arXiv subjects

Amos Ori

Publications and source records attributed to Amos Ori.

At least 37 records · Page 2Linked to original sources

arXiv2015

Adaptive gauge method for long-time double-null simulations of spherical black-hole spacetimes

Double-null coordinates are highly useful in numerical simulations of dynamical spherically-symmetric black holes (BHs). However, they become problematic in long-time simulations: Along the event horizon, the truncation error grows exponentially in the outgoing Eddington null coordinate - which we denote $v_e$ - and runs out of control for a sufficiently long interval of $v_e$. This problem, if not properly addressed, would destroy the numerics both inside and outside the black hole at late times (i.e. large $v_e$). In this paper we explore the origin of this problem, and propose a resolution based on adaptive gauge for the ingoing null coordinate $u$. This resolves the problem outside the BH - and also inside the BH, if the latter is uncharged. However, in the case of a charged BH, an analogous large-$v_e$ numerical problem occurs at the inner horizon. We thus generalize our adaptive-gauge method in order to overcome the IH problem as well. This improved adaptive gauge, to which we refer as the maximal-$σ$ gauge, allows long-$v$ double-null numerical simulation across both the event horizon and the (outgoing) inner horizon, and up to the vicinity of the spacelike $r=0$ singularity. We conclude by presenting a few numerical results deep inside a perturbed charged BH, in the vicinity of the contracting Cauchy Horizon.

gr-qc↗

arXiv2015

Pragmatic mode-sum regularization method for semiclassical black-hole spacetimes

Computation of the renormalized stress-energy tensor is the most serious obstacle in studying the dynamical, self-consistent, semiclassical evaporation of a black hole in 4D. The difficulty arises from the delicate regularization procedure for the stress-energy tensor, combined with the fact that in practice the modes of the field need be computed numerically. We have developed a new method for numerical implementation of the point-splitting regularization in 4D, applicable to the renormalized stress-energy tensor as well as to $\left\langle ϕ^{2}\right\rangle _{ren}$, namely the renormalized $\left\langle ϕ^{2}\right\rangle$. So far we have formulated two variants of this method: t-splitting (aimed for stationary backgrounds) and angular splitting (for spherically-symmetric backgrounds). In this paper we introduce our basic approach, and then focus on the t-splitting variant, which is the simplest of the two (deferring the angular-splitting variant to a forthcoming paper). We then use this variant, as a first stage, to calculate $\left\langle ϕ^{2}\right\rangle _{ren}$ in Schwarzschild spacetime, for a massless scalar field in the Boulware state. We compare our results to previous ones, obtained by a different method, and find full agreement. We discuss how this approach can be applied (using the angular-splitting variant) to analyze the dynamical self-consistent evaporation of black holes.

gr-qc↗

arXiv2013

Two-dimensional semiclassical static black holes: Finite-mass correction to the Hawking temperature and outflux

In the two-dimensional framework, the surface gravity of a (classical) black hole is independent of its mass $M$. As a consequence, the Hawking temperature and outflux are also independent of $M$ at the large-$M$ limit. (This contrasts with the four-dimensional framework, in which the surface gravity and temperature scale as 1/M.) However, when the semiclassical backreaction effects on the black-hole geometry are taken into account, the surface gravity is no longer $M$-independent, and the same applies to the Hawking temperature and outflux. This effect, which vanishes at the large-$M$ limit, increases with decreasing $M$. Here we analyze the semiclassical field equations for a two-dimensional static black hole, and calculate the leading-order backreaction effect ($\propto 1/M$) on the Hawking temperature and outflux. We then confirm our analytical result by numerically integrating the semiclassical field equations.

gr-qc↗

arXiv2013

Late-time tails in extremal Reissner-Nordstrom spacetime

This note discusses the late-time decay of perturbations outside extremal Reissner-Nordstrom black hole. We consider individual spherical-harmonic modes $l$ of massless scalar field. The initial data are assumed to be of compact support, with generic regular behavior across the horizon. The scalar perturbations are found to decay at late time as $t^{-(2l+2)}$. We also provide the spatial dependence of the late-time tails, including the exact overall pre-factor.

gr-qc↗

arXiv2012

Outgoing gravitational shock-wave at the inner horizon: The late-time limit of black hole interiors

We investigate the interiors of 3+1 dimensional asymptotically flat charged and rotating black holes as described by observers who fall into the black holes at late times, long after any perturbations of the exterior region have decayed. In the strict limit of late infall times, the initial experiences of such observers are precisely described by the region of the limiting stationary geometry to the past of its inner horizon. However, we argue that late infall-time observers encounter a null shockwave at the location of the would-be outgoing inner horizon. In particular, for spherically symmetric black hole spacetimes we demonstrate that freely-falling observers experience a metric discontinuity across this shock, that is, a gravitational shock-wave. Furthermore, the magnitude of this shock is at least of order unity. A similar phenomenon of metric discontinuity appears to take place at the inner horizon of a generically-perturbed spinning black hole. We compare the properties of this null shockwave singularity with those of the null weak singularity that forms at the Cauchy horizon.

gr-qc↗

arXiv2012

Finite-mass correction to 2D Black-hole evaporation rate

We numerically analyze the evolution of a two-dimensional dilatonic black hole, within the CGHS model. We focus our attention on the finite-mass corrections to the universal evaporation rate which applies at the large-mass limit. Our numerical results confirm a previous theoretical prediction for the first-order ($\propto 1/M$) correction. In addition, our results strongly suggest that the next-order ($\propto 1/M^{2}$) term vanishes, and provide a rough estimate for the third-order term.

gr-qc↗

arXiv2011

Extended time-travelling objects in Misner space

Misner space is a two-dimensional (2D) locally-flat spacetime which elegantly demonstrates the emergence of closed timelike curves from causally well-behaved initial conditions. Here we explore the motion of rigid extended objects in this time-machine spacetime. This kind of 2D time-travel is found to be risky due to inevitable self-collisions (i.e. collisions of the object with itself). However, in a straightforward four-dimensional generalization of Misner space (a physically more relevant spacetime obviously), we find a wide range of "safe" time-travel orbits free of any self-collisions.

gr-qc↗

arXiv2010

Approximate solution to the CGHS field equations for two-dimensional evaporating black holes

Callan, Giddings, Harvey and Strominger (CGHS) previously introduced a two-dimensional semiclassical model of gravity coupled to a dilaton and to matter fields. Their model yields a system of field equations which may describe the formation of a black hole in gravitational collapse as well as its subsequent evaporation. Here we present an approximate analytical solution to the semiclassical CGHS field equations. This solution is constructed using the recently-introduced formalism of flux-conserving hyperbolic systems. We also explore the asymptotic behavior at the horizon of the evaporating black hole.

gr-qc↗

arXiv2010

Flux-conserving hyperbolic systems and two-dimensional evaporating black holes

A class of semi-linear hyperbolic systems in 1+1 dimensions was investigated several years ago by Ori and Gorbonos. This class, to which we shall refer as "flux-conserving systems", exhibits a variety of interesting mathematical properties. Here we demonstrate how the formalism of flux-conserving systems can be applied to the problem of black-hole evaporation in 1+1-dimensions. More specifically, we show how the semiclassical CGHS field equations may be approximated by a certain flux-conserving system.

gr-qc↗

arXiv2010

Interior design of a two-dimensional semiclassical black hole: Quantum transition across the singularity

We study the internal structure of a two-dimensional dilatonic evaporating black hole, based on the CGHS model. At the semiclassical level, a (weak) spacelike singularity was previously found to develop inside the black hole. We employ here a simplified quantum formulation of spacetime dynamics in the neighborhood of this singularity, using a minisuperspace-like approach. Quantum evolution is found to be regular and well-defined at the semiclassical singularity. A well-localized initial wave-packet propagating towards the singularity bounces off the latter and retains its well-localized form. Our simplified quantum treatment thus suggests that spacetime may extend semiclassically beyond the singularity, and also signifies the specific extension.

gr-qc↗

arXiv2009

Interior design of a two-dimensional semiclassic black hole

We look into the inner structure of a two-dimensional dilatonic evaporating black hole. We establish and employ the homogenous approximation for the black-hole interior. The field equations admit two types of singularities, and their local asymptotic structure is investigated. One of these singularities is found to develop, as a spacelike singularity, inside the black hole. We then study the internal structure of the evaporating black hole from the horizon to the singularity.

gr-qc↗

arXiv2008

Frequency-domain calculation of the self force: the high-frequency problem and its resolution

The mode-sum method provides a practical means for calculating the self force acting on a small particle orbiting a larger black hole. In this method, one first computes the spherical-harmonic $l$-mode contributions $F^μ_l$ of the "full force" field $F^μ$, evaluated at the particle's location, and then sums over $l$ subject to a certain regularization procedure. In the frequency-domain variant of this scheme the quantities $F^μ_l$ are obtained by fully decomposing the particle's self field into Fourier-harmonic modes $l m ω$, calculating the contribution of each such mode to $F^μ_l$, and then summing over $ω$ and $m$ for given $l$. This procedure has the advantage that one only encounters {\it ordinary} differential equations. However, for eccentric orbits, the sum over $ω$ is found to converge badly at the particle's location. This problem (reminiscent of the familiar Gibbs phenomenon) results from the discontinuity of the time-domain $F^μ_l$ field at the particle's worldline. Here we propose a simple and practical method to resolve this problem. The method utilizes the {\it homogeneous} modes $l m ω$ of the self field to construct $F^μ_l$ (rather than the inhomogeneous modes, as in the standard method), which guarantees an exponentially-fast convergence to the correct value of $F^μ_l$, even at the particle's location. We illustrate the application of the method with the example of the monopole scalar-field perturbation from a scalar charge in an eccentric orbit around a Schwarzschild black hole. Our method, however, should be applicable to a wider range of problems, including the calculation of the gravitational self-force using either Teukolsky's formalism, or a direct integration of the metric perturbation equations.

gr-qc↗

arXiv2007

Formation of closed timelike curves in a composite vacuum/dust asymptotically-flat spacetime

We present a new asymptotically-flat time-machine model made solely of vacuum and dust. The spacetime evolves from a regular spacelike initial hypersurface S and subsequently develops closed timelike curves. The initial hypersurface S is asymptotically flat and topologically trivial. The chronology violation occurs in a compact manner; namely the first closed causal curves form at the boundary of the future domain of dependence of a compact region in S (the core). This central core is empty, and so is the external asymptotically flat region. The intermediate region surrounding the core (the envelope) is made of dust with positive energy density. This model trivially satisfies the weak, dominant, and strong energy conditions. Furthermore it is governed by a well-defined system of field equations which possesses a well-posed initial-value problem.

gr-qc↗

arXiv2007

A Simplified Mathematical Model for the Formation of Null Singularities Inside Black Holes I - Basic Formulation and a Conjecture

Einstein's equations are known to lead to the formation of black holes and spacetime singularities. This appears to be a manifestation of the mathematical phenomenon of finite-time blowup: a formation of singularities from regular initial data. We present a simple hyperbolic system of two semi-linear equations inspired by the Einstein equations. We explore a class of solutions to this system which are analogous to static black-hole models. These solutions exhibit a black-hole structure with a finite-time blowup on a characteristic line mimicking the null inner horizon of spinning or charged black holes. We conjecture that this behavior - namely black-hole formation with blow-up on a characteristic line - is a generic feature of our semi-linear system. Our simple system may provide insight into the formation of null singularities inside spinning or charged black holes in the full system of Einstein equations.

gr-qc↗

arXiv2006

Inside an evaporating two-dimensional charged black hole

We investigate the inner structure of an evaporating charged black hole, within the context of semiclassical dilaton gravity in two dimensions. The matter fields are charged, allowing the evaporation of both the mass and charge of the black hole. We find that the semiclassical effects cause the inner horizon to expand (by a finite factor), rather than to shrink to a point singularity. Although this expansion is a quantum phenomenon, the overall expansion factor is found to be independent of the magnitude of the quantum terms in the effective theory.

gr-qc↗

arXiv2005

A new time-machine model with compact vacuum core

We present a class of curved-spacetime vacuum solutions which develope closed timelike curves at some particular moment. We then use these vacuum solutions to construct a time-machine model. The causality violation occurs inside an empty torus, which constitutes the time-machine core. The matter field surrounding this empty torus satisfies the weak, dominant, and strong energy conditions. The model is regular, asymptotically-flat, and topologically-trivial. Stability remains the main open question.

gr-qc↗

arXiv2004

On the Resolution of the Time-Like Singularities in Reissner-Nordstrom and Negative-Mass Schwarzschild

Certain time-like singularities are shown to be resolved already in classical General Relativity once one passes from particle probes to scalar waves. The time evolution can be defined uniquely and some general conditions for that are formulated. The Reissner-Nordstrom singularity allows for communication through the singularity and can be termed "beam splitter" since the transmission probability of a suitably prepared high energy wave packet is 25%. The high frequency dependence of the cross section is w^{-4/3}. However, smooth geometries arbitrarily close to the singular one require a finite amount of negative energy matter. The negative-mass Schwarzschild has a qualitatively different resolution interpreted to be fully reflecting. These 4d results are similar to the 2d black hole and are generalized to an arbitrary dimension d>4.

hep-th↗

arXiv2003

Harmonic-gauge dipole metric perturbations for weak-field circular orbits in Schwarzschild spacetime

We calculate the harmonic-gauge even l=1 mode of the linear metric perturbation (MP) produced by a particle in a weak-field circular orbit around a Schwarzschild black hole (BH). We focus on the Newtonian limit, i.e. the limit in which the mass M of the central BH approaches zero (while fixing the orbital radius and the small-object mass), and obtain explicit expressions for the MP in this limit. We find that the MP are anomalous in this limit, namely, they do not approach their standard, Coulomb-like, flat-space values. Instead, the MP grows on approaching the BH, and this growth becomes worse as M decreases. This anomalous behavior leads to some pathologies which we briefly discuss. We also derive here the next-order correction (in the orbital frequency $Ω$) to the MP.

gr-qc↗