More on the SW-QNM correspondence

We exploit the recently proposed correspondence between gravitational perturbations and quantum Seiberg-Witten curves to compute the spectrum of quasi-normal modes of asymptotically flat Kerr Newman black holes and establish detailed gauge/gravity dictionaries for a large class of black holes, D-branes and fuzzballs in diverse dimensions. QNM frequencies obtained from the quantum periods of SU(2) $$ \mathcal{N} $$ N = 2 SYM with Nf = 3 flavours are compared against numerical results, WKB (eikonal) approximation and geodetic motion showing remarkable agreement. Starting from the master example relating quasi-normal modes of Kerr-Newman black holes in AdS4 to SU(2) gauge theory with Nf = 4, we illustrate the procedure for some simple toy-models that allow analytic solutions. We also argue that the AGT version of the gauge/gravity correspondence may give precious hints as to the physical/geometric origin of the quasi-normal modes/Seiberg-Witten connection and further elucidate interesting properties (such as tidal Love numbers and grey-body factors) that can help discriminating black holes from fuzzballs.

Null geodesics and QNMs in the field of regular black holes

In this paper, we analyze the null geodesics of regular black holes (BHs). A detailed analysis of geodesic structure, both null geodesics and timelike geodesics, has been investigated for the said BH. As an application of null geodesics, we calculate the radius of photon sphere and gravitational bending of light. We also study the shadow of the BH spacetime. Moreover, we determine the relation between radius of photon sphere [Formula: see text] and the shadow observed by a distance observer. Furthermore, we discuss the effect of various parameters on the radius of shadow [Formula: see text]. Also, we compute the angle of deflection for the photons as a physical application of null-circular geodesics. We find the relation between null geodesics and quasinormal mode (QNM) frequency in the eikonal approximation by computing the Lyapunov exponent. It is also shown that (in the eikonal limit) the QNMs of BHs are governed by the parameter of null-circular geodesics. The real part of QNMs frequency determines the angular frequency, whereas the imaginary part determines the instability timescale of the circular orbit. Next, we study the massless scalar perturbations and analyze the effective potential graphically. Massive scalar perturbations are also discussed. As an application of timelike geodesics, we compute the innermost stable circular orbit (ISCO) and marginally bound circular orbit (MBCO) of the regular BHs which are closely related to the BH accretion disk theory. In the appendix, we calculate the relation between angular frequency and Lyapunov exponent for null-circular geodesics.

Holographic teleportation in higher dimensions

We study higher-dimensional traversable wormholes in the context of Rindler-AdS/CFT. The hyperbolic slicing of a pure AdS geometry can be thought of as a topological black hole that is dual to a conformal field theory in the hyperbolic space. The maximally extended geometry contains two exterior regions (the Rindler wedges of AdS) which are connected by a wormhole. We show that this wormhole can be made traversable by a double trace deformation that violates the average null energy condition (ANEC) in the bulk. We find an analytic formula for the ANEC violation that generalizes Gao-Jafferis-Wall result to higher-dimensional cases, and we show that the same result can be obtained using the eikonal approximation. We show that the bound on the amount of information that can be transferred through the wormhole quickly reduces as we increase the dimensionality of spacetime. We also compute a two-sided commutator that diagnoses traversability and show that, under certain conditions, the information that is transferred through the wormhole propagates with butterfly speed $$ {\upsilon}_B=\frac{1}{d-1} $$ υ B = 1 d − 1 .

A functional approach to the next-to-eikonal approximation of high energy gravitational scattering

The Fradkin–Schwinger functional methods to represent a Green function in an external gravitational field are used to study the eikonal and the next-to-eikonal limit, including the nonlinear gravitational interactions, of the scattering amplitudes of an ultra-relativistic scalar particle on a static super-massive scalar target in the nearly forward limit. The functional approach confirms the exponentiation of the leading eikonal which also applies to the first non-leading power in the energy of the light particle, moreover includes the interaction at impact parameter much larger than the Schwarzschild radius associated with the center of mass energy in the ultra-relativistic limit.

Quasinormal modes in the field of a dyon-like dilatonic black hole

Quasinormal modes of massless test scalar field in the background of gravitational field for a non-extremal dilatonic dyonic black hole are explored. The dyon-like black hole solution is considered in the gravitational 4d model involving two scalar fields and two 2-forms. It is governed by two 2-dimensional dilatonic coupling vectors $${\lambda }_i$$ λ i obeying $${\lambda }_i ({\lambda }_1 + {\lambda }_2) > 0$$ λ i ( λ 1 + λ 2 ) > 0 , $$i =1,2$$ i = 1 , 2 . The first law of black hole thermodynamics is given and the Smarr relation is verified. Quasinormal modes for a massless scalar (test) field in the eikonal approximation are obtained and analysed. These modes depend upon a dimensionless parameter a ($$0 < a \le 2$$ 0 < a ≤ 2 ) which is a function of $${\lambda }_i$$ λ i . For limiting strong ($$a = +0$$ a = + 0 ) and weak ($$a = 2$$ a = 2 ) coupling cases, they coincide with the well-known results for the Schwarzschild and Reissner–Nordström solutions. It is shown that the Hod conjecture, connecting the damping rate and the Hawking temperature, is satisfied for $$0 < a \le 1$$ 0 < a ≤ 1 and all allowed values of parameters.

Quantum evolution: From particles to non-relativistic fields

Chapter 4 has introduced the functional integral representation of the quantum statistical operators and thus, formally, evolution in imaginary or Euclidean time. By contrast, to calculate the evolution operator and the scattering S-matrix elements, quantities relevant to particle physics, it is necessary to make a continuation from imaginary to real time. However, the representation of the S-matrix follows from additional considerations. To illustrate the power of the formalism, we show how to recover the perturbative expansion of the scattering amplitude, some semi-classical approximations, and the eikonal approximation. When the asymptotic states at large time are eigenstates of the harmonic oscillator, instead of free particles, the holomorphic formalism becomes useful. A simple generalization of the path integral of Chapter 4 leads to the corresponding path integral representation of the S-matrix. In the case of the Bose gas, the evolution operator is then given by a holomorphic field integral. A parallel formalism leads to an analogous representation for the evolution operator of a system of non-relativistic fermions.

Extremal black hole scattering at $$ \mathcal{O} $$(G3): graviton dominance, eikonal exponentiation, and differential equations

We use $$ \mathcal{N} $$ N = 8 supergravity as a toy model for understanding the dynamics of black hole binary systems via the scattering amplitudes approach. We compute the conservative part of the classical scattering angle of two extremal (half-BPS) black holes with minimal charge misalignment at $$ \mathcal{O} $$ O (G3) using the eikonal approximation and effective field theory, finding agreement between both methods. We construct the massive loop integrands by Kaluza-Klein reduction of the known D-dimensional massless integrands. To carry out integration we formulate a novel method for calculating the post-Minkowskian expansion with exact velocity dependence, by solving velocity differential equations for the Feynman integrals subject to modified boundary conditions that isolate conservative contributions from the potential region. Motivated by a recent result for universality in massless scattering, we compare the scattering angle to the result found by Bern et. al. in Einstein gravity and find that they coincide in the high-energy limit, suggesting graviton dominance at this order.

On the impact of non-factorisable corrections in VBF single and double Higgs production

We study the non-factorisable QCD corrections, computed in the eikonal approximation, to Vector-Boson Fusion single and double Higgs production and show the combined factorisable and non-factorisable corrections for both processes at $$ \mathcal{O}\left({\alpha}_s^2\right) $$ O α s 2 . We investigate the validity of the eikonal approximation with and without selection cuts, and carry out an in-depth study of the relative size of the non-factorisable next-to-next-to-leading order corrections compared to the factorisable ones. In the case of single Higgs production, after selection cuts are applied, the non-factorisable corrections are found to be mostly contained within the factorisable scale uncertainty bands. When no cuts are applied, instead, the non-factorisable corrections are slightly outside the scale uncertainty band. Interestingly, for double Higgs production, we find that both before and after applying cuts, non-factorisable corrections are enhanced compared to the single Higgs case. We trace this enhancement to the existence of delicate cancellations between the various leading-order Feynman diagrams, which are partly spoiled by radiative corrections. All contributions studied here have been implemented in proVBFH v1.2.0 and proVBFHH v1.1.0.