Seminar is held on Tuesdays at 13:10 pm in the lecture room of the Institute
on the 10th floor of the department building at Trója, V Holešovičkách 2, Prague 8
The number of baryons in the observable universe is of the order of 10^{80}, as is the number of electrons. The number of photons is about nine orders of magnitude greater, 10^{89}, as is the estimated number of neutrinos. However, the number of gravitons could be much larger, from processes such as inflation or from the coalescence of black holes.
Regular black holes have become a popular alternative to the singular mathematical black holes predicted by general relativity as they circumvent mathematical pathologies associated with the singularity while preserving crucial black hole features such as the trapping of light. Here, we will analyze how to generate these geometries and study their thermodynamic properties within the framework of general relativity using nonlinear electrodynamics. Our study reveals that the regularization of the singularity, through the introduction of a minimal length scale, has a plethora of implications, one of which is the absence of the Hawking-Page phase transition. The presence of magnetic charge introduces this minimal length scale and leads to the phenomenon of birefringence, resulting in the splitting of circular light rays with different polarizations. One polarization propagates through the background geometry, while the other travels in an effective (optical) metric. We compare the light rings in both geometries and demonstrate that, for certain values of the minimal length scale parameter, a single light ring is possible for horizonless ultracompact objects. We extend our study to the dynamical case, showing that the internal energy in the first law of black hole thermodynamics is captured by the Misner-Sharp mass and demonstrating that the linear coefficient of the Misner-Sharp mass expansion near the outer apparent horizon suffices for a complete thermodynamic description. Additionally, we analyze the behavior of the null energy condition and find that it is violated in the vicinity of the outer horizon and satisfied in the vicinity of the inner horizon, which implies that the trapped spacetime region (as determined from the behavior of null geodesic congruences) is effectively separated into an NEC-violating and an NEC-non-violating domain. Moreover, we show that massive observers and particles can cross the inner and outer horizon on an ingoing geodesic, and thus entering and exiting the supposedly trapped spacetime region is possible.
Jiří Bičák Oldřich Semerák