Self-dual Black Holes Research Articles

Constraints on the rotating self-dual black hole with quasi-periodic oscillations

An impressive feature of loop quantum gravity (LQG) is that it can elegantly resolve both the big bang and black hole singularities. By using the Newman-Janis algorithm, a regular and effective rotating self-dual black hole (SDBH) metric could be constructed, which alters the Kerr geometry with a polymeric function P from the quantum effects of LQG geometry. In this paper, we investigate its impact on the frequency characteristics of the X-ray quasi-periodic oscillations (QPOs) from 5 X-ray binaries and contrast it with the existing results of the orbital, periastron precession and nodal precession frequencies within the relativistic precession model. We apply a Monte Carlo Markov Chain (MCMC) simulation to examine the possible LQG effects on the X-ray QPOs. We found that the best constraint result for the rotating self-dual geometry from LQG came from the QPOs of X-ray binary GRO J1655-40, which establish an upper bound on the polymeric function P less than 6.15 × 10-3 at 95% confidence level. This bound leads to a restriction on the polymeric parameter δ of LQG to be 0.66.

Self-dual black holes in celestial holography

We construct two-dimensional quantum states associated to four-dimensional linearized rotating self-dual black holes in (2, 2) signature Klein space. The states are comprised of global conformal primaries circulating on the celestial torus, the Kleinian analog of the celestial sphere. By introducing a generalized tower of Goldstone operators we identify the states as coherent exponentiations carrying an infinite tower of w1+∞ charges or soft hair. We relate our results to recent approaches to black hole scattering, including a connection to Wilson lines, S\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{S} $$\\end{document}-matrix results, and celestial holography in curved backgrounds.

Axial gravitational quasinormal modes of a self-dual black hole in loop quantum gravity

Axial gravitational quasinormal modes of a self-dual black hole in loop quantum gravity

Constraints on self-dual black hole in loop quantum gravity with S0-2 star in the galactic center

One of remarkable features of loop quantum gravity (LQG) is that it can provide resolutions to both the black hole and big bang singularities. In the mini-superspace approach based on the polymerization procedure in LQG, a quantum corrected black hole metric is constructed. This metric is also known as self-dual spacetime since the form of the metric is invariant under the exchange r ⟶ a 0/r with a 0 being proportional to the minimum area in LQG and r is the standard radial coordinate at asymptotic infinity. It modifies the Schwarzschild spacetime by the polymeric function P, purely due to the geometric quantum effects from LQG. Here P is related to the polymeric parameter δ which is introduced to define the paths one integrates the connection along to define the holonomies in the quantum corrected Hamiltonian constraint in the polymerization procedure in LQG. In this paper, we consider its effects on the orbital signatures of S0-2 star orbiting Sgr A* in the central region of our Milky Way, and compare it with the publicly available astrometric and spectroscopic data, including the astrometric positions, the radial velocities, and the orbital precession for the S0-2 star. We perform Monte Carlo Markov Chain (MCMC) simulations to probe the possible LQG effects on the orbit of S0-2 star. No significant evidence of the self-dual spacetime arisIng from LQG is found. We thus place an upper bounds at 95% confidence level on the polymeric function P < 0.043 and P < 0.056, for Gaussian and uniform priors on orbital parameters, respectively.

Quasinormal modes of self-dual black holes in loop quantum gravity

We study the evolution of a test scalar field on the background geometry of a regular loop quantum black hole characterized by two loop quantum gravity correction parameters, namely, the polymeric function and the minimum area gap. The calculations of quasinormal frequencies in asymptotically flat spacetime are performed with the help of higher-order Wentzel-Kramers-Brillouin expansion and related Pad\'e approximants, the improved asymptotic iteration method, and time-domain integration. The effects of free parameters of the theory on the quasinormal modes are studied and deviations from those of the Schwarzschild black holes are investigated. We show that the loop quantum gravity correction parameters have opposite effects on the quasinormal frequencies and the loop quantum black holes are dynamically stable.

Quasinormal modes of a massive scalar field nonminimally coupled to gravity in the spacetime of self-dual black hole

In this work, we investigate the quasinormal modes for a massive scalar field with a nonminimal coupling with gravity in the spacetime of a loop quantum black hole, known as the self-dual black hole. In this way, we have calculated the characteristic frequencies using the 3rd order WKB approach, where we can verify a strong dependence with the mass of scalar field, the parameter of nonminimal coupling with gravity, and parameters of the loop quantum gravity. From our results, we can check that the self-dual black hole is stable under the scalar perturbations when assuming small values for the parameters. Also, such results tell us that the quasinormal modes assume different values for the cases where the mass of field is null and the nonminimal coupling assumes xi =0 and xi =1/6, i.e., a possible breaking of the conformal invariance can be seen in the context of loop quantum black holes.

Absorption and scattering by a self-dual black hole

In this paper we investigate the process of massless scalar wave scattering due to a self-dual black hole through the partial wave method. We calculate the phase shift analytically at the low energy limit and we show that the dominant term of the differential scattering cross section at the small angle limit is modified by the presence of parameters related to the polymeric function and minimum area of a self-dual black hole. We also find that the result for the absorption cross section is given by the event horizon area of the self-dual black hole at the low frequency limit. We also show that, contrarily to the case of a Schwarzschild black hole, the differential scattering/absorption cross section of a self-dual black hole is nonzero at the zero mass limit. In addition, we verify these results by numerically solving the radial equation for arbitrary frequencies.

Polar gravitational perturbations and quasinormal modes of a loop quantum gravity black hole

In this work, we have calculated the polar gravitational quasinormal modes for a quantum corrected black hole model, that arises in the context of Loop Quantum Gravity, known as Self-Dual Black Hole. In this way, we have calculated the characteristic frequencies using the WKB approach, where we can verify a strong dependence with the Loop Quantum Gravity parameters. At the same time we check that the Self-Dual Black Hole is stable under polar gravitational perturbations, we can also verify that the spectrum of the polar quasinormal modes differs from the axial one \cite{Cruz:2015bcj}. Such a result tells us that isospectrality is broken in the context of Self Dual Black Holes.

Entropic corrected Newton’s law of gravitation and the loop quantum black hole gravitational atom

One proposal by Verlinde \cite{Verlinde:2010hp} is that gravity is not a fundamental, but an entropic force. In this way, Verlinde has provide us with a way to derive the Newton's law of gravitation from the Bekenstein-Hawking entropy-area formula. On the other hand, since it has been demonstrated that this formula is susceptible to quantum gravity corrections, one may hope that these corrections could be inherited by the Newton's law. In this way, the entropic interpretation of Newton's law could be a prolific way in order to get verifiable or falsifiable quantum corrections to ordinary gravity in an observationally accessible regimes. Loop quantum gravity is a theory that provide a way to approach the quantum properties of spacetime. From this theory, emerges a quantum corrected semiclassical black hole solution called loop quantum black holes or self-dual black holes. Among the interesting features of loop quantum black holes is the fact that they give rise to a modified entropy-area relation where quantum gravity corrections are present. In this work, we obtain the quantum corrected Newton's law from the entropy-area relation given by loop quantum black holes. In order to relate our results with the recent experimental activity, we consider the quantum mechanical properties of a huge gravitational atom consisting in a light neutral elementary particle in the presence of a loop quantum black hole.

Quasinormal frequencies of self-dual black holes

One simplified black hole model constructed from a semiclassical analysis of loop quantum gravity (LQG) is called self-dual black hole. This black hole solution depends on a free dimensionless parameter P known as the polymeric parameter and also on the $a_{0}$ area related to the minimum area gap of LQG. In the limit of P and $a_{0}$ going to zero, the usual Schwarzschild-solution is recovered. Here we investigate the quasinormal modes (QNMs) of massless scalar perturbations in the self-dual black hole background. We compute the QN frequencies using the sixth order WKB approximation method and compare them with numerical solutions of the Regge-Wheeler equation. Our results show that as the parameter P grows, the real part of the QN frequencies suffers an initial increase and then starts to decrease while the magnitude of the imaginary one decreases for fixed area gap $a_{0}$. This particular feature means that the damping of scalar perturbations in the self-dual black hole spacetimes are slower, and their oscillations are faster or slower according to the value of P.

Quantum-corrected self-dual black hole entropy in tunneling formalism with GUP

In this paper we focus on the Hamilton–Jacobi method to determine the entropy of a self-dual black hole by using linear and quadratic GUPs (generalized uncertainty principles). We have obtained the Bekenstein–Hawking entropy of self-dual black holes and its quantum corrections that are logarithm and also of several other types.

Gravitational lensing by self-dual black holes in loop quantum gravity

We study gravitational lensing by a recently proposed black hole solution in Loop Quantum Gravity. We highlight the fact that the quantum gravity corrections to the Schwarzschild metric in this model evade the `mass suppression' effects (that the usual quantum gravity corrections are susceptible to) by virtue of one of the parameters in the model being dimensionless, which is unlike any other quantum gravity motivated parameter. Gravitational lensing in the strong and weak deflection regimes is studied and a sample consistency relation is presented which could serve as a test of this model. We discuss that though the consistency relation for this model is qualitatively similar to what would have been in Brans-Dicke, in general it can be a good discriminator between many alternative theories. Although the observational prospects do not seem to be very optimistic even for a galactic supermassive black hole case, time delay between relativistic images for billion solar mass black holes in other galaxies might be within reach of future relativistic lensing observations.

Quantum tunneling radiation from self-dual black holes

Black holes are considered as objects that can reveal quantum aspects of spacetime. Loop Quantum Gravity (LQG) is a theory that propose a way to model the quantum spacetime behavior revealed by a black hole. One recent prediction of this theory is the existence of sub-Planckian black holes, which have the interesting property of self-duality. This property removes the black hole singularity and replaces it with another asymptotically flat region. In this work, we obtain the thermodynamical properties of this kind of black holes, called self-dual black holes, using the Hamilton–Jacobi version of the tunneling formalism. Moreover, using the tools of the tunneling approach, we investigate the emission spectrum of self-dual black holes, and investigate if some information about the black hole initial state can be recovered during the evaporation process. Back-reaction effects are included.

Stability of self-dual black holes

We study the stability properties of the Cauchy horizon for two different self-dual black hole solutions obtained in a model inspired by Loop Quantum Gravity. The self-dual spacetimes depend on a free dimensionless parameter called a polymeric parameter P. For the first metric the Cauchy horizon is stable for supermassive black holes only if this parameter is sufficiently small. For small black holes, however the stability is easily implemented. The second metric analyzed is not only self-dual but also form-invariant under the transformation r→r⁎2/r and r⁎=2mP. We find that this symmetry protects the Cauchy horizon for any value of the polymeric parameter.

Self-dual black holes in loop quantum gravity: Theory and phenomenology

In this paper we have recalled the semiclassical metric obtained from a classical analysis of the loop quantum black hole (LQBH). We show that the regular Reissner--Nordstr\om-like metric is self-dual in the sense of $T$-duality: the form of the metric obtained in loop quantum gravity is invariant under the exchange $r\ensuremath{\rightarrow}{a}_{0}/r$ where ${a}_{0}$ is proportional to the minimum area in loop quantum gravity and $r$ is the standard Schwarzschild radial coordinate at asymptotic infinity. Of particular interest, the symmetry imposes that if an observer in $r\ensuremath{\rightarrow}+\ensuremath{\infty}$ sees a black hole of mass $m$ an observer in the other asymptotic infinity beyond the horizon (at $r\ensuremath{\approx}0$) sees a dual mass ${m}_{P}/m$. We then show that small LQBH are stable and could be a component of dark matter. Ultralight LQBHs created shortly after the big bang would now have a mass of approximately ${10}^{\ensuremath{-}5}{m}_{P}$ and emit radiation with a typical energy of about ${10}^{13}--{10}^{14}\text{ }\text{ }\mathrm{eV}$ but they would also emit cosmic rays of much higher energies, albeit few of them. If these small LQBHs form a majority of the dark matter of the Milky Way's Halo, the production rate of ultra-high-energy-cosmic-rays (UHECR) by these ultralight black holes would be compatible with the observed rate of the Auger detector.