No Arabic abstract
The singularity of a spherical (Schwarzschild) black hole is a surface, not a point. A freely-falling, non-rotating observer sees Hawking radiation with energy density diverging with radius as $rho propto r^{-6}$ near the Schwarzschild singular surface. Spacetime inside a rotating (Kerr) black hole terminates at the inner horizon because of the Poisson-Israel mass inflation instability. If the black hole is accreting, as all realistic black holes do, then generically inflation gives way to Belinski-Khalatnikov-Lifshitz oscillatory collapse to a strong, spacelike singular surface.
We numerically compute the renormalized expectation value $langlehat{Phi}^{2}rangle_{ren}$ of a minimally-coupled massless quantum scalar field in the interior of a four-dimensional Reissner-Nordstrom black hole, in both the Hartle-Hawking and Unruh states. To this end we use a recently developed mode-sum renormalization scheme based on covariant point splitting. In both quantum states, $langlehat{Phi}^{2}rangle_{ren}$ is found to approach a emph{finite} value at the inner horizon (IH). The final approach to the IH asymptotic value is marked by an inverse-power tail $r_{*}^{-n}$, where $r_{*}$ is the Regge-Wheeler tortoise coordinate, and with $n=2$ for the Hartle-Hawking state and $n=3$ for the Unruh state. We also report here the results of an analytical computation of these inverse-power tails of $langlehat{Phi}^{2}rangle_{ren}$ near the IH. Our numerical results show very good agreement with this analytical derivation (for both the power index and the tail amplitude), in both quantum states. Finally, from this asymptotic behavior of $langlehat{Phi}^{2}rangle_{ren}$ we analytically compute the leading-order asymptotic behavior of the trace $langlehat{T}_{mu}^{mu}rangle_{ren}$ of the renormalized stress-energy tensor at the IH. In both quantum states this quantity is found to diverge like $b(r-r_{-})^{-1}r_{*}^{-n-2}$ (with $n$ specified above, and with a known parameter $b$). To the best of our knowledge, this is the first fully-quantitative derivation of the asymptotic behavior of these renormalized quantities at the inner horizon of a four-dimensional Reissner-Nordstrom black hole.
In this paper, we demonstrate that a phenomenon described as topological inflation during which inflation occurs inside the core of topological defects, has a non-topological counterpart. This appears in a simple set-up containing Einstein gravity coupled minimally to an electromagnetic field as well as a self-interacting, complex valued scalar field. The U(1) symmetry of the model is unbroken and leads to the existence of globally regular solutions, so-called boson stars, that develop a horizon for sufficiently strong gravitational coupling. We also find that the same phenomenon exists for black holes with scalar hair.
The possibility that rotating black holes could be natural particle accelerators has been subject of intense debate. While it appears that for extremal Kerr black holes arbitrarily high center of mass energies could be achieved, several works pointed out that both theoretical as well as astrophysical arguments would severely dampen the attainable energies. In this work we study particle collisions near Kerr--Newman black holes, by reviewing and extending previously proposed scenarios. Most importantly, we implement the hoop conjecture for all cases and we discuss the astrophysical relevance of these collisional Penrose processes. The outcome of this investigation is that scenarios involving near-horizon target particles are in principle able to attain, sub-Planckian, but still ultra high, center of mass energies of the order of $10^{21}-10^{23}$ eV. Thus, these target particle collisional Penrose processes could contribute to the observed spectrum of ultra high-energy cosmic rays, even if the hoop conjecture is taken into account, and as such deserve further scrutiny in realistic settings.
Classical black holes shield us from the singularities that inevitably appear in general relativity. Being singularity regularization one of the main landmarks for a successful theory of quantum gravity, quantum black holes are not obliged to hide their inner core from the outside world. Notwithstanding the aforesaid, it is often implicitly assumed that quantum gravity effects must remain confined to black hole interiors. In this essay we argue in the opposite direction, discussing theoretical evidence for the existence of strong correlations between the physics inside and outside non-singular black holes. We conclude that astronomical tests of the surroundings of black holes can provide invaluable information about their so-far unexplored interiors.
We show that a single imperfect fluid can be used as a source to obtain the generalized McVittie metric as an exact solution to Einsteins equations. The mass parameter in this metric varies with time thanks to a mechanism based on the presence of a temperature gradient. This fully dynamical solution is interpreted as an accreting black hole in an expanding universe if the metric asymptotes to Schwarzschild-de Sitter at temporal infinity. We present a simple but instructive example for the mass function and briefly discuss the structure of the apparent horizons and the past singularity.