We will introduce GHP-formalism in the context of cosmological perturbation theory. We will obtain an interesting result in perturbations of FLRW spacetimes. Perturbations in f(R)-cosmologies will be introduced in the second part of my talk. We will mention mathematical apparatus of scalar perturbations in f(R)-gravities in the late universe and we'll talk about physical applications of our result.
We study static scalar and Maxwell fields created by a source in a static D-dimensional spacetime. We demonstrate that the corresponding equation for these field is invariant under a special transformation of the background metric. This transformation consists of the static conformal transformation of the spatial part of the metric accompanied by a properly chosen transformation of the red-shift factor. Both transformations are determined by one function of the spatial coordinates. We show that in a case of higher dimensional spherically symmetric black holes one can find such a bi-conformal transformation that the symmetry of the D-dimensional metric is enhanced after its application. Namely, the metric becomes a direct sum of the metric on a unit sphere and the metric of the anti-de Sitter space. The method of the heat kernels allows one to obtain static Green functions in the original space of the static black hole. The general useful representation of static Green functions is obtained in the Schwarzschild-Tangherlini spacetimes of arbitrary dimension. Using this method we obtained the exact closed form for the potentials of massless scalar and Maxwell fields created by static charges near four- and five-dimensional charged black holes.
In 2012, Almheiri, Marolf, Polchinski and Sully (AMPS) published a surprising result that the equivalence principle is in conflict with the assumption that the information is conserved during the black hole formation and evaporation. In standard GR, an observer freely falling into the black hole does not encounter anything unusual, while AMPS argue that such an observer will be burnt by a firewall. The aim of the seminar is to provide a brief introduction to the firewall paradox and to present the argumentation of AMPS.
In proceeding from Lagrangian to Hamiltonian, it may happen that not all momenta are independent functions of the velocities, so one cannot express all velocities as functions of momenta and coordinates only. One thus gets constraints. In this seminar we show how to write down eguations of motion in such a case. We introduce the notion of Dirac brackets, apply the formalism to two simple Lagrangians and also compute the relativistic particle in flat space-time.
(Second part of a mini-course on numerical relativity:) In 1993 Abrahams and Evans presented numerical simulations of gravitational waves. They evolved members of one-parameter families of initial data which either settled to flat-space or collapsed to form a black hole if the strength parameter was sufficiently large. Tuning to the threshold of black-hole formation they found evidence of critical behavior. Despite several attempts this result has not been reproduced. In this talk I will discuss a new attack on the problem.
In my last talk I will focus on the principle question: what is the consequence of the gauge freedom of general relativity in building free-evolution formulations for numerical relativity.
Light rays passing close to a black hole experience very strong deflections and can give rise to infinite sequences of images for any given source. We show how these images can be analytically described for any kinds of static or rotating metrics. We also discuss the caustics of the Kerr metric, which become larger and larger for higher orders. Some perspectives for observations of the strong deflection phenomenology come from the black hole in the Galactic center, where high resolution observational efforts are being concentrated. Finally, we consider metrics falling as 1/r^n, which are characterized by quite peculiar phenomena related to violations of the energy conditions.
After a brief description of NuSTAR - a NASA hard X-ray satellite in orbit since June 13, 2012 - and of its scientific objectives and main results, I will present and discuss the activities and results of the AGN Physics Working Group. In particular, I will discuss the NuSTAR impact on our understanding of: the hot corona responsible for the main X-ray emission; the strong gravity effects close to the BH; the absorption/reflection components from distant matter; the soft X-ray emission.
There is a considerable interest in the strong-field behavior of Lorentz-violating gravity theories. One point is whether or not the notion of a black hole as an absolute causal boundary persists in these theories where signals can sometimes propagate infinitely fast. Past work on spherically-symmetric black holes reveal that absolute causal boundaries exist in spite of these infinitely-fast propagating modes. The causal boundaries have come to be known as universal horizons. In this talk, I shall discuss black holes in two popular Lorentz-violating theories, Hořava gravity and Einstein-aether theory, and showcase progress made in exploring their rotating black holes. For Hořava gravity, I shall discuss three-dimensional black holes in its infrared sector. Within this setting, we have derived the most general class of stationary, circularly symmetric, asymptotically anti–de Sitter black hole solutions. I also discuss slowly rotating black holes in four-dimensional Einstein-aether theory, which we construct numerically. Most notably, we learn from these solutions that universal horizons may not be a generic feature of black holes in Lorentz-violating theories.