Upper bound on the GUP parameter using the black hole shadow

Physics

Motivated by the recent study about the extended uncertainty principle (EUP) black holes, we present in this study its extension called the generalized extended uncertainty principle (GEUP) black holes. In particular, we investigated the GEUP effects on astrophysical and quantum black holes. First, we derive the expression for the shadow radius to investigate its behavior as perceived by a static observer located near and far from the black hole. Constraints to the large fundamental length scale, L*, up to two standard deviations level were also found using the Event Horizont Telescope (EHT) data: for black hole Sgr. A*, L*=5.716×1010 m, while for M87* black hole, L*=3.264×1013 m. Under the GEUP effect, the value of the shadow radius behaves the same way as in the Schwarzschild case due to a static observer, and the effect only emerges if the mass, M, of the black hole is around the order of magnitude of L* (or the Planck length, lPl). In addition, the GEUP effect increases the shad...

The European Physical Journal C

The links between the deformation parameter $$\beta $$ β of the generalized uncertainty principle (GUP) to the two free parameters $$\hat{\omega }$$ ω ^ and $$\gamma $$ γ of the running Newtonian coupling constant of the Asymptotic Safe gravity (ASG) program, has been conducted recently in [Phys. Rev. D 105 (2022) 12, 124054. https://doi.org/10.1103/PhysRevD.105.124054] In this paper, we test these findings by calculating and examining the shadow and quasinormal modes of black holes, and demonstrate that the approach provides a theoretical framework for exploring the interplay between quantum gravity and GUP. Our results confirm the consistency of ASG and GUP, and offer new insights into the nature of black holes and their signatures. The implications of these findings for future studies in quantum gravity are also discussed.

We compute the corrections to the Schwarzschild metric necessary to reproduce the Hawking temperature derived from a Generalized Uncertainty Principle (GUP), so that the GUP deformation parameter is directly linked to the deformation of the metric. Using this modified Schwarzschild metric, we compute corrections to the standard General Relativistic predictions for the light deflection and perihelion precession, both for planets in the solar system and for binary pulsars. This analysis allows us to set bounds for the GUP deformation parameter from well-known astronomical measurements.

The Astrophysical Journal, 2020

The Event Horizon Telescope (EHT), a global submillimeter wavelength very long baseline interferometry array, unveiled event-horizon-scale images of the supermassive black hole M87 * as an asymmetric bright emission ring with a diameter of 42±3 μas, and it is consistent with the shadow of a Kerr black hole of general relativity. A Kerr black hole is also a solution of some alternative theories of gravity, while several modified theories of gravity admit non-Kerr black holes. While earlier estimates for the M87 * black hole mass, depending on the method used, fall in the range »´-Ḿ M 3 10 7 10 9 9   , the EHT data indicated a mass for the M87 * black hole of (6.5 ± 0.7)×10 9 M e. This offers another promising tool to estimate black hole parameters and to probe theories of gravity in its most extreme region near the event horizon. The important question arises: Is it possible by a simple technique to estimate black hole parameters from its shadow, for arbitrary models? In this paper, we present observables, expressed in terms of ordinary integrals, characterizing a haphazard shadow shape to estimate the parameters associated with black holes, and then illustrate its relevance to four different models: Kerr, Kerr-Newman, and two rotating regular models. Our method is robust, accurate, and consistent with the results obtained from existing formalism, and it is applicable to more general shadow shapes that may not be circular due to noisy data. Unified Astronomy Thesaurus concepts: Astrophysical black holes (98); Galactic center (565); Black hole physics (159); Gravitation (661); Gravitational lensing (670)

Monthly Notices of the Royal Astronomical Society, 2015

A large international effort is under way to assess the presence of a shadow in the radio emission from the compact source at the centre of our Galaxy, Sagittarius A * (Sgr A *). If detected, this shadow would provide the first direct evidence of the existence of black holes and that Sgr A * is a supermassive black hole. In addition, the shape of the shadow could be used to learn about extreme gravity near the event horizon and to determine which theory of gravity better describes the observations. The mathematical description of the shadow has so far used a number of simplifying assumptions that are unlikely to be met by the real observational data. We here provide a general formalism to describe the shadow as an arbitrary polar curve expressed in terms of a Legendre expansion. Our formalism does not presume any knowledge of the properties of the shadow, e.g. the location of its centre, and offers a number of routes to characterize the distortions of the curve with respect to reference circles. These distortions can be implemented in a coordinate-independent manner by different teams analysing the same data. We show that the new formalism provides an accurate and robust description of noisy observational data, with smaller error variances when compared to previous approaches for the measurement of the distortion.

Arxiv preprint arXiv:1107.0708, 2011

The Generalized Uncertainty Principle suggests corrections to the Uncertainty Principle as the energy increases towards the Planck value. It provides a natural transition between the expressions for the Compton wavelength below the Planck mass and the black hole event horizon ...

2021

In this paper, we discussed the possible effects of dark matter on a Schwarzschild black hole with extended uncertainty principle (EUP) correction such as the parameter α and the large fundamental length scale L∗. In particular, we surrounded the EUP black hole of mass m with a static spherical shell of dark matter described by the parameters mass M , inner radius rs, and thickness ∆rs. Considering only the case where the EUP event horizon coincides rs, the study finds that there is no deviation in the event horizon, which readily implies that the black hole temperature due to the Hawking radiation is independent of any dark matter concentration. In addition, we explored the deviations in the innermost stable circular orbit (ISCO) radius of time-like particles, photonsphere, shadow radius, and weak deflection angle. It is found that time-like orbits are sensitive to deviation even for low values of mass M. A greater dark matter density is needed to have considerable deviations to nu...

2015

In this paper, we calculate the modification to the thermodynamics of a Schwarzschild black hole in higher dimensions because of Generalized Uncertainty Principle (GUP). We use the fact that the leading order corrections to the entropy of a black hole has to be logarithmic in nature to restrict the form of GUP. We observe that in six dimensions, the usual GUP produces the correct form for the leading order corrections to the entropy of a black hole. However, in five and seven dimensions a linear GUP, which is obtained by a combination of DSR with the usual GUP, is needed to produce the correct form of the corrections to the entropy of a black hole. Finally, we demonstrate that in five dimensions, a new form of GUP containing quadratic and cubic powers of the momentum also produces the correct form for the leading order corrections to the entropy of a black hole.

New Astronomy Reviews, 2012

Shadow formation around supermassive black holes were simulated. Due to enormous progress in observational facilities and techniques of data analysis researchers approach to opportunity to measure shapes and sizes of the shadows at least for the closest supermassive black hole at the Galactic Center. Measurements of the shadow sizes around the black holes can help to evaluate parameters of black hole metric. Theories with extra dimensions (Randall-Sundrum II braneworld approach, for instance) admit astrophysical objects (supermassive black holes, in particular) which are rather different from standard ones. Different tests were proposed to discover signatures of extra dimensions in supermassive black holes since the gravitational field may be different from the standard one in the general relativity (GR) approach. In particular, gravitational lensing features are different for alternative gravity theories with extra dimensions and general relativity. Therefore, there is an opportunity to find signatures of extra dimensions in supermassive black holes. We show how measurements of the shadow sizes can put constraints on parameters of black hole in spacetime with extra dimensions.

The Astrophysical Journal

The knowledge about the black hole mass function (BHMF) and its evolution would help to understand the origin of the BHs and how BH binaries formed at different stages of the history of the Universe. We demonstrate the ability of future third generation gravitational wave (GW) detector-the Einstein Telescope (ET) to infer the slope of the BHMF and its evolution with redshift. We perform the Monte Carlo simulation of the measurements of chirp signals from binary BH systems (BBH) that could be detected by ET, including the BH masses and their luminosity distances (d L). We use the mass of a primary black hole in each binary system to infer the BHMF as a power-law function with slope parameter as α. Taking into account the bias that could be introduced by the uncertainty of measurements and by the selection effect, we carried out the numerical tests and find that only one thousand of GW events registered by ET (∼ 1% amount of its yearly detection rate) could accurately infer the α with a precision of α ∼ 0.1. Furthermore, we investigate the validity of our method to recover a scenario where α evolves with redshift as α(z) = α 0 + α 1 z 1+z. Taking a thousand of GW events and using d L as the redshift estimator, our tests show that one could infer the value of evolving parameter α 1 accurately with the uncertainty level of ∼ 0.5. Our numerical tests verify the reliability of our method. The uncertainty levels of the inferred parameters can be trusted directly for the several sets of the parameter we assumed, yet shouldn't be treated as a universal level for the general case.