux of the radiation as a function
of time. To find an explicit expression for the flux we develop an analytical
approximation for the bending angle and time delay for null rays emitted by a
collapsing surface. In the case of the bending angle this approximation is an
improved version of the earlier proposed Beloborodov-Leahy-approximation. For
rays emitted at the accuracy of the proposed improved approximations
for the bending angle and time delay is of order (or less) than 2-3%. By using
this approximation we obtain an approximate analytical expression for the
observed flux and study its properties.Comment: 13 pages, 10 figures;Typos in equations and refrences are corrected.
No change in the results and discussion
Are black holes in alternative theories serious astrophysical candidates? The case for Einstein-Dilaton-Gauss-Bonnet black holes
It is generally accepted that Einstein's theory will get some as yet unknown
corrections, possibly large in the strong field regime. An ideal place to look
for these modifications is around the vicinities of compact objects such as
black holes. Our case study here are Dilatonic Black Holes, which arise in the
framework of Gauss-Bonnet couplings and one-loop corrected four-dimensional
effective theory of heterotic superstrings at low energies. These are
interesting objects as a prototype for alternative, yet well-behaved gravity
theories: they evade the "no-hair" theorem of General Relativity but were
proved to be stable against radial perturbations. We investigate the viability
of these black holes as astrophysical objects and try to provide some means to
distinguish them from black holes in General Relativity. We start by extending
previous works and establishing the stability of these black holes against
axial perturbations. We then look for solutions of the field equations
describing slowly rotating black holes and study geodesic motion around this
geometry. Depending on the values of mass, dilaton charge and angular momentum
of the solution, one can have measurable differences in the ISCO location and
orbital frequency, relatively to black holes in General Relativity. Such
differences may be useful in future experiments, to discriminate between
alternative theories of gravity.Comment: 17 pages - v1: references added - v2: Minor correction
Probing the interiors of the ice giants: Shock compression of water to 700 GPa and 3.8 g/ccm
Recently there has been tremendous increase in the number of identified
extra-solar planetary systems. Our understanding of their formation is tied to
exoplanet internal structure models, which rely upon equations of state of
light elements and compounds like water. Here we present shock compression data
for water with unprecedented accuracy that shows water equations of state
commonly used in planetary modeling significantly overestimate the
compressibility at conditions relevant to planetary interiors. Furthermore, we
show its behavior at these conditions, including reflectivity and isentropic
response, is well described by a recent first-principles based equation of
state. These findings advocate this water model be used as the standard for
modeling Neptune, Uranus, and "hot Neptune" exoplanets, and should improve our
understanding of these types of planets.Comment: Accepted to Phys. Rev. Lett.; supplementary material attached
including 2 figures and 2 tables; to view attachments, please download and
extract the gzipped tar source file listed under "Other formats
Photon redshift and the appearance of a naked singularity
In this paper we analyze the redshift as observed by an external observer
receiving photons which terminate in the past at the naked singularity formed
in a Tolman-Bondi dust collapse. Within the context of models considered here
it is shown that photons emitted from a weak curvature naked singularity are
always finitely redshifted to an external observer. Certain cases of strong
curvature naked singularities, including the self-similar one, where the
photons are infinitely redshifted are also pointed out.Comment: Latex file, 14 pages, no figures, one change in the reference.
Accepted for publication in Phys. Rev.
The growth of structure in the Szekeres inhomogeneous cosmological models and the matter-dominated era
This study belongs to a series devoted to using Szekeres inhomogeneous models
to develop a theoretical framework where observations can be investigated with
a wider range of possible interpretations. We look here into the growth of
large-scale structure in the models. The Szekeres models are exact solutions to
Einstein's equations that were originally derived with no symmetries. We use a
formulation of the models that is due to Goode and Wainwright, who considered
the models as exact perturbations of an FLRW background. Using the Raychaudhuri
equation, we write for the two classes of the models, exact growth equations in
terms of the under/overdensity and measurable cosmological parameters. The new
equations in the overdensity split into two informative parts. The first part,
while exact, is identical to the growth equation in the usual linearly
perturbed FLRW models, while the second part constitutes exact non-linear
perturbations. We integrate numerically the full exact growth rate equations
for the flat and curved cases. We find that for the matter-dominated era, the
Szekeres growth rate is up to a factor of three to five stronger than the usual
linearly perturbed FLRW cases, reflecting the effect of exact Szekeres
non-linear perturbations. The growth is also stronger than that of the
non-linear spherical collapse model, and the difference between the two
increases with time. This highlights the distinction when we use general
inhomogeneous models where shear and a tidal gravitational field are present
and contribute to the gravitational clustering. Additionally, it is worth
observing that the enhancement of the growth found in the Szekeres models
during the matter-dominated era could suggest a substitute to the argument that
dark matter is needed when using FLRW models to explain the enhanced growth and
resulting large-scale structures that we observe today (abridged)Comment: 18 pages, 4 figures, matches PRD accepted versio
- …