Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userAnalysis of linear waves near the Cauchy horizon of cosmological black holes
212
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We show that linear scalar waves are bounded and continuous up to the Cauchy horizon of Reissner-Nordstrom-de Sitter and Kerr-de Sitter spacetimes, and in fact decay exponentially fast to a constant along the Cauchy horizon. We obtain our results by modifying the spacetime beyond the Cauchy horizon in a suitable manner, which puts the wave equation into a framework in which a number of standard as well as more recent microlocal regularity and scattering theory results apply. In particular, the conormal regularity of waves at the Cauchy horizon - which yields the boundedness statement - is a consequence of radial point estimates, which are microlocal manifestations of the blue-shift and red-shift effects.
rate research
Read More
Collisions of particles in black holes ergospheres may result in an arbitrarily large center of mass energy. This led recently to the suggestion (Banados et al., 2009) that black holes can act as ultimate particle accelerators. If the energy of an outgoing particle is larger than the total energy of the infalling particles the energy excess must come from the rotational energy of the black hole and hence this must involve a Penrose process. However, while the center of mass energy diverges the position of the collision makes it impossible for energetic particles to escape to infinity. Following an earlier work on collisional Penrose processes (Piran & Shaham 1977) we show that even under the most favorable idealized conditions the maximal energy of an escaping particle is only a modest factor above the total initial energy of the colliding particles. This implies that one shouldnt expect collisions around a black hole to act as spectacular cosmic accelerators.
We prove the linear stability of slowly rotating Kerr black holes as solutions of the Einstein vacuum equation: linearized perturbations of a Kerr metric decay at an inverse polynomial rate to a linearized Kerr metric plus a pure gauge term. We work in a natural wave map/DeTurck gauge and show that the pure gauge term can be taken to lie in a fixed 7-dimensional space with a simple geometric interpretation. Our proof rests on a robust general framework, based on recent advances in microlocal analysis and non-elliptic Fredholm theory, for the analysis of resolvents of operators on asymptotically flat spaces. With the mode stability of the Schwarzschild metric as well as of certain scalar and 1-form wave operators on the Schwarzschild spacetime as an input, we establish the linear stability of slowly rotating Kerr black holes using perturbative arguments; in particular, our proof does not make any use of special algebraic properties of the Kerr metric. The heart of the paper is a detailed description of the resolvent of the linearization of a suitable hyperbolic gauge-fixed Einstein operator at low energies. As in previous work by the second and third authors on the nonlinear stability of cosmological black holes, constraint damping plays an important role. Here, it eliminates certain pathological generalized zero energy states; it also ensures that solutions of our hyperbolic formulation of the linearized Einstein equation have the stated asymptotics and decay for general initial data and forcing terms, which is a useful feature in nonlinear and numerical applications.
We examine the late-time evolution of a qubit (or Unruh-De Witt detector) that hovers very near to the event horizon of a Schwarzschild black hole, while interacting with a free quantum scalar field. The calculation is carried out perturbatively in the dimensionless qubit/field coupling $g$, but rather than computing the qubit excitation rate due to field interactions (as is often done), we instead use Open EFT techniques to compute the late-time evolution to all orders in $g^2 t/r_s$ (while neglecting order $g^4 t/r_s$ effects) where $r_s = 2GM$ is the Schwarzschild radius. We show that for qubits sufficiently close to the horizon the late-time evolution takes a simple universal form that depends only on the near-horizon geometry, assuming only that the quantum field is prepared in a Hadamard-type state (such as the Hartle-Hawking or Unruh vacua). When the redshifted energy difference, $omega_infty$, between the two qubit states (as measured by a distant observer looking at the detector) satisfies $omega_infty r_s ll 1$ this universal evolution becomes Markovian and describes an exponential approach to equilibrium with the Hawking radiation, with the off-diagonal and diagonal components of the qubit density matrix relaxing to equilibrium with different characteristic times, both of order $r_s/g^2$.
One of the pronounced characteristics of gravity, distinct from other interactions, is that there are no local observables which are independent of the choice of the spacetime coordinates. This property acquires crucial importance in the quantum domain in that the structure of the Hilbert space pertinent to different observers can be drastically different. Such intriguing phenomena as the Hawking radiation and the Unruh effect are all rooted in this feature. As in these examples, the quantum effect due to such observer-dependence is most conspicuous in the presence of an event horizon and there are still many questions to be clarified in such a situation. In this paper, we perform a comprehensive and explicit study of the observer dependence of the quantum Hilbert space of a massless scalar field in the vicinity of the horizon of the Schwarzschild black holes in four dimensions, both in the eternal (two-sided) case and in the physical (one-sided) case created by collapsing matter. Specifically, we compare and relate the Hilbert spaces of the three types of observers, namely (i) the freely falling observer, (ii) the observer who stays at a fixed proper distance outside of the horizon and (iii) the natural observer inside of the horizon analytically continued from outside. The concrete results we obtain have a number of important implications on black hole complementarity pertinent to the quantum equivalence principle and the related firewall phenomenon, on the number of degrees of freedom seen by each type of observer, and on the thermal-type spectrum of particles realized in a pure state.
We investigate the asymptotic supersymmetry group of the near horizon region of the BMPV black holes, which are the rotating BPS black holes in five dimensions. When considering only bosonic fluctuations, we show that there exist consistent boundary conditions and the corresponding asymptotic symmetry group is generated by a chiral Virasoro algebra with the vanishing central charge. After turning on fermionic fluctuations with the boundary conditions, we also show that the asymptotic supersymmetry group is generated by a chiral super-Virasoro algebra with the vanishing central extension. The super-Virasoro algebra is originated in the AdS2 isometry supergroup of the near horizon solution.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
