arXiv subjects

R. Kh. Karimov

Publications and source records attributed to R. Kh. Karimov.

29 records · Page 2Linked to original sources

arXiv2026

Thin accretion disks around a Schwarzschild acoustic black hole

We investigate the properties of a thin accretion disk in the Novikov-Thorne framework around a Schwarzschild acoustic black hole characterized by a nonzero background fluid four-velocity $v_{r} = \sqrt{2Mξ/r}$, where $ξ$ is a tuning parameter. The Novikov-Thorne formalism is used here phenomenologically, with the Schwarzschild acoustic black hole treated as an effective background geometry for comparing disk observables with those of the Schwarzschild black hole. We show that the acoustic black hole exhibits two regimes depending on $ξ$. For $0 < ξ\leq 2.8$, the disk is in a strengthening regime, in which the radiative characteristics are enhanced relative to the Schwarzschild case. For $ξ> 2.8$, the disk is in a weakening regime, in which the radiative characteristics are reduced relative to the Schwarzschild case. The most pronounced change in the radiative characteristics is associated with the behaviour of the marginally stable orbit radius $r_{ms}$, whose branch change near $ξ\approx 2.8$ produces a sharp modification of the flux, temperature, and luminosity profiles. For the numerical illustrations, we adopt a toy model with black hole mass $M = 15M_{\odot}$ and compare the corresponding flux, temperature, spectral luminosity, efficiency, and Eddington luminosity with those of the Schwarzschild black hole. These differences may provide phenomenological diagnostics for comparing effective compact object geometries.

gr-qc↗

arXiv2023

Modified gravity black hole lensing observables in weak and strong field of gravity

We extend a recent work on weak field first order light deflection in the MOdified Gravity (MOG) by comprehensively analyzing the actual observables in gravitational lensing both in the weak and strong field regime. The static spherically symmetric black hole (BH) obtained by Moffat is what we call here the Schwarzschild-MOG (abbreviated as SMOG) containing repulsive Yukawa-like force characterized by the MOG parameter $α>0$ diminishing gravitational attraction. We point out a remarkable feature of SMOG, viz., it resembles a regular \textit{brane-world} BH in the range $-1<α<0$ giving rise to a negative "tidal charge" $Q$ ($=\frac{1}{4}\frac{α}{1+α}$) interpreted as an imprint from the $5D$ bulk with an imaginary source charge $q$ in the brane. The Yukawa-like force of MOG is attractive in the brane-world range enhancing gravitational attraction. For $-\infty <α<-1$, the SMOG represents a naked singularity. Specifically, we shall investigate the effect of $α$ or Yukawa-type forces on the weak (up to third PPN order) and strong field lensing observables. For illustration, we consider the supermassive BH SgrA* with $α=0.055$ for the weak field to quantify the deviation of observables from GR but in general we leave $α$ unrestricted both in sign and magnitude so that future accurate lensing measurements, which are quite challenging, may constrain $α$.

gr-qc↗

arXiv2020

Can accretion properties distinguish between a naked singularity, wormhole and black hole?

We first advance a mathematical novelty that the three geometrically and topologically distinct objects mentioned in the title can be exactly obtained from the Jordan frame vacuum Brans I solution by a combination of coordinate transformations, trigonometric identities and complex Wick rotation. Next, we study their respective accretion properties using the Page-Thorne model which studies accretion properties exclusively for $r\geq r_{\text{ms}}$ (the minimally stable radius of particle orbits), while the radii of singularity/ throat/ horizon $r<r_{\text{ms}}$. Also, its Page-Thorne efficiency $ε$ is found to increase with decreasing $r_{\text{ms}}$ and also yields $ε=0.0572$ for Schwarzschild black hole (SBH). But in the singular limit $r\rightarrow r_{s}$ (radius of singularity), we have $ε\rightarrow 1$ giving rise to $100 \%$ efficiency in agreement with the efficiency of the naked singularity constructed in [10]. We show that the differential accretion luminosity $\frac{d\mathcal{L}_{\infty}}{d\ln{r}}$ of Buchdahl naked singularity (BNS) is always substantially larger than that of SBH, while Eddington luminosity at infinity $L_{\text{Edd}}^{\infty}$ for BNS could be arbitrarily large at $r\rightarrow r_{s}$ due to the scalar field $ϕ$ that is defined in $(r_{s}, \infty)$. It is concluded that BNS accretion profiles can still be higher than those of regular objects in the universe.

gr-qc↗

arXiv2020

String effect on the relative time delay in the Kerr-Sen black hole

A well known solution of heterotic string theory is the spinning Kerr-Sen black hole (KSBH) characterized by a string parameter $ξ$. Kerr black hole is recovered at $ξ=0$. The purpose of this paper is to investigate the effect of $ξ$ on a new diagnostic of relative time delay (RTD) to see how the latter deviates from that in general relativity. Assuming KSBH as the spinning lens partner in PSR-BH binary systems, which provide the best laboratory for testing the time delay predictions, we study here the RTD up to third PPN order in $\left(1/r\right)$ in the thin-lens approximation. We work out a useful generalization of the RTD formulas applicable to the experimentally viable \textit{finite} distance lens scales, while\ terms higher than the zeroth order are shown to contain the effect of $ξ$. We shall also relate RTD to the observable image magnification factor determined by $β/θ_{E}$, where $β$ is the angular separation between the source and the observer and $θ_{E}$ is the "Einstein angle" determined by an "effective" non-aligned static lens equivalent to the original aligned spinning lens. Numerical estimates for two typical binary lens systems show $μ$sec level delay at the zeroth order consistent with predictions in the literature. However, the string effect at higher orders is too tiny to be measurable even in the far future leading to the conclusion that the stringy and general relativity BHs are yet observationally indistinguishable.

gr-qc↗

arXiv2020

Accretion disk around the rotating Damour-Solodukhin wormhole

A new rotating generalization of the Damour-Solodukhin wormhole (RDSWH), called Kerr-like wormhole, has recently been proposed and investigated by Bueno \textit{et al} for echoes in the gravitational wave signal. We show a novel feature of the RDSWH, viz., that the kinematic properties such as the ISCO\ or marginally stable radius $r_{\text{ms}}$, efficiency $ε$ and the disk potential $V_{\text{eff}}$ are \textit{independent} of $λ$ (which means they are identical to their KBH counterparts for any given spin). Differences however appear in the emissivity properties for higher values $0.1<λ\leq 1$ (say) and for the extreme spin $a_{\star}=0.998$. The kinematic and emissivity are generic properties as variations of the wormhole mass and the rate of accretion within the model preserve these properties. Specifically, the behavior of the luminosity peak is quite opposite to each other for the two objects, which could be useful from the viewpoint of observations. Apart from this, an estimate of the difference $Δ_λ$ in the maxima of flux of radiation $F(r)$ shows non-zero values but is too tiny to be observable at present for $λ< 10^{-3}$ permitted by the strong lensing bound. The broad conclusion is that RDSWH\ are experimentally indistinguishable from KBH by accretion characteristics.

gr-qc↗

arXiv2020

Accretion disks around the Gibbons-Maeda-Garfinkle-Horowitz-Strominger charged black holes

It seems surprising that the emissivity properties of the accretion disk (\textit{à la} Page and Thorne) surrounding the Gibbons-Maeda-Garfinkle-Horowitz-Strominger (GMGHS) black holes of heterotic string theory have not yet been studied. To fill this gap in the literature, we study the emissivity properties of the thin accretion disks around these black holes both in the Einstein and in the string frame using the Page-Thorne model. For illustration, we choose as a toy model a stellar-sized spherically symmetric black hole and find that, while the emissivity properties do not significantly differ from those of Reissner-Nordström and Schwarzschild black holes, they remarkably differ at GMGHS extreme limits corresponding to naked singularity and wormhole at higher frequencies. These differences provide a novel way to speculatively conclude about different types of objects from the observational point of view.

gr-qc↗

arXiv2019

Vacuum Brans-Dicke theory in the Jordan and Einstein frames: can they be distinguished by lensing?

Vacuum Brans-Dicke theory can be self-consistently described in two frames, the Jordan frame (JF) and the conformally rescaled Einstein frame (EF), the transformations providing an easy passage from one frame to the other at the level of actions and solutions. Despite this, the conformal frames are inequivalent describing different geometries. It is shown that the predictions of the weak field lensing (WFL) observables in the EF are different from those recently obtained in the JF for the vacuum Brans-Dicke class 1 solution. The value of the Brans-Dicke coupling parameter $ω$ from the Cassini spacecraft experiment reveals the degree of accuracy needed to experimentally distinguish the WFL measurements including the total magnification factor in the two frames.

gr-qc↗

arXiv2019

Upper limit on NUT charge from the observed terrestrial Sagnac effect

The \textit{exact} Sagnac delay in the Kerr-Taub-NUT (Newman-Unti-Tamburino) spacetime is derived in the equatorial plane for non-geodesic as well as geodesic circular orbits. The resulting formula, being exact, can be directly applied to motion in the vicinity of any spinning object including black holes but here we are considering only the terrestrial case since observational data are available. The formula reveals that, in the limit of spin $a\rightarrow 0$, the delay does not vanish. This fact is similar to the non-vanishing of Lense-Thirring precession under $a\rightarrow 0$ even though the two effects originate from different premises. Assuming\ a reasonable input that the Kerr-Taub-NUT\ corrections are subsumed in the average residual uncertainty in the measured Sagnac delay, we compute upper limits on the NUT charge $n$. It is found that the upper limits on $n$ are far larger than the Earth's gravitational mass, which has not been detected in observations, implying that the Sagnac effect cannot constrain $n$ to smaller values near zero. We find a curious difference between the delays for non-geodesic and geodesic clock orbits and point out its implication for the well known "twin paradox" of special relativity.

gr-qc↗

arXiv2018

Terrestrial Sagnac delay constraining modified gravity models

Modified gravity theories include $f(\mathbf{R})-$gravity models that are usually constrained by the cosmological evolutionary scenario. However, it has been recently shown that they can also be constrained by the signatures of accretion disk around constant Ricci curvature Kerr-$f(\mathbf{R}_{0})$ stellar sized black holes. Our aim here is to use another experimental fact, viz., the terrestrial Sagnac delay to constrain the parameters of specific $f(\mathbf{R})-$gravity prescriptions. We shall assume that a Kerr-$f(\mathbf{R}_{0})$ solution asymptotically describes Earth's weak gravity near its surface. In this spacetime, we shall study oppositely directed light beams from source/observer moving on non-geodesic and geodesic circular trajectories and calculate the time gap, when the beams re-unite. We obtain the \textit{exact }time gap called Sagnac delay in both cases and expand it to show how the flat space value is corrected by the Ricci curvature, the mass and the spin of the gravitating source. Under the assumption that the magnitude of corrections are of the order of residual uncertainties in the delay measurement, we derive the allowed intervals for Ricci curvature. We conclude that the terrestrial Sagnac delay can be used to constrain the parameters of specific $f(\mathbf{R})$ prescriptions. Despite using the weak field gravity near Earth's surface, it turns out that the model parameter ranges still remain the same as those obtained from the strong field accretion disk phenomenon.

gr-qc↗

arXiv2017

Sagnac delay in the Kerr-dS space-time: Implications for Mach's principle

Relativistic twin paradox can have important implications for Mach's principle. It has been recently argued that the behavior of the time asynchrony (different aging of twins) between two flying clocks along closed loops can be attributed to the existence of an absolute spacetime, which makes Mach's principle unfeasible. In this paper, we shall revisit, and support, this argument from a different viewpoint using the Sagnac delay. This is possible since the above time asynchrony is known to be exactly the same as the Sagnac delay between two circumnavigating light rays re-uniting at the orbiting source/receiver. We shall calculate the effect of mass $M$ and cosmological constant $Λ$ on the delay in the general case of Kerr-de Sitter spacetime. It follows that, in the independent limits $M\rightarrow 0$, spin $a\rightarrow 0$ and $Λ\rightarrow 0$, while the Kerr-dS metric reduces to Minkowski metric, the clocks need not tick in consonance since there will still appear a non-zero observable Sagnac delay. While we do not measure spacetime itself, we do measure the Sagnac effect, which signifies an absolute substantive Minkowski spacetime instead of a void. We shall demonstrate a completely different limiting behavior of Sagnac delay, heretofore unknown, between the case of non-geodesic and geodesic source/observer motion.

gr-qc↗

arXiv2015

Initial length scale estimate for waveguides with some random singular potentials

In this work we consider three examples of random singular perturbations in multi-dimensional models of waveguides. These perturbations are described by a large potential supported on a set of a small measure, by a compactly supported fast oscillating potential, and by a delta-potential. In all cases we prove initial length scale estimate.

math.SP↗