arXiv subjects
Publications and source records attributed to Lior M. Burko.
We compute the force acting on a free, static electric charge outside a uniform dielectric sphere. We view this force as a self-interaction force, and compute it by applying the Lorentz force directly to the charge's electric field at its location. We regularize the divergent bare force using two different methods: A direct application of the Quinn-Wald Comparison Axiom, and Mode-Sum Regularization.
We study the phenomenon of mass loss by a scalar charge -- a point particle which acts as a source for a (non-interacting) scalar field -- in (1+1)-dimensional and (2+1)-dimensional flat spacetime. We find that such particles are unstable against self interaction: they lose their mass through the emission of monopole radiation. This is in sharp contrast with scalar charges in (3+1)-dimensional flat spacetime, where no such phenomenon occurs.
We study the self force acting on a particle endowed with scalar charge, which is held static (with respect to an undragged, static observer at infinity) outside a stationary, axially-symmetric black hole. We find that the acceleration due to the self force is in the same direction as the black hole's spin, and diverges when the particle approaches the outer boundary of the black hole's ergosphere. This acceleration diverges more rapidly approaching the ergosphere's boundary than the particle's acceleration in the absence of the self force. At the leading order this self force is a (post)$^2$-Newtonian effect. For scalar charges with high charge-to-mass ratio, the acceleration due to the self force starts dominating over the regular acceleration already far from the black hole. The self force is proportional to the rate at which the black hole's rotational energy is dissipated. This self force is local (i.e., only the Abraham-Lorentz-Dirac force and the local coupling to Ricci curvature contribute to it). The non-local, tail part of the self force is zero.
We study the spacetime singularity in 2+1 dimensional AdS-scalar black hole with circular symmetry using a quasi-homogeneous model. We show that this is a spacelike, scalar curvature, deformationally strong singularity.
We study the self force acting on static electric or scalar charges inside or outside a spherical, massive, thin shell. The regularization of the self force is done using the recently-proposed Mode Sum Regularization Prescription. In all cases the self force acting on the charge is repulsive. We find that in the scalar case the force is quadratic in the mass of the shell, and is a second post-Newtonian effect. For the electric case the force is linear in the shell's mass, and is a first post-Newtonian effect. When the charge is outside the shell our results correct the known zero self force in the scalar case or the known repulsive, inverse-cubic force law in the electric case, for the finite size of the shell. When the charge is near the center of the shell the charge undergoes harmonic oscillations.
We calculate the self force acting on a scalar particle which is falling radially into a Schwarzschild black hole. We treat the particle's self-field as a linear perturbation over the fixed Schwarzschild background. The force is calculated by numerically solving the appropriate wave equation for each mode of the field in the time domain, calculating its contribution to the self force, and summing over all modes using Ori's mode-sum regularization prescription. The radial component of the force is attractive at large distances, and becomes repulsive as the particle approaches the event horizon.
We study the self force acting on a scalar charge in uniform circular motion around a Schwarzschild black hole. The analysis is based on a direct calculation of the self force via mode decomposition, and on a regularization procedure based on Ori's mode-sum regularization prescription. We find the four self-force at arbitrary radii and angular velocities (both geodesic and non-geodesic), in particular near the black hole, where general-relativistic effects are strongest, and for fast motion. We find the radial component of the self force to be repulsive or attractive, depending on the orbit.
We overview the recently proposed mode-sum regularization prescription (MSRP) for the calculation of the local radiation-reaction forces, which are crucial for the orbital evolution of binaries. We then describe some new results which were obtained using MSRP, and discuss their importance for gravitational-wave astronomy.
We study the self forces acting on static scalar and electric test charges in the spacetime of a Schwarzschild black hole. The analysis is based on a direct, local calculation of the self forces via mode decomposition, and on two independent regularization procedures: A spatially-extended particle model method, and on a mode-sum regularization prescription. In all cases we find excellent agreement with the known exact results.
We analyze radiation reaction for synchrotron radiation by computing, via a multipole expansion, the near field evaluated on the world-line of the charge. We find that the temporal component of the self four-force agrees with the radiated power, which one calculates in the radiation zone. This is the case for each mode in the multipole decomposition. We also find agreement with the Abraham-Lorentz-Dirac equation.
We study analytically the Cauchy horizon singularity inside spherically-symmetric charged black holes, coupled to a spherical self-gravitating, minimally-coupled, massless scalar field. We show that all causal geodesics terminate at the Cauchy horizon at a null singularity, which is weak according to the Tipler classification. The singularity is also deformationally-weak in the sense of Ori. Our results are valid at arbitrary points along the null singularity, in particular at late retarded times, when non-linear effects are crucial.
We discuss a piecewise-conserved constant of motion for a simple dissipative oscillatory mechanical system. The system is a harmonic oscillator with sliding (dry) friction. The piecewise-conserved constant of motion corresponds to the time average of the energy of the system during one half-period of the motion, and changes abruptly at the turning points of the motion. At late times the piecewise-conserved constant of motion degenerates to a constant of motion in the usual sense.
We study the linear metric perturbations of the Reissner-Nordström solution for the case of axial perturbation modes. We find that the well-known perturbative analysis fails for the case of dipole $(l=1)$ perturbations, although valid for higher multipoles. We define new radial functions, with which the perturbation formalism is generalized to all multipole orders, including the dipole. We then complete the solution by constructing the perturbed metric and Maxwell tensors.
We study analytically the spacelike singularity inside a spherically-symmetric, charged black hole coupled to a self-gravitating spherical massless scalar field. We assume spatial homogeneity, and find a generic solution in terms of a formal series expansion. This solution is tested against fully-nonlinear and inhomogeneous numerical simulations. We find full compliance between our analytical solution and the pointwise behavior of the singularity in the numerical simulations. This is a strong scalar-curvature monotonic spacelike singularity, which connects to a weak null singularity at asymptotically-late advanced time.
We study the singularity created in the supercritical collapse of a spherical massless scalar field. We first model the geometry and the scalar field to be homogeneous, and find a generic solution (in terms of a formal series expansion) describing a spacelike singularity which is monotonic, scalar polynomial and strong. We confront the predictions of this analytical model with the pointwise behavior of fully-nonlinear and inhomogeneous numerical simulations, and find full compliance. We also study the phenomenology of the spatial structure of the singularity numerically. At asymptotically late advanced time the singularity approaches the Schwarzschild singularity, in addition to discrete points at finite advanced times, where the singularity is Schwarzschild-like. At other points the singularity is different from Schwarzschild due to the nonlinear scalar field.
The electromagnetic radiation that falls into a Reissner-Nordström black hole is known to develop a ``blue sheet'', namely, an infinite concentration of energy density at the Cauchy horizon. The interaction of these divergent electromagnetic fields with infalling matter was recently analyzed (L. M. burko and A. Ori, Phys. Rev. Lett. 74, 1064 (1995)). Here, we give a more detailed description of that analysis: We consider classical electromagnetic fields (that were produced during the collapse and then backscattered into the black hole), and investigate the blue-sheet effects of these fields on infalling objects within two simplified models of a classical and a quantum absorber. These effects are found to be finite and even negligible for typical parameters of a supermassive black hole.
We study analytically the features of the Cauchy horizon (CH) singularity inside a spherically-symmetric charged black hole, nonlinearly perturbed by a self-gravitating massless scalar field. We derive exact expressions for the divergence rate of the blue-shift factors, namely the derivatives in the outgoing direction of the scalar field $Φ$ and the area coordinate $r$. Both derivatives are found to grow along the contracting CH exactly like $1/r$. Our results are valid everywhere along the CH singularity, up to the point of full focusing. These exact analytic expressions are verified numerically.
Recent numerical simulations have found that the Cauchy horizon inside spherical charged black holes, when perturbed nonlinearly by a self-gravitating, minimally-coupled, massless, spherically-symmetric scalar field, turns into a null weak singularity which focuses monotonically to $r=0$ at late times, where the singularity becomes spacelike. Our main objective is to study this spacelike singularity. We study analytically the spherically-symmetric Einstein-Maxwell-scalar equations asymptotically near the singularity. We obtain a series-expansion solution for the metric functions and for the scalar field near $r=0$ under the simplifying assumption of homogeneity. Namely, we neglect spatial derivatives and keep only temporal derivatives. We find that there indeed exists a generic spacelike singularity solution for these equations (in the sense that the solution depends on enough free parameters), with similar properties to those found in the numerical simulations. This singularity is strong in the Tipler sense, namely, every extended object would inevitably be crushed to zero volume. In this sense this is a similar singularity to the spacelike singularity inside uncharged spherical black holes. On the other hand, there are some important differences between the two cases. Our model can also be extended to the more general inhomogeneous case. The question of whether the same kind of singularity evolves in more realistic models (of a spinning black hole coupled to gravitational perturbations) is still an open question.