Showing papers in "Classical and Quantum Gravity in 2020"

Quantum Gravity from Causal Dynamical Triangulations: A Review

Abstract: This topical review gives a comprehensive overview and assessment of recent results in Causal Dynamical Triangulations (CDT), a modern formulation of lattice gravity, whose aim is to obtain a theory of quantum gravity nonperturbatively from a scaling limit of the lattice-regularized theory. In this manifestly diffeomorphism-invariant approach one has direct, computational access to a Planckian spacetime regime, which is explored with the help of invariant quantum observables. During the last few years, there have been numerous new and important developments and insights concerning the theory's phase structure, the roles of time, causality, diffeomorphisms and global topology, the application of renormalization group methods and new observables. We will focus on these new results, primarily in four spacetime dimensions, and discuss some of their geometric and physical implications.

A guide to LIGO–Virgo detector noise and extraction of transient gravitational-wave signals

Abstract: The LIGO Scientific Collaboration and the Virgo Collaboration have cataloged eleven confidently detected gravitational-wave events during the first two observing runs of the advanced detector era. All eleven events were consistent with being from well-modeled mergers between compact stellar-mass objects: black holes or neutron stars. The data around the time of each of these events have been made publicly available through the gravitational-wave open science center. The entirety of the gravitational-wave strain data from the first and second observing runs have also now been made publicly available. There is considerable interest among the broad scientific community in understanding the data and methods used in the analyses. In this paper, we provide an overview of the detector noise properties and the data analysis techniques used to detect gravitational-wave signals and infer the source properties. We describe some of the checks that are performed to validate the analyses and results from the observations of gravitational-wave events. We also address concerns that have been raised about various properties of LIGO–Virgo detector noise and the correctness of our analyses as applied to the resulting data.

Concerns regarding the use of black hole shadows as standard rulers

Abstract: Recently, Tsupko et al. have put forward the very interesting proposal to use the shadows of high-redshift supermassive black holes (SMBHs) as standard rulers. This would in principle allow us to probe the expansion history within a redshift range which would otherwise be challenging to access. In this short note, we critically examine this proposal, and identify a number of important issues which had been previously overlooked. These include difficulties in obtaining reliable SMBH mass estimates and reaching the required angular resolution, and an insufficient knowledge of the accretion dynamics of high-redshift SMBHs. While these issues currently appear to prevent high-redshift SMBH shadows from being used as robust standard rulers, we hope that our flagging them early will help in making this probe theoretically mature by the time it will be experimentally feasible.

Model Comparison from LIGO-Virgo Data on GW170817's Binary Components and Consequences for the Merger Remnant

Abstract: GW170817 is the very first observation of gravitational waves originating from the coalescence of two compact objects in the mass range of neutron stars, accompanied by electromagnetic counterparts, and offers an opportunity to directly probe the internal structure of neutron stars. We perform Bayesian model selection on a wide range of theoretical predictions for the neutron star equation of state. For the binary neutron star hypothesis, we find that we cannot rule out the majority of theoretical models considered. In addition, the gravitational-wave data alone does not rule out the possibility that one or both objects were low-mass black holes. We discuss the possible outcomes in the case of a binary neutron star merger, finding that all scenarios from prompt collapse to long-lived or even stable remnants are possible. For long-lived remnants, we place an upper limit of 1.9 kHz on the rotation rate. If a black hole was formed any time after merger and the coalescing stars were slowly rotating, then the maximum baryonic mass of non-rotating neutron stars is at most 3.05M⊙, and three equations of state considered here can be ruled out. We obtain a tighter limit of 2.67M⊙ for the case that the merger results in a hypermassive neutron star.

Characterization of systematic error in Advanced LIGO calibration

Abstract: The raw outputs of the detectors within the Advanced Laser Interferometer Gravitational-Wave Observatory need to be calibrated in order to produce the estimate of the dimensionless strain used for astrophysical analyses. The two detectors have been upgraded since the second observing run and finished the year-long third observing run. Understanding, accounting, and/or compensating for the complex-valued response of each part of the upgraded detectors improves the overall accuracy of the estimated detector response to gravitational waves. We describe improved understanding and methods used to quantify the response of each detector, with a dedicated effort to define all places where systematic error plays a role. We use the detectors as they stand in the first half (six months) of the third observing run to demonstrate how each identified systematic error impacts the estimated strain and constrain the statistical uncertainty therein. For this time period, we estimate the upper limit on systematic error and associated uncertainty to be $< 7\%$ in magnitude and $< 4$ deg in phase ($68\%$ confidence interval) in the most sensitive frequency band 20-2000 Hz. The systematic error alone is estimated at levels of $< 2\%$ in magnitude and $< 2$ deg in phase.

The missing link in gravitational-wave astronomy: discoveries waiting in the decihertz range

Abstract: The gravitational-wave astronomical revolution began in 2015 with LIGO's observation of the coalescence of two stellar-mass black holes. Over the coming decades, ground-based detectors like LIGO will extend their reach, discovering thousands of stellar-mass binaries. In the 2030s, the space-based LISA will enable gravitational-wave observations of the massive black holes in galactic centres. Between LISA and ground-based observatories lies the unexplored decihertz gravitational-wave frequency band. Here, we propose a Decihertz Observatory to cover this band, and complement observations made by other gravitational-wave observatories. The decihertz band is uniquely suited to observation of intermediate-mass ($\sim 10^2-10^4$ M$_\odot$) black holes, which may form the missing link between stellar-mass and massive black holes, offering a unique opportunity to measure their properties. Decihertz observations will be able to detect stellar-mass binaries days to years before they merge and are observed by ground-based detectors, providing early warning of nearby binary neutron star mergers, and enabling measurements of the eccentricity of binary black holes, providing revealing insights into their formation. Observing decihertz gravitational-waves also opens the possibility of testing fundamental physics in a new laboratory, permitting unique tests of general relativity and the Standard Model of particle physics. Overall, a Decihertz Observatory will answer key questions about how black holes form and evolve across cosmic time, open new avenues for multimessenger astronomy, and advance our understanding of gravitation, particle physics and cosmology.

Deflection angle and shadow behaviors of quintessential black holes in arbitrary dimensions

Abstract: Motivated by M-theory/superstring inspired models, we investigate certain behaviors of the deflection angle and the shadow geometrical shapes of higher dimensional quintessential black holes associated with two values of the dark energy (DE) state parameter, being \omega=-\frac{1}{3} and \omega=-\frac{2}{3}. Concretely, we derive the geodesic equation of photons on such backgrounds. Thanks to the Gauss-Bonnet theorem corresponding to the optical metric, we compute the leading terms of the deflection angle in the so-called weak-limit approximation. After that, we inspect the effect of DE and the space-time dimension d on the calculated optical quantities. Introducing DE via the field intensity c and the state parameter \omega, we find that the shadow size and the deflection angle increase by increasing values of the field intensity c. However, we observe that the high dimensions decrease such quantities for \omega-models exhibiting similar behaviors. Then, we consider the effect of the black hole charge, on these optical quantities, by discussing the associated behaviors. The present investigation recovers certain known results appearing in ordinary four dimensional models.

ELGAR - a European Laboratory for Gravitation and Atom-interferometric Research

Abstract: Gravitational Waves (GWs) were observed for the first time in 2015, one century after Einstein predicted their existence. There is now growing interest to extend the detection bandwidth to low frequency. The scientific potential of multi-frequency GW astronomy is enormous as it would enable to obtain a more complete picture of cosmic events and mechanisms. This is a unique and entirely new opportunity for the future of astronomy, the success of which depends upon the decisions being made on existing and new infrastructures. The prospect of combining observations from the future space-based instrument LISA together with third generation ground based detectors will open the way towards multi-band GW astronomy, but will leave the infrasound (0.1 Hz to 10 Hz) band uncovered. GW detectors based on matter wave interferometry promise to fill such a sensitivity gap. We propose the European Laboratory for Gravitation and Atom-interferometric Research (ELGAR), an underground infrastructure based on the latest progress in atomic physics, to study space-time and gravitation with the primary goal of detecting GWs in the infrasound band. ELGAR will directly inherit from large research facilities now being built in Europe for the study of large scale atom interferometry and will drive new pan-European synergies from top research centers developing quantum sensors. ELGAR will measure GW radiation in the infrasound band with a peak strain sensitivity of 3.3×10-22/sqrt(Hz) at 1.7 Hz. The antenna will have an impact on diverse fundamental and applied research fields beyond GW astronomy, including gravitation, general relativity, and geology.

Energy conditions in general relativity and quantum field theory

Abstract: This review summarizes the current status of the energy conditions in general relativity and quantum field theory. We provide a historical review and a summary of technical results and applications, complemented with a few new derivations and discussions. We pay special attention to the role of the equations of motion and to the relation between classical and quantum theories. Pointwise energy conditions were first introduced as physically reasonable restrictions on matter in the context of general relativity. They aim to express e.g. the positivity of mass or the attractiveness of gravity. Perhaps more importantly, they have been used as assumptions in mathematical relativity to prove singularity theorems and the non-existence of wormholes and similar exotic phenomena. However, the delicate balance between conceptual simplicity, general validity and strong results has faced serious challenges, because all pointwise energy conditions are systematically violated by quantum fields and also by some rather simple classical fields. In response to these challenges, weaker statements were introduced, such as quantum energy inequalities and averaged energy conditions. These have a larger range of validity and may still suffice to prove at least some of the earlier results. One of these conditions, the achronal averaged null energy condition, has recently received increased attention. It is expected to be a universal property of the dynamics of all gravitating physical matter, even in the context of semiclassical or quantum gravity.

Ringing of the regular black-hole/wormhole transition

Abstract: A simple one-parameter generalization of the Schwarzschild spacetime was recently suggested by A Simpson and M Visser [2019 J. Cosmol. Astropart. Phys. JCAP02(2019)042] as a toy model describing the regular black hole and traversable wormhole states separated by the border (one-way wormhole) state. We study quasinormal modes of all the three states and show that the black-hole/wormhole transition is characterized by echoes, while the remnant of the black hole state is kept in the time-domain profile of the wormhole perturbation at the initial stage of the exponential fall off. Calculations of quasinormal modes using the WKB method with Pade expansion and the time-domain integration are in good agreement. An analytical formula governing quasinormal modes in the eikonal regime is given.

The Kiselev black hole is neither perfect fluid, nor is it quintessence

Abstract: The Kiselev black hole spacetime is an extremely popular toy model, with over 200 direct and indirect citations as of 2019. Unfortunately, despite repeated assertions to the contrary, this is not a perfect fluid spacetime. The relative pressure anisotropy and average pressure are easily calculated, and the relative pressure anisotropy is generally non-zero, (except for the special case where Kiselev’s model degenerates to Schwarzschild-(anti)–de Sitter spacetime). Kiselev’s original paper was very careful to point this out in the calculation, but then in the discussion made a somewhat unfortunate choice of terminology which has (with very limited exceptions) been copied into the subsequent literature. Perhaps worse, Kiselev’s use of the word ‘quintessence’ does not match the standard usage in the cosmology community, leading to another level of unfortunate and unnecessary confusion. Very few of the subsequent follow-up papers get these points right, so a brief explicit comment is warranted.

Spherically symmetric loop quantum gravity: analysis of improved dynamics

Abstract: We study the "improved dynamics" for the treatment of spherically symmetric space-times in loop quantum gravity introduced by Chiou {\em et al.} in analogy with the one that has been constructed by Ashtekar, Pawlowski and Singh for the homogeneous space-times. In this dynamics the polymerization parameter is a well motivated function of the dynamical variables, reflecting the fact that the quantum of area depends on them. Contrary to the homogeneous case, its implementation does not trigger undesirable physical properties. We identify semiclassical physical states in the quantum theory and derive the corresponding effective semiclassical metrics. We then discuss some of their properties. Concretely, the space-time approaches sufficiently fast the Schwarzschild geometry at low curvatures. Besides, regions where the singularity is in the classical theory get replaced by a regular but discrete effective geometry with finite and Planck order curvature, regardless of the mass of the black hole. This circumvents trans-Planckian curvatures that appeared for astrophysical black holes in the quantization scheme without the improvement. It makes the resolution of the singularity more in line with the one observed in models that use the isometry of the interior of a Schwarzschild black hole with the Kantowski--Sachs loop quantum cosmologies. One can observe the emergence of effective violations of the null energy condition in the interior of the black hole as part of the mechanism of the elimination of the singularity.

Cosmological viable models in $f(T,B)$ gravity as solutions to the $H_0$ tension

Abstract: In this work we present a further investigation about teleparallel gravity cosmology. We demonstrate that according to the current astrophysical data (CC + Pantheon + BAO samplers with late Universe measurements SH0ES + H0LiCOW), an f(T, B) theory can provide another interpretation to the oscillatory behaviour of the dark energy equation of state when applied to late times. The four f(T, B) cosmological viable models proposed here can undergo an epoch of late-time acceleration and reproduce quintessence and phantom regimes with a transition along the phantom-divided line, making this theory a good approach to modify the standard ΛCDM model.

Amorphous optical coatings of present gravitational-wave interferometers

Abstract: We report on the results of an extensive campaign of optical and mechanical characterization of the ion-beam sputtered oxide layers (Ta$_2$O$_5$, TiO$_2$, Ta$_2$O$_5$-TiO$_2$, SiO$_2$) within the high-reflection coatings of the Advanced LIGO, Advanced Virgo and KAGRA gravitational-wave detectors: refractive index, thickness, optical absorption, composition, density, internal friction and elastic constants have been measured; the impact of deposition rate and post-deposition annealing on coating internal friction has been assessed. For Ta$_2$O$_5$ and SiO$_2$ layers, coating internal friction increases with the deposition rate, whereas the annealing treatment either erases or largely reduces the gap between samples with different deposition history. For Ta$_2$O$_5$-TiO$_2$ layers, the reduction of internal friction due to TiO$_2$ doping becomes effective only if coupled with annealing. All measured samples showed a weak dependence of internal friction on frequency ($\phi_c(f) = af^{b}$, with $-0.208 < b < 0.140$ depending on the coating material considered). SiO$_2$ films showed a mode-dependent loss branching, likely due to spurious losses at the coated edge of the samples. The reference loss values of the Advanced LIGO and Advanced Virgo input (ITM) and end (ETM) mirror HR coatings have been updated by using our estimated value of Young's modulus of Ta$_2$O$_5$-TiO$_2$ layers (120 GPa) and are about 10\% higher than previous estimations.

The first round result from the TianQin-1 satellite

Abstract: The TianQin-1 satellite (TQ-1), which is the first technology demonstration satellite for the TianQin project, was launched on 20 December 2019. The first round of experiment had been carried out from 21 December 2019 until 1 April 2020. The residual acceleration of the satellite is found to be about 1 × 10−10 m/s2/Hz1/2 at 0.1 Hz and about 5 × 10−11 m/s2/Hz1/2 at 0.05 Hz, measured by an inertial sensor with a sensitivity of 5 × 10−12 m/s2/Hz1/2 at 0.1 Hz. The micro-Newton thrusters has demonstrated a thrust resolution of 0.1 μN and a thrust noise of 0.3 μN/Hz1/2 at 0.1 Hz. The residual noise of the satellite with drag-free control is 3 × 10−9 m/s2/Hz1/2 at 0.1 Hz. The noise level of the optical readout system is about 30 pm/Hz1/2 at 0.1 Hz. The temperature stability at temperature monitoring position is controlled to be about ±3 mK per orbit, and the mismatch between the center-of-mass of the satellite and that of the test mass is measured with a precision of better than 0.1 mm.

Spinning and excited black holes in Einstein-scalar-Gauss-Bonnet theory

Abstract: We construct rotating black holes in Einstein-scalar-Gauss-Bonnet theory with a quadratic coupling function. We map the domain of existence of the rotating fundamental solutions, we construct radially excited rotating black holes (including their existence lines), and we show that there are angularly excited rotating black holes. The bifurcation points of the radially and angularly excited solutions branching out of the Schwarzschild solution follow a regular pattern.

Opening the Pandora’s box at the core of black holes

Abstract: We present a geometric classification of all spherically symmetric spacetimes that could result from singularity regularization, using a kinematic construction that is both exhaustive and oblivious to the dynamics of the fields involved. Due to the minimal geometric assumptions underlying it, this classification encompasses virtually all modified gravity theories, and any theory of quantum gravity in which an effective description in terms of an effective metric is available. The first noteworthy conclusion of our analysis is that the number of independent classes of geometries that can be constructed is remarkably limited, with no more than a handful of qualitatively different possibilities. But our most remarkable result is that this catalogue of possibilities clearly demonstrates that the degree of internal consistency and the strength of deviations with respect to general relativity are strongly, and positively, correlated. Hence, either quantum fluctuations of spacetime come to the rescue and solve these internal consistency issues, or singularity regularization will percolate to macroscopic (near-horizon) scales, radically changing our understanding of black holes and opening new opportunities to test quantum gravity.

Constraining teleparallel gravity through Gaussian processes

Abstract: We apply Gaussian processes (GP) in order to impose constraints on teleparallel gravity and its $f(T)$ extensions. We use available $H(z)$ observations from (i) cosmic chronometers data (CC); (ii) Supernova Type Ia (SN) data from the compressed Pantheon release together with the CANDELS and CLASH Multi-Cycle Treasury programs; and (iii) baryonic acoustic oscillation (BAO) datasets from the Sloan Digital Sky Survey. For the involved covariance functions, we consider four widely used choices, namely the square exponential, Cauchy, Matern and rational quadratic kernels, which are consistent with one another within 1$\sigma$ confidence levels. Specifically, we use the GP approach to reconstruct a model-independent determination of the Hubble constant $H_0$, for each of these kernels and dataset combinations. These analyses are complemented with three recently announced literature values of $H_0$, namely (i) Riess $H_0^{\rm R} = 74.22 \pm 1.82 \,{\rm km\, s}^{-1} {\rm Mpc}^{-1}$; (ii) H0LiCOW Collaboration $H_0^{\rm HW} = 73.3^{+1.7}_{-1.8} \,{\rm km\, s}^{-1} {\rm Mpc}^{-1}$; and (iii) Carnegie-Chicago Hubble Program $H_0^{\rm TRGB} = 69.8 \pm 1.9 \,{\rm km\, s}^{-1} {\rm Mpc}^{-1}$. Additionally, we investigate the transition redshift between the decelerating and accelerating cosmological phases through the GP reconstructed deceleration parameter. Furthermore, we reconstruct the model-independent evolution of the dark energy equation of state, and finally reconstruct the allowed $f(T)$ functions. As a result, the $\Lambda$CDM model lies inside the allowed region at 1$\sigma$ in all the examined kernels and datasets, however a negative slope for $f(T)$ versus $T$ is slightly favored.

Superconformal indices at large N and the entropy of AdS5 × SE5 black holes

Abstract: The large $N$ limit of the four-dimensional superconformal index was computed and successfully compared to the entropy of a class of AdS$_5$ black holes only in the particular case of equal angular momenta. Using the Bethe Ansatz formulation, we compute the index at large $N$ with arbitrary chemical potentials for all charges and angular momenta, for general $\\mathcal{N}=1$ four-dimensional conformal theories with a holographic dual. We conjecture and bring some evidence that a particular universal contribution to the sum over Bethe vacua dominates the index at large $N$. For $\\mathcal{N}=4$ SYM, this contribution correctly leads to the entropy of BPS Kerr-Newman black holes in AdS$_5 \\times S^5$ for arbitrary values of the conserved charges, thus completing the microscopic derivation of their microstates. We also consider theories dual to AdS$_5 \\times \\mathrm{SE}_5$, where SE$_5$ is a Sasaki-Einstein manifold. We first check our results against the so-called universal black hole. We then explicitly construct the near-horizon geometry of BPS Kerr-Newman black holes in AdS$_5 \\times T^{1,1}$, charged under the baryonic symmetry of the conifold theory and with equal angular momenta. We compute the entropy of these black holes using the attractor mechanism and find complete agreement with the field theory predictions.

A cryogenic silicon interferometer for gravitational-wave detection

Abstract: The detection of gravitational waves from compact binary mergers by LIGO has opened the era of gravitational wave astronomy, revealing a previously hidden side of the cosmos. To maximize the reach of the existing LIGO observatory facilities, we have designed a new instrument able to detect gravitational waves at distances 5 times further away than possible with Advanced LIGO, or at greater than 100 times the event rate. Observations with this new instrument will make possible dramatic steps toward understanding the physics of the nearby Universe, as well as observing the Universe out to cosmological distances by the detection of binary black hole coalescences. This article presents the instrument design and a quantitative analysis of the anticipated noise floor.

De Sitter Space and Entanglement

Abstract: We argue that the notion of entanglement in de Sitter space arises naturally from the non-trivial Lorentzian geometry of the spacetime manifold, which consists of two disconnected boundaries and a causally disconnected interior. In four bulk dimensions, we propose an holographic description of an inertial observer in terms of a thermofield double state in the tensor product of the two boundaries Hilbert spaces, whereby the Gibbons–Hawking formula arises as the holographic entanglement entropy between the past and future conformal infinities. When considering the bulk entanglement between the two causally disconnected Rindler wedges, we show that the corresponding entanglement entropy is given by one quarter of the area of the pair of codimension two minimal surfaces that define the set of fixed points of the dS orbifold.

Generating black holes in $4D$ Einstein-Gauss-Bonnet gravity

Abstract: In recent times there is a surge of interest in constructing Einstein–Gauss–Bonnet (EGB) gravity, in the limit D → 4, of the D-dimensional EGB gravity. Interestingly, the static spherically symmetric solutions in the various proposed D → 4 regularized EGB gravities coincide, and incidentally some other theories also admit the same solution. We prove a theorem that characterizes a large family of nonstatic or radiating spherically symmetric solutions to the 4D EGB gravity, representing, in general, spherically symmetric type II fluid. An extension of the theorem, given without proof as being similar to the original theorem, generates static spherically symmetric black hole solutions of the theory. It not only enables us to identify available known black hole solutions as particular cases but also to generate several new solutions of the 4D EGB gravity.

Gravitational-wave versus X-ray tests of strong-field gravity

Abstract: Electromagnetic observations of the radiation emitted by an accretion disk around a black hole, as well as gravitational wave observations of coalescing binaries, can be used to probe strong-field gravity. We here compare the constraints that these two types of observations can impose on theory-agnostic, parametric deviations from the Schwarzschild metric. On the gravitational wave side, we begin by computing the leading-order deviation to the Hamiltonian of a binary system in a quasi-circular orbit within the post-Newtonian approximation, given a parametric deformation of the Schwarzschild metrics of each binary component. We then compute the leading-order deviation to the gravitational waves emitted by such a binary in the frequency domain, assuming purely Einsteinian radiation-reaction. We compare this model to the LIGO-Virgo collaboration gravitational wave detections and place constraints on the metric deformation parameters, concluding with an estimate of the constraining power of aLIGO at design sensitivity. On the electromagnetic side, we first simulate observations with current and future X-ray instruments of an X-ray binary with a parametrically-deformed Schwarzschild black hole, and we then estimate constraints on the deformation parameters using these observations. We find that current gravitational wave observations have already placed constraints on the metric deformation parameters than are slightly more stringent than what can be achieved with current X-ray instruments. Moreover, future gravitational wave observations with aLIGO at design sensitivity by 2026 will be even more stringent, becoming stronger that constraints achievable with future ATHENA X-ray observations before it flies in 2034.

Constraining extra-spatial dimensions with observations of GW170817

Abstract: We derive the modifications introduced by extra-spatial dimensions beyond the four dimensional spacetime on the macroscopic properties of neutron stars, which in turn affect the gravitational wave spectrum of their binaries. It turns out that the mass-radius relation of the neutron stars, and their tidal deformability, are affected non-trivially by the presence of extra dimensions, and can be used to constrain parameters associated with those dimensions. Implications for I-Love-Q universality relations are also discussed and utilized to obtain a constraint on one such parameter. Importantly, we show, for the first time, that measurements of the component masses and tidal deformabilities of the binary neutron star system GW170817, constrain the brane tension in the single brane-world model of Randall and Sundrum to be greater than $35.1~\textrm{GeV}^{4}$. This work opens up the possibility of making such a constraint more robust by improving the modelling of binaries on the brane in the future.

Multi-band gravitational wave tests of general relativity

Abstract: The violent collisions of black holes provide for excellent test-beds of Einstein’s general relativity in the strong/dynamical gravity regime. We here demonstrate the resolving power one can gain upon the use of multi-band observations of gravitational waves from both ground- and space-based detectors. We find significant improvement in both generic parameterized tests of general relativity and consistency tests of inspiral-merger-ringdown parts of the waveform over single-band detections. Such multi-band observations are crucial for unprecedented probes of e.g. parity-violation in gravity.

Particle motion near high-spin black holes

Abstract: General relativity predicts that the Kerr black hole develops qualitatively new and surprising features in the limit of maximal spin. Most strikingly, the region of spacetime near the event horizon stretches into an infinitely long throat and displays an emergent conformal symmetry. Understanding dynamics in this NHEK (Near-Horizon Extreme Kerr) geometry is necessary for connecting theory to upcoming astronomical observations of high-spin black holes. We review essential properties of NHEK and its relationship to the rapidly rotating Kerr black hole. We then completely solve the geodesic equation in the NHEK region and describe how the resulting trajectories transform under the action of its enhanced symmetries. In the process, we derive explicit expressions for the angular integrals appearing in the Kerr geodesic equation and obtain a useful formula, valid at arbitrary spin, for a particle's polar angle in terms of its radial motion. These results will aid in the analytic computation of astrophysical observables relevant to ongoing and future experiments.

The coupling of matter and spacetime geometry

Abstract: The geometrical formulation of gravity is not unique and can be set up in a variety of spacetimes. Even though the gravitational sector enjoys this freedom of different geometrical interpretations, consistent matter couplings have to be assured for a steady foundation of gravity. In generalised geometries, further ambiguities arise in the matter couplings unless the minimal coupling principle (MCP) is adopted that is compatible with the principles of relativity, universality and inertia. In this work, MCP is applied to all Standard Model gauge fields and matter fields in a completely general (linear) affine geometry. This is also discussed from an effective field theory perspective. It is found that the presence of torsion generically leads to theoretical problems. However, symmetric teleparallelism, wherein the affine geometry is integrable and torsion-free, is consistent with MCP. The generalised Bianchi identity is derived and shown to determine the dynamics of the connection in a unified fashion. Also, the parallel transport with respect to a teleparallel connection is shown to be free of second clock effects.