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): $T_{\infty}\geq 4\pi M$, where $M$ 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 $R > 2R_g$ 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