Connecting black holes and black strings

Static vacuum spacetimes with one compact dimension include black holes with localized horizons but also uniform and nonuniform black strings where the horizon wraps over the compact dimension. We present new numerical solutions for these localized black holes in 5 and 6 dimensions. Combined with previous 6D nonuniform string results, these provide evidence that the black hole and nonuniform string branches join at a topology changing solution.     

Primordial black holes and third order scalar induced gravitational waves

The process of primordial black hole (PBH) formation is inevitably accompanied by scalar induced gravitational waves (SIGWs). The strong correlation between PBH and SIGW signals may offer a promising approach to detecting PBHs in upcoming gravitational wave experiments, such as the Laser Interferometer Space Antenna (LISA). We investigate third order SIGWs during a radiation-dominated era in the case of the monochromatic primordial power spectrum \begin{document}$ \mathcal{P}_{\zeta}=A_{\zeta}k_*\delta\left(k-k_*\right) $\end{document}. For LISA observations, the relationships between the signal-to-noise ratio (SNR) and monochromatic primordial power spectrum are studied systematically, revealing that the effects of third order SIGWs extend the cutoff frequency from \begin{document}$ 2f_* $\end{document} to \begin{document}$ 3f_* $\end{document} and lead to an approximately 200% increase in the SNR for the frequency band from \begin{document}$ 10^{-5} $\end{document}Hz to \begin{document}$ 1.6\times 10^{-3} $\end{document}Hz, corresponding to PBHs with masses in the range \begin{document}$4\times 10^{-12}M_{\odot} \sim 10^{-7}M_{\odot}$\end{document}. We find that there is a critical value, \begin{document}$ A_*=1.76\times 10^{-2} $\end{document}, for the amplitude of the monochromatic primordial power spectra, such that when \begin{document}$ A_{\zeta}>A_* $\end{document}, the energy density of third order SIGWs is larger than that of second order SIGWs.     

Primordial black holes and secondary gravitational waves from chaotic infiation

Chaotic inflation is inconsistent with the observational constraint at 68% CL. Here, we show that the enhancement mechanism with a peak function in the noncanonical kinetic term not only helps the chaotic model V(φ) = V_0φ~(1/3) satisfy the observational constraint at large scales but also enhances the primordial scalar power spectrum by seven orders of magnitude at small scales.The enhanced curvature perturbations can produce primordial black holes of different masses and secondary gravitational waves with different peak frequencies. We also show that the non-Gaussianities of curvature perturbations have little effect on the abundance of primordial black holes and energy density of the scalar-induced secondary gravitational waves.     

Formation of black hole and emission of gravitational waves

Numerical simulations were performed for the formation process of rotating black holes. It is suggested that Kerr black holes are formed for wide ranges of initial parameters. The nature of gravitational waves from a test particle falling into a Kerr black hole as well as the development of 3D numerical relativity for the coalescing binary neutron stars are discussed.     

Initial data for black holes and black strings in 5D

We explore time-symmetric hypersurfaces containing apparent horizons of black objects in a 5D spacetime with one coordinate compactified on a circle. We find a phase transition within the family of such hypersurfaces: the horizon has different topology for different parameters. The topology varies from S3 to S2 x S1. This phase transition is discontinuous--the topology of the horizon changes abruptly. We explore the behavior around the critical point and present a possible phase diagram.     

Inverted black holes and anisotropic collapse

The structure of static vacuum and electrovacuum fields with the most simple symmetry is discussed within the framework of the general theory of relativity. The general electrovacuum fields with plane and pseudospherical symmetries and the special case of fields with cylindrical symmetry contain horizons with the R and T regions interchanged by comparison with the Schwarzschild solution (the inverted black hole structure); the horizons disappear in the presence of a massless scalar field and for small deviations from plane symmetry. The physical consequences of this structure for the simplest models of anisotropic collapse are briefly discussed. A simple method is described for constructing the Penrose diagrams for a given metric, and examples are given of the construction of new diagrams for the electrovacuum solutions with a term.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 32–38, June, 1979.     

Numerical modeling of black holes as sources of gravitational waves in a nutshell

These notes summarize basic concepts underlying numerical relativity and in particular the numerical modeling of black hole dynamics as a source of gravitational waves. Main topics are the 3+1 decomposition of general relativity, the concept of a well-posed initial value problem, the construction of initial data for general relativity, trapped surfaces and gravitational waves. Also, a brief summary is given of recent progress regarding the numerical evolution of black hole binary systems.     

The phase transition between caged black holes and black strings

Black-hole uniqueness is known to fail in higher dimensions, and the multiplicity of black hole phases leads to phase transitions physics in General Relativity. The black-hole black-string transition is a prime realization of such a system and its phase diagram has been the subject of considerable study in the last few years. The most surprising results seem to be the appearance of critical dimensions where the qualitative behavior of the system changes, and a novel kind of topology change. Recently, a full phase diagram was determined numerically, confirming earlier predictions for a merger of the black-hole and black-string phases and giving very strong evidence that the end-state of the Gregory–Laflamme instability is a black hole (in the dimension range 5?D?13$5?D?13$). Here this progress is reviewed, illustrated with figures, put into a wider context, and the still open questions are listed.     

Strong gravitational lensing by regular electrically charged black holes

In nonlinear electrodynamics a photon does not follow null geodesics of background geometry, but moves along null geodesics of a corresponding effective geometry. Therefore, in the strong deflection limit, in order to study the gravitational lensing of the regular electrically charged black holes obtained by coupling general relativity to nonlinear electrodynamics, one should firstly obtain the corresponding effective geometry, which is a necessary and key step. I obtain the deflection angle of the photon in the strong deflection limit, and further calculate the angular position and magnification of relativistic images. It is found that, the electric charge has significant effect on the gravitational lensing of regular black holes. With the increase of the electric charge q, the angular position of the relativistic images \(\theta _{\infty }\) and the relative magnification \(\mathcal {R}_{m}\) as a function of q decrease, while the angular separation between the outermost relativistic image and the others \(\mathcal {S}\) as a function of q increases. I also discuss the measurement of observables for the black hole at the center of our Galaxy in the cases of regular electrically charged black hole effective metrics.