Kerr-like Spacetime Research Articles

Chaotic behavior of geodesics in Kerr-like spacetime

In recent years, experimental and theoretical research on the nature of supermassive bodies that inhabit the central regions of galaxies has grown significantly. In this contribution, we study the motion of unitary mass test particles in a perturbed Kerr-like metric. The metric represents the approximate exterior spacetime of a massive rotating body with mass quadrupole moment $q$. Through extensive study of the geodesics, it is found that the chaotic behavior proliferates as the $q$ parameter increases. Several structures are found in the phase space, such as Birkhoff chains of islands and hyperbolic points if $q\ensuremath{\ne}0$. Additionally, chaotic regions crossing the null radial momentum axis (${p}_{r}=0$) are studied by analyzing the rotation number, and several islands of stability are found that are preserved as the deformation of the rotating body increases, while others are destroyed. Furthermore, chaotic behavior is found to be dictated by stickiness, chaotic orbits that remain attached to stable ones for a long time before they become divergent and are attracted to the event horizon.

Superradiance scattering off Kerr-like black hole and its shadow in the bumblebee gravity with noncommutative spacetime

We consider a bumblebee gravity-based Kerr-like black hole in a noncommutative (NC) background and study the superradiance effect and the shadow cast. We extensively study the different aspects of the black hole associated with a generalized Kerr-like spacetime metric endowed with the corrections jointly linked with Lorentz violation and NC spacetime effect. We examine the deviation of shape, and size of the ergosphere, energy emission rate, in this generalized situation. We also examine the influence of admissible values of Lorentz violating parameter ell and NC parameter b on the superradiance effect and shadow of the black hole. The admissible range has been determined from the observation of the Event Horizon Telescope (EHT) collaboration concerning M87^{*} astronomical black hole. We observe that the superradiance phenomena has a crucial dependence on the parameter ell and b apart from its dependence on a or {hat{a}}= sqrt{ell +1}a which is linked with the spin of the black hole. We also observe that with the increase in Lorentz violating parameter ell , the size of the black hole shadow increases, and with the increase in the NC parameter b the size of the black hole decreases. We have made an attempt to constrain the NC parameters b of this modified Kerr-like black hole by using the data available from the Event Horizon Telescope (EHT) collaboration. This study shows that black holes associated with NC Kerr-like spacetime may be a suitable candidate for the astrophysical black holes.

Astrophysically viable Kerr-like spacetime

Based on carefully selected physical requirements, we develop and analyze a rotating regular black hole with asymptotically Minkowski core. This Kerr-like geometry possesses the full ``Killing tower'' of nontrivial Killing tensor, Killing-Yano tensor, and principal tensor. The Hamilton-Jacobi equation, Klein-Gordon equation, and Maxwell's equations are separable. Energy-condition violating physics is pushed into an arbitrarily small region in the deep core. Extraction of astrophysical observables falsifiable/verifiable by the observational community is straightforward.

Multipole moments of compact objects with NUT charge: Theoretical and observational implications

We derive the multipole moments of the Kerr-NUT black hole spacetime using the Geroch-Hansen formalism, even though the spacetime is not asymptotically flat. Intriguingly, in the presence of the NUT charge, the absence of reflection symmetry about the equatorial plane, leads to mass and spin multipole moments of all orders, in stark contrast to Kerr-like spacetimes. This leads to a drastic departure of the multipolar structure of a compact object with NUT charge, whose implications for gravitational wave observations have been explored. Our analysis of multipole moments for the Kerr-NUT spacetime is also in tune with the Thorne's approach.

Hamiltonian approach to black hole entropy: Kerr-like spacetimes

Black hole entropy of the Kerr-like family of spacetimes is introduced as the canonical charge on the horizon. Treating these spacetimes in the framework of Poincar\'e gauge theory either as Riemannian solutions or as solutions with torsion, it is shown that these geometrically different setups lead to the same black hole entropy.

Completing characterization of photon orbits in Kerr and Kerr-Newman metrics

Recently, several new characteristics have been introduced to describe null geodesic structure of stationary spacetimes, such as photon regions (PR) and transversely trapping surfaces (TTS). The former are three-dimensional domains confining the spherical photon orbits, while the latter are closed two-surface of spherical topology which fill other regions called TTR. It is argued that in generic stationary axisymmetric spacetime it is natural to consider also the non-closed TTSs of the geometry of spherical cups, satisfying the same conditions ("partial" TTS or PTTS), which fill the three-dimensional regions, PTTR. We then show that PR, TTR and PTTR together with the corresponding anti-trapping regions constitute the complete set of regions filling the entire three-space (where timelike surfaces are defined) of Kerr-like spacetimes. This construction provides a novel optical description of such spacetimes without recurring to explicit solution of the geodesic equations. Applying this analysis to Kerr-Newman metrics (including the overspinning ones) we reveal four different optical types for different sets of the rotation and charge parameters. To illustrate their properties we extend Synge analysis of photon escape in the Schwarzschild metric to stationary spacetimes and construct density graphs describing escape of photons from all the above regions.

Chen–Nester–Tung quasi-local energy and Wang–Yau quasi-local mass

In this paper, we show that the Chen-Nester-Tung (CNT) quasi-local energy is closely related to the Wang-Yau (WY) quasi-local mass. As a particular example, we compute the second variation of the CNT quasi-local energy for axially symmetric Kerr-like spacetimes with axially symmetric embeddings at the obvious critical point (0,0) and find that it is a saddle critical point in most of the cases. Also, as a byproduct, we generalize a previous result about the coincidence of CNT quasi-local energy and Brown-York mass for Kerr-like spacetimes by Tam and the first author to general spacetimes.

X-ray probes of black hole accretion disks for testing the no-hair theorem

The spins of a number of supermassive and stellar-mass black holes have been measured based on detections of thermal continuum emission and relativistically broadened iron lines in their x-ray spectra. Likewise, quasiperiodic variability has been observed in several sources. Such measurements commonly make the assumption that black holes are described by the Kerr metric, which according to the no-hair theorem characterizes black holes uniquely in terms of their masses and spins. This fundamental property of black holes can be tested observationally by measuring potential deviations from the Kerr metric introduced by a parametrically deformed Kerr-like spacetime. Thermal spectra, iron lines, and variability have already been studied extensively in several such metrics, which usually depend on only one particular type of deviation or contain unphysical regions outside of the compact object. In this paper, I study these x-ray probes in the background of a new Kerr-like metric which depends on four independent deviation functions and is free of pathological regions outside of the event horizon. I show that the observed signals depend significantly on primarily two types of deviations and that the strong correlation between the spin and the deviation parameters found previously in other Kerr-like metrics is partially broken for rapidly spinning black holes. This suggests that high-spin sources are the best candidates for tests of the no-hair theorem with x-rays and I obtain first constraints on such deviations from the stellar-mass black hole Cygnus X-1.

The Sagnac effect in conformal Weyl gravity

We investigate the Sagnac effect, representing the difference in travel time or phase shift observed for relativistic matter or light beams counter-propagating in a rotating interferometer. This is done for the Schwarzschild-like and Kerr-like vacuum solutions of conformal gravity which describe the field around a massive static and rotating object respectively, in the fourth order theory. To do this we employ the formal analogy between the Sagnac and Aharonov–Bohm effects that has been used earlier to study this effect in flat and curved spacetimes in general relativity. In particular we show that the linear term in the static metric of conformal gravity has a diminishing effect on the Sagnac time delay. Moreover using the expression for the Sagnac effect in the rotating Kerr-like spacetime, we show that the detection of the Weyl gravity contributions to the Sagnac time delay in the case of the Earth, lies beyond the capability of current experiments.

Inner accretion disk edges in a Kerr-like spacetime

According to the no-hair theorem, astrophysical black holes are uniquely described by the Kerr metric. In order to test this theorem with observations in either the electromagnetic or gravitational-wave spectra, several Kerr-like spacetimes have been constructed which describe potential deviations from the Kerr spacetime in parametric form. For electromagnetic tests of the no-hair theorem, such metrics allow for the proper modeling of the accretion flows around candidate black holes and the radiation emitted from them. In many of these models, the location of the inner edge of the accretion disk is of special importance. This inner edge is often taken to coincide with the innermost stable circular orbit, which can serve as a direct probe of the spin and the deviation from the Kerr metric. In certain cases, however, an innermost stable circular orbit does not exist, and the inner edge of an accretion disk is instead determined by an instability against small perturbations in the direction vertical to the disk. In this paper, I analyze the properties of accretion disks in the Kerr-like metric proposed by Johannsen and Psaltis [Phys. Rev. D 83, 124015 (2011)], whose inner edges are located at the radii where this vertical instability occurs. I derive expressions of the energy and axial angular momentum of disk particles that move on circular equatorial orbits and calculate the locations of the inner disk edges. As a possible observable of such accretion disks, I simulate profiles of relativistically broadened iron lines and show that they depend significantly on the values of the spin and the deviation parameter.

Testing General Relativity in the Strong-Field Regime with Observations of Black Holes in the Electromagnetic Spectrum

General relativity has been tested by many experiments, which, however, almost exclusively probe weak spacetime curvatures. In this thesis, I create two frameworks for testing general relativity in the strong-field regime with observations of black holes in the electromagnetic spectrum using current or near-future instruments. In the first part of this thesis, I design tests of the no-hair theorem, which uniquely characterizes the nature of black holes in general relativity in terms of their masses and spins and which states that these compact objects are described by the Kerr metric. I investigate a quasi-Kerr metric and construct a Kerr-like spacetime, both of which contain an independent parameter in addition to mass and spin. If the no-hair theorem is correct, then any deviation from the Kerr metric has to be zero. I show that already moderate changes of the deviation parameters in either metric lead to significant modifications of the observed signals. I apply this framework to the imaging of supermassive black holes using very-long baseline interferometry as well as to the quasi-periodic variability and relativistically broadened iron lines observed in both galactic and supermassive black holes. In the second part of this thesis, I devise a method to test the predicted evaporation of black holes in Randall-Sundrum-type braneworld gravity through the orbital evolution of black-hole X-ray binaries and obtain constraints on the size of the extra dimension from A0620-00 and XTE J1118+480.

Testing the No-Hair Theorem with Sgr A*

The no-hair theorem characterizes the fundamental nature of black holes in general relativity. This theorem can be tested observationally by measuring the mass and spin of a black hole as well as its quadrupole moment, which may deviate from the expected Kerr value. Sgr A*, the supermassive black hole at the center of the Milky Way, is a prime candidate for such tests thanks to its large angular size, high brightness, and rich population of nearby stars. In this paper, I discuss a new theoretical framework for a test of the no-hair theorem that is ideal for imaging observations of Sgr A* with very long baseline interferometry (VLBI). The approach is formulated in terms of a Kerr-like spacetime that depends on a free parameter and is regular everywhere outside of the event horizon. Together with the results from astrometric and timing observations, VLBI imaging of Sgr A* may lead to a secure test of the no-hair theorem.

Spinning loop black holes

In this paper, we construct four Kerr-like spacetimes starting from the loop black hole (LBH) Schwarzschild solutions and applying the Newman–Janis transformation. In previous papers, the Schwarzschild LBH was obtained replacing the Ashtekar connection with holonomies on a particular graph in a minisuperspace approximation which describes the black hole interior. Starting from this solution, we use a Newman–Janis transformation and restrict our study to two different and natural complexifications inspired from the complexifications of the Schwarzschild and Reissner–Nordström metrics. We show explicitly that the spacetimes obtained in this way are singularity free and thus there are no naked singularities. We show that the transformation moves, if any, the causality violating regions of the Kerr metric far from r = 0. We study the spacetime structure paying particular attention to the shape of the horizons. We conclude the paper with a discussion on a regular Reissner–Nordström black hole derived from the Schwarzschild LBH and then apply again the Newmann–Janis transformation.

Testing the no-hair theorem with observations of black holes in the electromagnetic spectrum

According to the no-hair theorem, astrophysical black holes are uniquely described by their mass and spin. In this paper, we review a new framework for testing the no-hair hypothesis with observations in the electromagnetic spectrum. The approach is formulated in terms of a Kerr-like spacetime containing a quadrupole moment that is independent of both mass and spin. If the no-hair theorem is correct, then any deviation from the Kerr metric quadrupole has to be zero. We show how upcoming VLBI imaging observations of Sgr A∗ as well as spectroscopic observations of iron lines from accreting black holes with IXO may lead to the first astrophysical test of the no-hair theorem.

New Kerr-like space-time

A new solution of the Einstein field equations depending on four arbitrary constants was obtained by the method of complex coordinate transformations. It is of type II and possesses a wire-like singularity.