Seminář se koná v úterý ve 13:10 v posluchárně ÚTF MFF UK
v 10. patře katedrové budovy v Tróji, V Holešovičkách 2, Praha 8
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.
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.
Jiří Bičák Oldřich Semerák