Narrow Results

We consider quasi-extreme Kerr and quasi-extreme Schwarzschild–de Sitter black holes. From the known analytical expressions obtained for their quasi-normal modes frequencies, we suggest an area quantization prescription for those objects.

We study the massless scalar wave propagation in the time-dependent Schwarzschild black hole background. We find that the Kruskal coordinate is an appropriate framework to investigate the time-dependent spacetime. A time-dependent scattering potential is derived by considering dynamical black hole with parameters changing with time. It is shown that in the quasinormal ringing both the decay time-scale and oscillation are modified in the time-dependent background.

In this paper, we have studied a black hole in de Sitter space which has a conformally coupled scalar field in the background. This black hole is also known as the MTZ black hole. We have obtained exact values for the quasi-normal mode (QNM) frequencies under massless scalar field perturbations. We have demonstrated that when the black hole is near-extremal, that the wave equation for the massless scalar field simplifies to a Schrödinger type equation with the well-known Pöschl–Teller potential. We have also used sixth-order WKB approximation to compute QNM frequencies to compare with exact values obtained via the Pöschl–Teller method for comparison. As an application, we have obtained the area spectrum using modified Hods approach and show that it is equally spaced.

We derive proper time Lyapunov exponent $({\lambda }_p)$ and coordinate time Lyapunov exponent $({\lambda }_c)$ for a regular Hayward class of black hole. The proper time corresponds to $\tau$ and the coordinate time corresponds to $t$, where $t$ is measured by the asymptotic observers both for Hayward black hole and for special case of Schwarzschild black hole. We compute their ratio as $\frac{{\lambda }_p}{{\lambda }_c}=\frac{(r_{\sigma }^3+2l^{2}m)}{\sqrt{{(r_{\sigma }^2+2l^{2}m)}^3-3m{r}_{\sigma }^5}}$ for time-like geodesics. In the limit of $l=0$ that means for Schwarzschild black hole this ratio reduces to $\frac{{\lambda }_p}{{\lambda }_c}=\sqrt{\frac{r_{\sigma }}{(r_{\sigma }-3m)}}$. Using Lyapunov exponent, we investigate the stability and instability of equatorial circular geodesics. By evaluating the Lyapunov exponent, which is the inverse of the instability time scale, we show that, in the eikonal limit, the real and imaginary parts of quasi-normal modes (QNMs) is specified by the frequency and instability time scale of the null circular geodesics. Furthermore, we discuss the unstable photon sphere and radius of shadow for this class of black hole.

The frequency band used by cellular telephones includes the eigenfrequencies of a dielectric sphere with physical characteristics close to those of a human head. Proceeding from the spatial features of the natural modes of such a sphere, we propose an independent and clear evident accuracy test for the complicated numerical calculations which are conducted when estimating the potential hazard due to the use of cellular telephones, in particular, for the check of the proper handling of the electromagnetic shape resonances of a human head.

The properties of relativistic perturbations of neutron stars and black holes are discussed. They are of great relevance in the study of gravitational wave astronomy. In this work, we review the properties of quasi-normal modes of neutron stars and Schwarzschild black holes and the main features of their detection by actual gravitational wave interferometers.

The inspiral of a stellar-mass astrophysical object into a massive black hole may be modeled within perturbation theory of General Relativity via the so-called self-force. In this paper, we present a novel method for the calculation of the self-force which is based on the Green function (GF) of the wave equation satisfied by the field created by the smaller object. We review the results in [M. Casals, S. Dolan, A. C. Ottewill and B. Wardell, Phys. Rev. D88 (2013) 044022; B. Wardell, C. R. Galley, A. Zenginoğlu, M. Casals, S. R. Dolan and A. C. Ottewill, Phys. Rev. D89 (2014) 084021] on the GF and the self-force on a scalar charge (as a model for the gravitational case) moving on a Schwarzschild black hole spacetime. This GF method offers an appealing geometrical insight into the origin of the self-force and is a promising candidate for practical self-force calculations.

General Relativity is a hugely successful description of gravitation. However, both theory and observations suggest that General Relativity might have significant classical and quantum corrections in the Strong Gravity regime. Testing the strong field limit of gravity is one of the main objectives of the future gravitational wave detectors. One way to detect strong gravity is through the polarization of gravitational waves. For quasi-normal modes of black-holes in General Relativity, the two polarization states of gravitational waves have the same amplitude and frequency spectrum. Using the principle of energy conservation, we show that the polarizations differ for modified gravity theories. We obtain a diagnostic parameter for polarization mismatch that provides a unique way to distinguish General Relativity and modified gravity theories in gravitational wave detectors.

In this paper, two numerical methods are used to calculate quasi-normal modes (QNMs) of near-extremal black holes/strings in the generalized spherically/cylindrically symmetric background, the Asymptotic Iteration Method (AIM) and the Spectral Method. The numerical results confirm the accuracy of the approximate analytic formula using the Pöschl–Teller potential. Our analytic formula is used to investigate the Strong Cosmic Censorship conjecture of extremal and near-extremal black holes in (P. Burikham, S. Ponglertsakul and T. Wuthicharn, Eur. Phys. J. C80 (2020) 954, arXiv:2010.05879 [gr-qc]).

We provide the full asymptotic description of the quasi-normal modes (resonances) in any strip of fixed width for Dirac fields in slowly rotating Kerr–Newman–de Sitter black holes. The resonances split in a way similar to the Zeeman effect. The method is based on the extension to Dirac operators of techniques applied by Dyatlov in [Quasi-normal modes and exponential energy decay for the Kerr–de Sitter black hole, Commun. Math. Phys.306(1) (2011) 119–163; Asymptotic distribution of quasi-normal modes for Kerr–de Sitter black holes, Ann. Henri Poincaré13(5) (2012) 1101–1166] to the (uncharged) Kerr–de Sitter black holes. We show that the mass of the Dirac field does not have an effect on the two leading terms in the expansions of resonances. We give an expansion of the solution of the evolution equation for the Dirac fields in the outer region of the slowly rotating Kerr–Newman–de Sitter black hole which implies the exponential decay of the local energy. Moreover, using the $r$-normal hyperbolicity of the trapped set and applying the techniques from [Asymptotics of linear waves and resonances with applications to black holes, Commun. Math. Phys.335 (2015) 1445–1485; Resonance projectors and asymptotics for $r$-normally hyperbolic trapped sets, J. Amer. Math. Soc.28 (2015) 311–381], we give location of the resonance free band and the Weyl-type formula for the resonances in the band near the real axis.

We analyze the quasi-normal mode spectrum of realistic neutron stars by studying axial and polar modes. We consider different equations of state satisfying the 2M_⊙ constraint, most of them containing exotic matter. New phenomenological relations between the frequency and damping time of the modes are obtained. These new relations are independent of the equation of state and relate the quasi-normal mode spectrum to the global properties of the star. Hence they could be used to constrain the equation-of-state of neutron stars. Also, We present new universal relations between quasi-normal modes and I-LOVE-Q parameters for neutron stars including exotic mater.