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Register a new userPhoton Spheres and Sonic Horizons in Black Holes from Supergravity and Other Theories
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We study closed photon orbits in spherically-symmetric static solutions of supergravity theories, a Horndeski theory, and a theory of quintessence. These orbits lie in what we shall call a photon sphere (anti-photon sphere) if the orbit is unstable (stable). We show that in all the asymptotically flat solutions we examine that admit a regular event horizon, and whose energy-momentum tensor satisfies the strong energy condition, there is one and only one photon sphere outside the event horizon. We give an example of a Horndeski theory black hole (whose energy-momentum tensor violates the strong energy condition) whose metric admits both a photon sphere and an anti-photon sphere. The uniqueness and non-existence also holds for asymptotically anti-de Sitter solutions in gauged supergravity. The latter also exhibit the projective symmetry that was first discovered for the Schwarzschild-de Sitter metrics: the unparameterised null geodesics are the same as when the cosmological or gauge coupling constant vanishes. We also study the closely related problem of accretion flows by perfect fluids in these metrics. For a radiation fluid, Bondis sonic horizon coincides with the photon sphere. For a general polytropic equation of state this is not the case. Finally we exhibit counterexamples to a conjecture of Hods.
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In an accretion of fluid, its velocity may transit from subsonic to supersonic. The point at which such transition occurs is called sonic point and often mathematically special. We consider a steady-state and spherically symmetric accretion problem of ideal photon gas in general static spherically symmetric spacetime neglecting back reaction. Our main result is that the EOS of ideal photon gas leads to correspondence between its sonic point and the photon sphere of the spacetime in general situations. Despite of the dependence of the EOS on the dimension of spacetime, this correspondence holds for spacetimes of arbitrary dimensions.
A stationary and spherically symmetric black hole (For example, Reissner-Nordstrom black hole or Kerr-Newman black hole) has at most one singularity and two horizons. One horizon is the outer event horizon and the other is the inner Cauchy horizon. Can we construct static and spherically symmetric black hole solutions with N horizons and M singularities? De Sitter cosmos has only one apparent horizon. Can we construct cosmos solutions with N horizons? In this article, we present the static and spherically symmetric black hole and cosmos solutions with N horizons and M singularities in the vector-tensor theories. Following these motivations, we also construct the black hole solutions with a firewall. The deviation of these black hole solutions from the usual ones can be potentially tested by future measurements of gravitational waves.
We show that photon spheres of supermassive black holes generate high-frequency stochastic gravitational waves through the photon-graviton conversion. Remarkably, the frequency is universally determined as $m_esqrt{m_e /m_p} simeq 10^{20} text{Hz}$ in terms of the proton mass $m_p$ and the electron mass $m_e$. It turns out that the density parameter of the stochastic gravitational waves $ Omega_{ text{gw}}$ could be $ 10^{-12}$. Since the existence of the gravitational waves from photon spheres is robust, it is worth seeking methods of detecting high-frequency gravitational waves around $10^{20}$Hz.
Along this review, we focus on the study of several properties of modified gravity theories, in particular on black-hole solutions and its comparison with those solutions in General Relativity, and on Friedmann-Lemaitre-Robertson-Walker metrics. The thermodynamical properties of fourth order gravity theories are also a subject of this investigation with special attention on local and global stability of paradigmatic f(R) models. In addition, we revise some attempts to extend the Cardy-Verlinde formula, including modified gravity, where a relation between entropy bounds is obtained. Moreover, a deep study on cosmological singularities, which appear as a real possibility for some kind of modified gravity theories, is performed, and the validity of the entropy bounds is studied.
The formation of primordial black hole (PBH) dark matter and the generation of scalar induced secondary gravitational waves (SIGWs) have been studied in the generic no-scale supergravity inflationary models. By adding an exponential term to the Kahler potential, the inflaton experiences a period of ultra-slow-roll and the amplitude of primordial power spectrum is enhanced to $mathcal{O}(10^{-2})$. The enhanced power spectra of primordial curvature perturbations can have both sharp and broad peaks. A wide mass range of PBH is realized in our model, and the frequencies of the scalar induced gravitational waves are ranged form nHz to Hz. We show three benchmark points where the PBH mass generated during inflation is around $mathcal{O}(10^{-16}M_{odot})$, $mathcal{O}(10^{-12}M_{odot})$ and $mathcal{O}(M_{odot})$. The PBHs with masses around $mathcal{O}(10^{-16}M_{odot})$ and $ mathcal{O}(10^{-12}M_{odot})$ can make up almost all the dark matter, and the associated SIGWs can be probed by the upcoming space-based gravitational wave (GW) observatory. Also, the wide SIGWs associated with the formation of solar mass PBH can be used to interpret the stochastic GW background in the nHz band, detected by the North American Nanohertz Observatory for Gravitational Waves, and can be tested by future interferometer-type GW observations.
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