arXiv subjects

Marc Casals

Publications and source records attributed to Marc Casals.

At least 55 records · Page 3Linked to original sources

arXiv2016

Horizon Instability of Extremal Kerr Black Holes: Nonaxisymmetric Modes and Enhanced Growth Rate

We show that the horizon instability of the extremal Kerr black hole is associated with a singular branch point in the Green function at the superradiant bound frequency. We study generic initial data supported away from the horizon and find an enhanced growth rate due to nonaxisymmetric modes. The growth is controlled by the conformal weight of each mode. We speculate on connections to near-extremal black holes and holographic duality.

gr-qc↗

arXiv2016

Quantum dress for a naked singularity

We investigate semiclassical backreaction on a conical naked singularity space-time with a negative cosmological constant in (2+1)-dimensions. In particular, we calculate the renormalized quantum stress-energy tensor for a conformally coupled scalar field on such naked singularity space-time. We then obtain the backreacted metric via the semiclassical Einstein equations. We show that, in the regime where the semiclassical approximation can be trusted, backreaction dresses the naked singularity with an event horizon, thus enforcing cosmic censorship.

hep-th↗

arXiv2015

High-order Tail in Schwarzschild Space-time

We present an analysis of the behaviour at late-times of linear field perturbations of a Schwarzschild black hole space-time. In particular, we give explicit analytic expressions for the field perturbations (for a specific multipole) of general spin up to the first four orders at late times. These expressions are valid at arbitrary radius and include, apart from the well-known power-law tail decay at leading order ($\sim t^{-2\ell-3}$), a new logarithmic behaviour at third leading order ($\sim t^{-2\ell-5}\ln t$). We obtain these late-time results by developing the so-called MST formalism and by expanding the various MST Fourier-mode quantities for small frequency. While we give explicit expansions up to the first four leading orders (for small-frequency for the Fourier modes, for late-time for the field perturbation), we give a prescription for obtaining expressions to arbitrary order within a `perturbative regime'.

gr-qc↗

arXiv2015

Geometric properties of a 2-D space-time arising in 4-D black hole physics

The Schwarzschild exterior space-time is conformally related to a direct product space-time, $\mathcal{M}_2 \times S_2$, where $\mathcal{M}_2$ is a two-dimensional space-time. This direct product structure arises naturally when considering the wave equation on the Schwarzschild background. Motivated by this, we establish some geometrical results relating to $\mathcal{M}_2$ that are useful for black hole physics. We prove that $\mathcal{M}_2$ has the rare property of being a causal domain. Consequently, Synge's world function and the Hadamard form for the Green function on this space-time are well-defined globally. We calculate the world function and the van Vleck determinant on $\mathcal{M}_2$ numerically and point out how these results will be used to establish global properties of Green functions on the Schwarzschild black hole space-time.

gr-qc↗

arXiv2014

Wavefront twisting by rotating black holes: orbital angular momentum generation and phase coherent detection

In this paper we study wave propagation and scattering near a rotating black hole. In particular, we assume a coherent emission source near the black hole and investigate the wavefront distortion as seen by a distant observer. Near the observer, the propagating wave can be decomposed using the Laguerre-Gaussian mode basis and its wavefront distortion can be characterized by the decomposition coefficient. We find that this decomposition spectrum is symmetric for wave sources located near a Schwarzschild black hole, but is generically asymmetric if the host black hole is rotating. The spectrum asymmetry, or the net orbital angular momentum carried by the wave, is intimately related to the black hole spin and mass, the wave frequency and the locations of the source and the observer. We present semi-analytical expressions and numerical results for these parameter-dependences. If the radiation is temporally coherent, our results show that the secondary images of the source can be almost as bright as its primary image. In the case of temporally-incoherent radiation, we show that the non-fundamental spectrum components could be resolved by spatially-separated telescopes, although that would be degenerate with the telescope direction. Finally, our results suggest that the black-hole-induced spectrum asymmetry is generally too weak to be observed in radio astronomy, even if the observer were located near a caustic point.

gr-qc↗

arXiv2014

Self-force via Green functions and worldline integration

A compact object moving in curved spacetime interacts with its own gravitational field. This leads to both dissipative and conservative corrections to the motion, which can be interpreted as a self-force acting on the object. The original formalism describing this self-force relied heavily on the Green function of the linear differential operator that governs gravitational perturbations. However, because the global calculation of Green functions in non-trivial black hole spacetimes has been an open problem until recently, alternative methods were established to calculate self-force effects using sophisticated regularization techniques that avoid the computation of the global Green function. We present a method for calculating the self-force that employs the global Green function and is therefore closely modeled after the original self-force expressions. Our quantitative method involves two stages: (i) numerical approximation of the retarded Green function in the background spacetime; (ii) evaluation of convolution integrals along the worldline of the object. This novel approach can be used along arbitrary worldlines, including those currently inaccessible to more established computational techniques. Furthermore, it yields geometrical insight into the contributions to self-interaction from curved geometry (back-scattering) and trapping of null geodesics. We demonstrate the method on the motion of a scalar charge in Schwarzschild spacetime. This toy model retains the physical history-dependence of the self-force but avoids gauge issues and allows us to focus on basic principles. We compute the self-field and self-force for many worldlines including accelerated circular orbits, eccentric orbits at the separatrix, and radial infall. This method, closely modeled after the original formalism, provides a promising complementary approach to the self-force problem.

gr-qc↗

arXiv2013

Self-Force and Green Function in Schwarzschild spacetime via Quasinormal Modes and Branch Cut

The motion of a small compact object in a curved background spacetime deviates from a geodesic due to the action of its own field, giving rise to a self-force. This self-force may be calculated by integrating the Green function for the wave equation over the past worldline of the small object. We compute the self-force in this way for the case of a scalar charge in Schwarzschild spacetime, making use of the semi-analytic method of matched Green function expansions. Inside a local neighbourhood of the compact object, this method uses the Hadamard form for the Green function in order to render regularization trivial. Outside this local neighbourhood, we calculate the Green function using a spectral decomposition into poles (quasinormal modes) and a branch cut integral in the complex-frequency plane. We show that both expansions overlap in a sufficiently large matching region for an accurate calculation of the self-force to be possible. The scalar case studied here is a useful and illustrative toy-model for the gravitational case, which serves to model astrophysical binary systems in the extreme mass-ratio limit.

gr-qc↗

arXiv2013

Kermions: quantization of fermions on Kerr space-time

We study a quantum fermion field on a background non-extremal Kerr black hole. We discuss the definition of the standard black hole quantum states (Boulware, Unruh and Hartle-Hawking), focussing particularly on the differences between fermionic and bosonic quantum field theory. Since all fermion modes (both particle and anti-particle) have positive norm, there is much greater flexibility in how quantum states are defined compared with the bosonic case. In particular, we are able to define a candidate `Boulware'-like state, empty at both past and future null infinity; and a candidate `Hartle-Hawking'-like equilibrium state, representing a thermal bath of fermions surrounding the black hole. Neither of these states have analogues for bosons on a non-extremal Kerr black hole and both have physically attractive regularity properties. We also define a number of other quantum states, numerically compute differences in expectation values of the fermion current and stress-energy tensor between two states, and discuss their physical properties.

gr-qc↗

arXiv2012

Analytic Investigation of the Branch Cut of the Green Function in Schwarzschild Space-time

The retarded Green function for linear field perturbations in Schwarzschild black hole space-time possesses a branch cut in the complex-frequency plane. This branch cut has remained largely unexplored: only asymptotic analyses either for small-frequency (yielding the known tail decay at late times of an initial perturbation of the black hole) or for large-frequency (quasinormal modes close to the branch cut in this regime have been linked to quantum properties of black holes) have been carried out in the literature. The regime along the cut inaccessible to these asymptotic analyses has so far remained essentially unreachable. We present a new method for the analytic calculation of the branch cut directly on the cut for general-spin fields in Schwarzschild space-time. This method is valid for any values of the frequency on the cut and so it provides analytic access to the whole branch cut for the first time. We calculate the modes along the cut and investigate their properties and connection with quasinormal modes. We also investigate the contribution from these branch cut modes to the self-force acting on a point particle on a Schwarzschild background space-time.

gr-qc↗

arXiv2012

Spectroscopy of the Schwarzschild Black Hole at Arbitrary Frequencies

Linear field perturbations of a black hole are described by the Green function of the wave equation that they obey. After Fourier decomposing the Green function, its two natural contributions are given by poles (quasinormal modes) and a largely unexplored branch cut in the complex-frequency plane. We present new analytic methods for calculating the branch cut on a Schwarzschild black hole for arbitrary values of the frequency. The branch cut yields a power-law tail decay for late times in the response of a black hole to an initial perturbation. We determine explicitly the first three orders in the power-law and show that the branch cut also yields a new logarithmic behaviour $T^{-2\ell-5}\ln(T)$ for late times. Before the tail sets in, the quasinormal modes dominate the black hole response. For electromagnetic perturbations, the quasinormal mode frequencies approach the branch cut at large overtone index $n$. We determine these frequencies up to $n^{-5/2}$ and, formally, to arbitrary order. Highly-damped quasinormal modes are of particular interest in that they have been linked to quantum properties of black holes.

gr-qc↗

arXiv2012

Regularization of static self-forces

Various regularization methods have been used to compute the self-force acting on a static particle in a static, curved spacetime. Many of these are based on Hadamard's two-point function in three dimensions. On the other hand, the regularization method that enjoys the best justification is that of Detweiler and Whiting, which is based on a four-dimensional Green's function. We establish the connection between these methods and find that they are all equivalent, in the sense that they all lead to the same static self-force. For general static spacetimes, we compute local expansions of the Green's functions on which the various regularization methods are based. We find that these agree up to a certain high order, and conjecture that they might be equal to all orders. We show that this equivalence is exact in the case of ultrastatic spacetimes. Finally, our computations are exploited to provide regularization parameters for a static particle in a general static and spherically-symmetric spacetime.

gr-qc↗

arXiv2012

A Kirchhoff integral approach to the calculation of Green's functions beyond the normal neighbourhood

We propose a new method for investigating the global properties of the retarded Green's function $G_R(x',x)$ for fields propagating on an arbitrary globally hyperbolic spacetime. Our method combines the Hadamard form for $G_R$ (this form is only valid within a normal neighbourhood of $x$) together with Kirchhoff's integral representation for the field in order to calculate $G_R$ outside the maximal normal neighbourhood of $x$. As an example, we apply this method to the case of a scalar field on a black hole toy-model spacetime, the Pleba{ń}ski-Hacyan spacetime, $\mathbb{M}_2\times\mathbb{S}^2$. The method allows us to determine in an exact manner that the singularity structure of the `direct' term in the Hadamard form for $G_R(x',x)$ changes from a form $δ(σ)$ to `$1/πσ$' after the null geodesic joining $x$ and $x'$ has crossed a caustic point, where $σ$ is the world function. Furthermore, there is a change of form from a $θ(-σ)$ to a `$-\ln|σ|/π$' in the `tail' term, which has not been explicitly noted before in the literature. We complement the results from the Kirchhoff integral method with an analysis for large-$\ell$ of the Green function modes. This analysis allows us to determine the singularity structure after null geodesics have crossed an arbitrary number of caustics, although it raises a causality issue which the Kirchhoff integral method resolves. Because of the similarity in the caustic structure of the spacetimes, we expect our main results for wave propagation to also be valid on Schwarzschild spacetime.

gr-qc↗

arXiv2012

The Branch Cut and Quasi-normal Modes at Large Imaginary Frequency in Schwarzschild Space-time

The 'retarded' Green function for fields propagating on a Schwarzschild black hole spacetime possesses a branch cut on the complex frequency plane. Classically, the branch cut is important, for example, in order to fully determine the response of the black hole to a linear field perturbation. The branch cut is also useful for the calculation of the self-force on a point particle moving in the Schwarzschild background. In this paper we use techniques of analytic-continuation to the complex plane of the radial coordinate in order to calculate the branch cut contribution to the Green function in the limit of large imaginary frequency. It is expected that the contribution of this frequency regime to the perturbation response and to the self-force will be mostly for short time intervals. We also determine the highly-damped quasinormal mode frequencies for electromagnetic perturbations in Schwarzschild for the first time (previously only the leading imaginary part was known), which seem to have a 'deep connection' with the branch cut. We find that these frequencies behave like $ω_{\ell,n}= -\dfrac{in}{2}-\dfrac{i[\ell(\ell+1)]^2}{2n}+\dfrac{π^{1/2}(1-i)[\ell(\ell+1)]^3}{2^{3/2}n^{3/2}}+O(n^{-2})$. The highly-damped quasinormal modes are particularly interesting for theories of quantum gravity in that they are believed to probe the small scale structure of the spacetime.

gr-qc↗

arXiv2010

Method of Matched Expansions & the Singularity Structure of the Green Function

We present the first successful application of the method of Matched Expansions for the calculation of the self-force on a point particle in a curved spacetime. We investigate the case of a scalar charge in the Nariai spacetime, which serves as a toy model for a point mass moving in the Schwarzschild black hole background. We discuss the singularity structure of the Green function beyond the normal neighbourhood and the interesting effect of caustics on null wave propagation.

gr-qc↗

arXiv2009

Phenomenology of Production and Decay of Spinning Extra-Dimensional Black Holes at Hadron Colliders

We present results of CHARYBDIS2, a new Monte Carlo simulation of black hole production and decay at hadron colliders in theories with large extra dimensions and TeV-scale gravity. The main new feature of CHARYBDIS2 is a full treatment of the spin-down phase of the decay process using the angular and energy distributions of the associated Hawking radiation. Also included are improved modelling of the loss of angular momentum and energy in the production process as well as a wider range of options for the Planck-scale termination of the decay. The new features allow us to study the effects of black hole spin and the feasibility of its observation in such theories.

hep-ph↗

arXiv2009

Pade Approximants of the Green Function in Spherically Symmetric Spacetimes

We investigate the scalar Green function for spherically symmetric spacetimes expressed as a coordinate series expansion in the separation of the points. We calculate the series expansion of the function $V(x,x')$ appearing in the Hadamard parametrix of the scalar Green function to very high order. This expansion is then used to investigate the convergence properties of the series and to estimate its radius of convergence. Using the method of Pade approximants, we show that the series can be extended beyond its radius of convergence to within a short distance of the normal neighborhood boundary.

gr-qc↗

arXiv2009

Self-Force Calculations with Matched Expansions and Quasinormal Mode Sums

We present the first application of the Poisson-Wiseman-Anderson method of matched expansions, to compute the self-force acting on a point particle moving in a curved spacetime. The method uses two expansions for the Green function, valid in `quasilocal' and `distant past' regimes, which are matched within the normal neighbourhood. We perform our calculation in a static region of the spherically symmetric Nariai spacetime (dS_2 x S^2), on which scalar perturbations are governed by a radial equation with a Pöschl-Teller potential. We combine (i) a very high order quasilocal expansion, and (ii) an expansion in quasinormal modes, to determine the Green function globally. We show it is singular everywhere on the null wavefront (even outside the normal neighbourhood), and apply asymptotic methods to determine its singular structure. We find the Green function undergoes a transition every time the null wavefront passes through a caustic: the singular part follows a repeating four-fold sequence $δ(σ)$, $1/πσ$, $-δ(σ)$, $-1/πσ$ etc., where $σ$ is Synge's world function. The matched expansion method provides new insight into the non-local properties of the self-force; we find the contribution from the segment of the worldline lying outside the normal neighbourhood is significant. We compute the scalar self-force acting on a static particle, and validate against an alternative method. Finally, we discuss wave propagation on black hole spacetimes (where any expansion in quasinormal modes will be augmented by a branch cut integral) and predict that the Green function in Schwarzschild spacetime will inherit the four-fold singular structure found here.

gr-qc↗

arXiv2008

Electromagnetic Quantum Field Theory on Kerr-Newman Black Holes

We study classical and quantum aspects of electromagnetic perturbations on black hole space-times. We develop an elegant formalism introduced by Wald, which sets up the theory of linear perturbations in a Type-D background in a compact and transparent manner. We derive expressions for the electromagnetic potential in terms of the single Newman-Penrose scalar ϕ_0.This enables the formulation of the quantum theory of the electromagnetic field as that of a complex scalar field. We study the separable field equations obeyed by the various Newman-Penrose scalars in the Kerr-Newman background and find, for various limits, the asymptotic behaviour of the radial and angular solutions. We correct and build on a study by Breuer, Ryan and Waller to find a uniformly valid asymptotic behaviour for large frequency of the angular solutions and the eigenvalues. We follow Candelas, Chrzanowski and Howard (CCH) in their canonical quantization of the electromagnetic potential and field. We perform an asymptotic analysis of the form of the renormalized stress-energy tensor (RSET) in the past Boulware state close to the horizon. Unlike results in CCH, its leading order behaviour close to the horizon corresponds to minus the stress tensor of a thermal distribution at the Hawking temperature rigidly rotating with the horizon. We prove that expressions in CCH for the expectation value of the stress tensor in the past Boulware, past Unruh and |CCH> states lead to a lack of symmetry of the RSET under parity, even though this is a symmetry of the physical system. We derive the correct symmetric expressions and present a detailed analysis of the resulting RSETs.

gr-qc↗