arXiv subjects

Amos Ori

Publications and source records attributed to Amos Ori.

At least 19 recordsLinked to original sources

arXiv2025

Net Charge Accretion in Magnetized Kerr Black Holes

We investigate the charging process of a rotating Kerr black hole of mass $M$ and angular momentum $J$ immersed in a stationary, axisymmetric, asymptotically uniform magnetic field of strength $B_{0}$. In Wald's classic analysis (Wald 1974), which was based on the assumption of vanishing injection energy, the black hole was predicted to acquire a universal "saturation charge" $Q_{\mathrm{w}}=2B_{0}J$. However, the physical mechanism that sets the saturation charge must ultimately be governed by the competition between the absorption rates of positively and negatively charged particles. Motivated by this observation, we revisit the problem in the framework of a simple accretion model, where two dilute, equivalent fluxes of charged particles of opposite signs are injected from infinity along the magnetic field lines. The problem then reduces to that of individual particle motion in the electromagnetic field of the magnetized Kerr black hole. Using a combination of numerical and analytical tools, we determine the domains of absorption and establish both lower and upper bounds on the corresponding absorption cross sections. At $Q=Q_\mathrm{w}$ these bounds reveal a systematic difference between the two charge signs. In particular, for sufficiently strong magnetic fields, the lower bound on the absorption cross section for the "attracted" charge exceeds the upper bound for the "repelled" one. This charge accretion imbalance (which we find to become extreme at the limit of large $B_{0}$) indicates a persistent net charge accretion at $Q=Q_{\mathrm{w}}$, implying that the actual saturation charge must differ from Wald's charge $Q_{\mathrm{w}}$.

gr-qc↗

arXiv2025

Computation of the semiclassical outflux emerging from a collapsing spherical null shell

We consider a minimally coupled, massless quantum scalar field $\hat{\Phi}$ propagating in the background geometry of a four-dimensional black hole formed by the collapse of a spherical thin null shell, with a Minkowski interior and a Schwarzschild exterior. The field is taken in the natural ``in'' vacuum state, namely, the quantum state in which no excitations arrive from past null infinity. Within the semiclassical framework, we analyze the vacuum polarization $\left\langle\hat{\Phi}^{2}\right\rangle _{\text{ren}}$ and the energy outflux density $\left\langle \hat{T}_{uu}\right\rangle _{\text{ren}}$ (where $u$ is the standard null Eddington coordinate) just outside the shell. Using the point-splitting method, we derive closed-form analytical expressions for both these semiclassical quantities. In particular, our result for $\left\langle \hat{T}_{uu}\right\rangle _{\text{ren}}$ reveals that it vanishes like $(1-2M_{0}/r_{0})^{2}$ as the shell collapses toward the event horizon, where $M_{0}$ is the shell's mass and $r_{0}$ is the value of the area coordinate $r$ at the evaluation point. This confirms that, along a late-time outgoing null geodesic (i.e., one that emerges from the shell very close to the event horizon and propagates toward future null infinity), the outflux gradually evolves (from virtually zero) up to its final Hawking-radiation value while the geodesic traverses the strong-field region (rather than the Hawking-radiation outflux being emitted entirely from the collapsing shell, which would lead to significant backreaction effects).

gr-qc↗

arXiv2024

Computation of $\langle \Phi^2\rangle$ and quantum fluxes at the polar interior of a spinning black hole

Renormalization of physical quantities for quantum field theories in curved spacetimes can be achieved via the consistent subtraction of counterterms within a regularization scheme such as a point-splitting method. Pragmatic mode-sum regularization (PMR) is a point-splitting method which is particularly suitable for rotating black hole spacetimes. We extend and tailor the t-splitting variant of PMR specifically for the interior of a Kerr black hole on the axis of rotation, focusing on a minimally-coupled massless scalar field in the physically-motivated Unruh state. The method addresses unique challenges in the black hole interior that do not occur outside. In particular, while the infinite sum over multipolar number l converges in the black hole exterior, it diverges in the interior, necessitating the subtraction of a so-called intermediate divergence which includes introducing an additional "small" split in the direction of the polar angle. This procedure is outlined and justified, along with the standard PMR method's counterterms subtraction. We apply this method to calculate the renormalized energy-momentum fluxes $\langle T_{uu}\rangle^U_\text{ren}$, $\langle T_{vv}\rangle^U_\text{ren}$ (where u and v are the standard Eddington coordinates) and the renormalized field square $\langle \Phi^2\rangle^U_\text{ren}$ throughout the black hole interior, spanning from (just off) the event horizon to (just off) the inner horizon. Special emphasis is placed on the inner horizon vicinity, where our t-splitting results for the fluxes asymptote to those obtained directly at the inner horizon using a different method in a previous work. In an Appendix, we develop an alternative t-splitting PMR variant which does not include the intermediate divergence subtraction. We utilize it for independent computations that are used to verify the standard t-splitting variant presented in the main text.

gr-qc↗

arXiv2022

Quantum fluxes at the inner horizon of a spinning black hole

Rotating or charged classical black holes in isolation possess a special surface in their interior, the Cauchy horizon, beyond which the evolution of spacetime (based on the equations of General Relativity) ceases to be deterministic. In this work, we study the effect of a quantum massless scalar field on the Cauchy horizon inside a rotating (Kerr) black hole that is evaporating via the emission of Hawking radiation (corresponding to the field being in the Unruh state). We calculate the flux components (in Eddington coordinates) of the renormalized stress-energy tensor of the field on the Cauchy horizon, as functions of the black hole spin and of the polar angle. We find that these flux components are generically non-vanishing. Furthermore, we find that the flux components change sign as these parameters vary. The signs of the fluxes are important, as they provide an indication of whether the Cauchy horizon expands or crushes (when backreaction is taken into account). Regardless of these signs, our results imply that the flux components generically diverge on the Cauchy horizon when expressed in coordinates which are regular there. This is the first time that irregularity of the Cauchy horizon under a semiclassical effect is conclusively shown for (four-dimensional) spinning black holes.

gr-qc↗

arXiv2022

Quantum fluxes at the inner horizon of a near-extremal spherical charged black hole

We analyze and compute the semiclassical stress-energy flux components, the outflux $\langle T_{uu}\rangle$ and the influx $\langle T_{vv}\rangle$ ($u$ and $v$ being the standard null Eddington coordinates), at the inner horizon (IH) of a Reissner-Nordström black hole (BH) of mass $M$ and charge $Q$, in the near-extremal domain in which $Q/M$ approaches $1$. We consider a minimally-coupled massless quantum scalar field, in both Hartle-Hawking ($H$) and Unruh ($U$) states, the latter corresponding to an evaporating BH. The near-extremal domain lends itself to an analytical treatment which sheds light on the behavior of various quantities on approaching extremality. We explore the behavior of the three near-IH flux quantities $\langle T_{uu}^-\rangle^U$, $\langle T_{vv}^-\rangle^U$, and $\langle T_{uu}^-\rangle^H=\langle T_{vv}^-\rangle^H$, as a function of the small parameter $Δ\equiv\sqrt{1-(Q/M)^2}$ (where the superscript "$-$" refers to the IH value). We find that in the near-extremal domain $\langle T_{uu}^-\rangle^U\cong\langle T_{uu}^-\rangle^H=\langle T_{vv}^-\rangle^H$ behaves as $\proptoΔ^5$. In contrast, $\langle T_{vv}^-\rangle^U$ behaves as $\proptoΔ^4$, and we calculate the prefactor analytically. It therefore follows that the semiclassical fluxes at the IH neighborhood of an evaporating near-extremal spherical charged BH are dominated by the influx $\langle T_{vv}\rangle^U$. In passing, we also find an analytical expression for the transmission coefficient outside a Reissner-Nordström BH to leading order in small frequencies (which turns out to be a crucial ingredient of our near-extremal analysis). Furthermore, we explicitly obtain the near-extremal Hawking-evaporation rate ($\proptoΔ^4$), with an analytical expression for the prefactor (obtained here for the first time to the best of our knowledge). [Abridged]

gr-qc↗

arXiv2022

Two-point function of a quantum scalar field in the interior region of a Kerr black hole

Quantum field effects on a classical background spacetime may be obtained from the semiclassical equations of General Relativity with the expectation value of the stress-energy tensor of the quantum field as a source. This expectation value can be calculated from Hadamard's elementary two-point function, which in practice is given in terms of sums of products of field modes evaluated at two spacetime points. We derive expressions for the two-point function for a massless scalar field in the Unruh state on a Kerr black hole spacetime. Our main result in this paper is a novel expression valid when the two points lie inside the black hole; we also (re-)derive, using a new method, the known expression valid when the two points lie outside the black hole. We achieve these expressions by finding relationships between Unruh modes, defined in terms of the retarded Kruskal coordinate, and Eddington modes, defined in terms of the Eddington coordinates. While our starting expression for the two-point function is written in terms of the Unruh modes, we give our final expression in terms of the Eddington modes, which have the computational advantage that they decompose into factors that obey ordinary differential equations. In an appendix we also derive expressions for the bare mode contributions to the flux components of the stress-energy tensor for a minimally-coupled massless scalar field inside the black hole. Our results thus lay the groundwork for future calculations of quantum effects inside a Kerr black hole.

gr-qc↗

arXiv2021

Analysis of quantum effects inside spherical charged black holes

We numerically compute the renormalized expectation value $\langle\hatΦ^{2}\rangle_{ren}$ of a minimally-coupled massless quantum scalar field in the interior of a four-dimensional Reissner-Nordstrom black hole, in both the Hartle-Hawking and Unruh states. To this end we use a recently developed mode-sum renormalization scheme based on covariant point splitting. In both quantum states, $\langle\hatΦ^{2}\rangle_{ren}$ is found to approach a \emph{finite} value at the inner horizon (IH). The final approach to the IH asymptotic value is marked by an inverse-power tail $r_{*}^{-n}$, where $r_{*}$ is the Regge-Wheeler "tortoise coordinate", and with $n=2$ for the Hartle-Hawking state and $n=3$ for the Unruh state. We also report here the results of an analytical computation of these inverse-power tails of $\langle\hatΦ^{2}\rangle_{ren}$ near the IH. Our numerical results show very good agreement with this analytical derivation (for both the power index and the tail amplitude), in both quantum states. Finally, from this asymptotic behavior of $\langle\hatΦ^{2}\rangle_{ren}$ we analytically compute the leading-order asymptotic behavior of the trace $\langle\hat{T}_μ^μ\rangle_{ren}$ of the renormalized stress-energy tensor at the IH. In both quantum states this quantity is found to diverge like $b(r-r_{-})^{-1}r_{*}^{-n-2}$ (with $n$ specified above, and with a known parameter $b$). To the best of our knowledge, this is the first fully-quantitative derivation of the asymptotic behavior of these renormalized quantities at the inner horizon of a four-dimensional Reissner-Nordstrom black hole.

gr-qc↗

arXiv2020

Quantum fluxes at the inner horizon of a spherical charged black hole

In an ongoing effort to explore quantum effects on the interior geometry of black holes, we explicitly compute the semiclassical flux components $\left\langle T_{uu}\right\rangle _{ren}$ and $\left\langle T_{vv}\right\rangle _{ren}$ ($u$ and $v$ being the standard Eddington coordinates) of the renormalized stress-energy tensor for a minimally-coupled massless quantum scalar field, in the vicinity of the inner horizon (IH) of a Reissner-Nordström black hole. These two flux components seem to dominate the effect of backreaction in the IH vicinity; and furthermore, their regularization procedure reveals remarkable simplicity. We consider the Hartle-Hawking and Unruh quantum states, the latter corresponding to an evaporating black hole. In both quantum states, we compute $\left\langle T_{uu}\right\rangle _{ren}$ and $\left\langle T_{vv}\right\rangle _{ren}$ in the IH vicinity for a wide range of $Q/M$ values. We find that both $\left\langle T_{uu}\right\rangle _{ren}$ and $\left\langle T_{vv}\right\rangle _{ren}$ attain finite asymptotic values at the IH. Depending on $Q/M$, these asymptotic values are found to be either positive or negative (or vanishing in-between). Note that having a nonvanishing $\left\langle T_{vv}\right\rangle _{ren}$ at the IH implies the formation of a curvature singularity on its ingoing section, the Cauchy horizon. Motivated by these findings, we also take initial steps in the exploration of the backreaction effect of these semiclassical fluxes on the near-IH geometry.

gr-qc↗

arXiv2019

Curing the Self-Force Runaway Problem in Finite-Difference Integration

The electromagnetic self-force equation of motion is known to be afflicted by the so-called runaway problem. A similar problem arises in the semiclassical Einstein's field equation and plagues the self-consistent semiclassical evolution of spacetime. Motivated to overcome the latter challenge, we first address the former (which is conceptually simpler), and present a pragmatic finite-difference method designed to numerically integrate the self-force equation of motion while curing the runaway problem. We restrict our attention here to a charged point-like mass in a one-dimensional motion, under a prescribed time-dependent external force $F_{ext}(t)$. We demonstrate the implementation of our method using two different examples of external force: a Gaussian and a Sin^4 function. In each of these examples we compare our numerical results with those obtained by two other methods (a Dirac-type solution and a reduction-of-order solution). Both external-force examples demonstrate a complete suppression of the undesired runaway mode, along with an accurate account of the radiation-reaction effect at the physically relevant time scale, thereby illustrating the effectiveness of our method in curing the self-force runaway problem.

gr-qc↗

arXiv2018

Mode-sum renormalization of $\langleΦ^{2}\rangle$ for a quantum scalar field inside a Schwarzschild black hole

The full computation of the renormalized expectation values $\langleΦ^{2}\rangle_{ren}$ and $\langle\hat{T}_{μν}\rangle_{ren}$ in 4D black hole interiors has been a long standing challenge, which has impeded the investigation of quantum effects on the internal structure of black holes for decades. Employing a recently developed mode sum renormalization scheme to numerically implement the point-splitting method, we report here the first computation of $\langleΦ^{2}\rangle_{ren}$ in Unruh state in the region inside the event horizon of a 4D Schwarzschild black hole. We further present its Hartle-Hawking counterpart, which we calculated using the same method, and obtain a fairly good agreement with previous results attained using an entirely different method by Candelas and Jensen in 1986. Our results further agree upon approaching the event horizon when compared with previous results calculated outside the black hole. Finally, the results we obtained for Hartle-Hawking state at the event horizon agree with previous analytical results published by Candelas in 1980. This work sets the stage for further explorations of $\langleΦ^{2}\rangle_{ren}$ and $\langle\hat{T}_{μν}\rangle_{ren}$ in 4D black hole interiors.

gr-qc↗

arXiv2018

Two-point function of a quantum scalar field in the interior region of a Reissner-Nordstrom black hole

We derive explicit expressions for the two-point function of a massless scalar field in the interior region of a Reissner-Nordstrom black hole, in both the Unruh and Hartle-Hawking quantum states. The two-point function is expressed in terms of the standard $lmω$ modes of the scalar field (those associated with a spherical harmonic $Y_{lm}$ and a temporal mode $e^{-iωt}$), which can be conveniently obtained by solving an ordinary differential equation, the radial equation. These explicit expressions are the internal analogs of the well known results in the external region (originally derived by Christensen and Fulling), in which the two-point function outside the black hole is written in terms of the external $lmω$ modes of the field. They allow the computation of $<Φ^{2}>_{ren}$ and the renormalized stress-energy tensor inside the black hole, after the radial equation has been solved (usually numerically). In the second part of the paper, we provide an explicit expression for the trace of the renormalized stress-energy tensor of a minimally-coupled massless scalar field (which is non-conformal), relating it to the d'Alembertian of $<Φ^{2}>_{ren}$. This expression proves itself useful in various calculations of the renormalized stress-energy tensor.

gr-qc↗

arXiv2016

Completion of metric reconstruction for a particle orbiting a Kerr black hole

Vacuum perturbations of the Kerr metric can be reconstructed from the corresponding perturbation in either of the two Weyl scalars $ψ_0$ or $ψ_4$, using a procedure described by Chrzanowski and others in the 1970s. More recent work, motivated within the context of self-force physics, extends the procedure to metric perturbations sourced by a particle in a bound geodesic orbit. However, the existing procedure leaves undetermined a certain stationary, axially-symmetric piece of the metric perturbation. In the vacuum region away from the particle, this "completion" piece corresponds simply to mass and angular-momentum perturbations of the Kerr background, with amplitudes that are, however, a priori unknown. Here we present and implement a rigorous method for finding the completion piece. The key idea is to impose continuity, off the particle, of certain gauge-invariant fields constructed from the full (completed) perturbation, in order to determine the unknown amplitude parameters of the completion piece. We implement this method in full for bound (eccentric) geodesic orbits in the equatorial plane of the Kerr black hole. Our results provide a rigorous underpinning of recent results by Friedman {\it et al.}\ for circular orbits, and extend them to non-circular orbits.

gr-qc↗

arXiv2016

Versatile method for renormalized stress-energy computation in black-hole spacetimes

We report here on a new method for calculating the renormalized stress-energy tensor (RSET) in black-hole (BH) spacetimes, which should also be applicable to dynamical BHs and to spinning BHs. This new method only requires the spacetime to admit a single symmetry. So far we developed three variants of the method, aimed for stationary, spherically symmetric, or axially symmetric BHs. We used this method to calculate the RSET of a minimally-coupled massless scalar field in Schwarzschild and Reissner-Nordstrom backgrounds, for several quantum states. We present here the results for the RSET in the Schwarzschild case in Unruh state (the state describing BH evaporation). The RSET is type I at weak field, and becomes type IV at $r\lesssim2.78M$. Then we use the RSET results to explore violation of the weak and null Energy conditions. We find that both conditions are violated all the way from $r\simeq4.9M$ to the horizon. We also find that the averaged weak energy condition is violated by a class of (unstable) circular timelike geodesics. Most remarkably, the circular null geodesic at $r=3M$ violates the averaged null energy condition.

gr-qc↗

arXiv2016

Renormalized stress-energy tensor of an evaporating spinning black hole

We employ a recently developed mode-sum regularization method to compute the renormalized stress-energy tensor of a quantum field in the Kerr background metric (describing a stationary spinning black hole). More specifically, we consider a minimally-coupled massless scalar field in the Unruh vacuum state, the quantum state corresponding to an evaporating black hole. The computation is done here for the case $a=0.7M$, using two different variants of the method: $t$-splitting and $φ$-splitting, yielding good agreement between the two (in the domain where both are applicable). We briefly discuss possible implications of the results for computing semiclassical corrections to certain quantities, and also for simulating dynamical evaporation of a spinning black hole.

gr-qc↗

arXiv2016

Numerical study of the gravitational shock wave inside a spherical charged black hole

We numerically investigate the interior of a four-dimensional, asymptotically flat, spherically symmetric charged black hole perturbed by a scalar field $Φ$. Previous study by Marolf and Ori indicated that late infalling observers will encounter an effective shock wave as they approach the left portion of the inner horizon. This shock manifests itself as a sudden change in the values of various fields, within a tremendously short interval of proper time $τ$ of the infalling observers. We confirm this prediction numerically for both test and self-gravitating scalar field perturbations. In both cases we demonstrate the effective shock in the scalar field by exploring $Φ(τ)$ along a family of infalling timelike geodesics. In the self-gravitating case we also demonstrate the shock in the area coordinate $r$ by exploring $r(τ)$. We confirm the theoretical prediction concerning the shock sharpening rate, which is exponential in the time of infall into the black hole. In addition we numerically probe the early stages of shock formation. We also employ a family of null (rather than timelike) ingoing geodesics to probe the shock in $r$. We use a finite-difference numerical code with double-null coordinates combined with a recently developed adaptive gauge method in order to solve the (Einstein + scalar) field equations and to evolve the spacetime (and scalar field) $ - $ from the region outside the black hole down to the vicinity of the Cauchy horizon and the spacelike $r=0$ singularity.

gr-qc↗

arXiv2016

Mode-sum regularization of $\left\langle ϕ^{2} \right\rangle$ in the angular-splitting method

The computation of the renormalized stress-energy tensor or $\left\langleϕ^{2}\right\rangle_{ren}$ in curved spacetime is a challenging task, at both the conceptual and technical levels. Recently we developed a new approach to compute such renormalized quantities in asymptotically-flat curved spacetimes, based on the point-splitting procedure. Our approach requires the spacetime to admit some symmetry. We already implemented this approach to compute $\left\langle ϕ^{2}\right\rangle _{ren}$ in a stationary spacetime using t-splitting, namely splitting in the time-translation direction. Here we present the angular-splitting version of this approach, aimed for computing renormalized quantities in a general (possibly dynamical) spherically-symmetric spacetime. To illustrate how the angular-splitting method works, we use it here to compute $\left\langle ϕ^{2}\right\rangle _{ren}$ for a quantum massless scalar field in Schwarzschild background, in various quantum states (Boulware, Unruh, and Hartle-Hawking states). We find excellent agreement with the results obtained from the t-splitting variant, and also with other methods. Our main goal in pursuing this new mode-sum approach was to enable the computation of the renormalized stress-energy tensor in a dynamical spherically symmetric background, e.g. an evaporating black hole. The angular-splitting variant presented here is most suitable to this purpose.

gr-qc↗

arXiv2016

A Generalized Sagnac-Wang-Fizeau formula

We present a special-relativistic analysis of deformable interferometers where counter propagating beams share a common optical path. The optical path is allowed to change rather arbitrarily and need not be stationary. We show that, in the absence of dispersion the phase shift has two contributions. To leading order in $v/c$ one contribution is given by Wang empirical formula for deformable Sagnac interferometers. The second contribution is due to the stretching of the optical path and we give an explicit formula for this stretch term valid to first order in $v/c$. The analysis provides a unifying framework incorporating the Sagnac, Wang and Fizeau effects in a single scheme and gives a rigorous proof of Wang empirical formula.

physics.optics↗

arXiv2016

Firewall or smooth horizon?

Recently, Almheiri, Marolf, Polchinski, and Sully found that for a sufficiently old black hole (BH), the set of assumptions known as the \emph{complementarity postulates} appears to be inconsistent with the assumption of local regularity at the horizon. They concluded that the horizon of an old BH is likely to be the locus of local irregularity, a "firewall". Here I point out that if one adopts a different assumption, namely that semiclassical physics holds throughout its anticipated domain of validity, then no inconsistency seems to arise, and the horizon retains its regularity. In this alternative view-point, the vast portion of the original BH information remains trapped inside the BH throughout the semiclassical domain of evaporation, and possibly leaks out later on. This appears to be an inevitable outcome of semiclassical gravity.

gr-qc↗