Narrow Results

As an alternative to the “no hair conjecture,” the “no short hair conjecture” for hairy black holes was established earlier. This theorem stipulates that hair must be present above 3/2 of the event horizon radius for a hairy black hole. It is assumed that the nonlinear behavior of the matter field plays a key role in the presence of such hair. Subsequently, it was established that the hair must extend beyond the photon sphere of the corresponding black hole. We have investigated the validity of the “no short hair conjecture” in pure Lovelock gravity. Our analysis has shown that irrespective of dimensionality and Lovelock order, the hair of a static, spherically symmetric black hole extends at least up to the photon sphere.

Black hole shadows and photon spheres offer valuable tools for investigating black hole properties. Recent observations by the Event Horizon Telescope Collaboration have confirmed the existence of rotating black holes. Black hole parameters influence the observed shadow size. This paper aims to extend the work in [V. Vertogradov and A. Övgün, Analyzing the influence of geometrical deformation on photon sphere and shadow radius: A new analytical approach — spherically symmetric spacetimes, Phys. Dark Univ.45 (2024) 101541] and explores the impact of geometrical deformations on black hole shadow size using gravitational decoupling to an axially symmetric spacetime. We find that the results are more complex than the spherically symmetric case. We compare shadows in the well-known models with those of a Kerr black hole. Our approach suggests that the influence of an accretion disc on the observed shadow shape can be accurately described despite negligible impact on the black hole geometry itself.

A special solution of Hořava–Lifshitz gravity is a black hole that in a certain limit reproduces Schwarzschild spacetime. It is shown here that the common feature of this class of Schwarzschild-like spacetimes is the presence of three distinct, non-overlapping sectors of circular geodesics corresponding to three distinct types of objects. It is also found that a photon sphere which separates ordinary matter and tachyonic sectors turns out to be a point of no return for massive particles' geodesics.

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.

In this paper, we analyze the null geodesics of regular black holes (BHs). A detailed analysis of geodesic structure, both null geodesics and timelike geodesics, has been investigated for the said BH. As an application of null geodesics, we calculate the radius of photon sphere and gravitational bending of light. We also study the shadow of the BH spacetime. Moreover, we determine the relation between radius of photon sphere $(r_{\mathrm{\text{ps}}})$ and the shadow observed by a distance observer. Furthermore, we discuss the effect of various parameters on the radius of shadow $R_s$. Also, we compute the angle of deflection for the photons as a physical application of null-circular geodesics. We find the relation between null geodesics and quasinormal mode (QNM) frequency in the eikonal approximation by computing the Lyapunov exponent. It is also shown that (in the eikonal limit) the QNMs of BHs are governed by the parameter of null-circular geodesics. The real part of QNMs frequency determines the angular frequency, whereas the imaginary part determines the instability timescale of the circular orbit. Next, we study the massless scalar perturbations and analyze the effective potential graphically. Massive scalar perturbations are also discussed. As an application of timelike geodesics, we compute the innermost stable circular orbit (ISCO) and marginally bound circular orbit (MBCO) of the regular BHs which are closely related to the BH accretion disk theory. In the appendix, we calculate the relation between angular frequency and Lyapunov exponent for null-circular geodesics.

Horizons and bound photon orbits are defining features of black holes that translate into key features of black hole images. We review a purely geometric proof that spherically symmetric, isolated objects with horizons in gravity theories with null-geodesic propagation of light must display bound photon orbits forming a photon sphere. Identifying the key elements of the proof, we articulate a simpler argument that carries over to more general situations with modified light propagation and implies the existence of equatorial spherical photon orbits in axisymmetric spacetimes with reflection symmetry. We conclude that the non-observation of photon rings with very-large-baseline interferometry would be a very strong indication against a horizon, irrespective of whether or not the image shows a central brightness depression.

This research surveys the impact of the flavor number parameter on a four-dimensional Black Hole (BH) solution in Einstein’s nonlinear sigma model-$SU(N)$ (NLSM) in accordance with the shadow, energy emission rate, sparsity, massless scalar, and electromagnetic quasinormal mode spectra. Related investigations are being carried out to explore the influence of the flavor number parameter. In particular, the findings show that shadow behavior and energy emission rate are antinomic processes in view of the flavor number parameter. On the other hand, the $SU(N)$-NLSM BH’s quasinormal modes are computed by first calculating the effective potential generated by the perturbation of scalar and electromagnetic fields, followed by a numerical analysis based on the sixth-order WKB approach. Our results show that the QNMs of the $SU(N)$-NLSM BH damp more slowly as flavor number N increases.

This work is aimed at the study of traversable wormholes, proposed by Morris and Thorne [Wormholes in spacetime and their use for interstellar travel: A tool for teaching general relativity, Am. J. Phys. 56 (1988) 395], in the framework of $f(R,T)=R+\alpha R^n+\lambda T$ gravity, where $\alpha$, $\lambda$ and $n$ are constants. The wormhole solutions are obtained and analyzed by using a simplest form of shape function. Further, the existence of photon spheres outside the throat of wormhole due to the gravitational lensing effect is detected.

In this paper, the effects of strong gravitational lensing are explored in the context of traversable wormholes by determining the existence of photon spheres. The redshift function is defined as $\mathrm{\Phi }(r)=\frac{\xi }{r}+\frac{\eta }{r^2}$, where $\xi$ and $\eta$ are constants. Using this redshift function, the points of maximum potentials are determined which consequently gives the radius of photon spheres. It is obtained that either the throat itself can act as an effective photon sphere or the photon sphere exists outside the throat of the wormhole. Further, the nature of matter supporting the wormhole solutions is examined by analyzing the energy conditions, and the stability of solutions is tested with the help of the TOV (Tolman–Oppenheimer–Volkoff) equation.

A uniqueness theorem for static and asymptotically flat Einstein-Maxwell spacetimes with a photon sphere P³ is considered. To do this we first modify the definition of the photon sphere for electrically charged spacetimes by adding the property that the one-form ι_ξF is normal to the photon sphere. We then set the magnetic charge to zero and assume that the lapse function regularly foliates the spacetime outside the photon sphere. As an auxiliary (and important in itself) result we prove that P³ has constant mean and scalar curvatures. Then, after deriving a few more equations, we give a proof of the main uniqueness theorem, i. e. the static asymptotically flat Einstein-Maxwell spacetimes with a non-extremal photon sphere are isometric to the Reissner-Nordström one with mass M and electric charge Q subject to $\frac{Q^2}{M^2}\le \frac{9}{8}.$