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
Charged and/or rotating black holes in General Relativity feature Cauchy horizons, which indicate a breakdown of predictability in the theory. Focusing on spherically symmetric charged black holes, we remark that the inevitability of Reissner-Nordstrom Cauchy horizon is due to the divergent electromagnetic self-energy of point charges. We demonstrate that any causal theory of nonlinear electrodynamics that regularizes the point charge self-energy also eliminates Cauchy horizons for weakly charged black holes. These black holes feature one (event) horizon and a spacelike singularity, analogous to the Schwarzschild metric. An example with Born-Infeld electrodynamics illustrates how this gives rise to an upper bound on the charge, which we compare with known bounds.
Spontaneous scalarization is a mechanism that allows black holes to develop a non-trivial profile of a scalar field “scalar hair” because of tachyonic instabilities, enabling tests of gravity beyond General Relativity. Motivated by stability and threshold issues in Gauss-Bonnet scalarization, we propose a new model characterized by two nonminimal couplings of the scalar field to both Gauss-Bonnet curvature and a U(1) gauge field (e.g. electromagnetic field). The presence of two distinct sources of tachyonic instability broadens the conditions for spontaneous scalarization. We track how the electric charge and the coupling constants govern the onset of the scalar field and derive new solution branches with nontrivial scalar profiles. Numerical integration shows multiple coexisting scalarized black hole solutions with adjustable thresholds, influenced by the relative strengths of curvature and matter couplings. We examine their scalar charge, horizon properties, and thermodynamic characteristics, demonstrating how the model can selectively activate or suppress scalarization phenomena. The matter source term modifies the scalarization onset and promotes stable solutions, as indicated by the evolution of the scalar charge and horizon quantities. These findings suggest an alternative approach to scalarization, may avoid the instabilities of curvature-only or matter-only models, and offer new ways to test strong-gravity effects in upcoming observations.
Extreme Mass Ratio Inspirals (EMRIs) are among the key gravitational-wave sources expected to be observed by the Laser Interferometer Space Antenna (LISA). Accurately modeling their waveforms requires accounting for various astrophysical effects, including the influence of surrounding matter, since black holes are rarely isolated. The presence of matter can break spacetime symmetries, making standard techniques inapplicable. However, by treating both the inspiraling body and the surrounding matter as independent perturbations, we can formulate the problem using a modified Teukolsky equation. In this presentation, we demonstrate how this equation can be solved in the spacetime of a Schwarzschild black hole surrounded by a ring, approximated by its leading multipoles. This calculation represents a first step toward the relativistic modeling of EMRIs in general spacetime backgrounds.
We present a large family of twisting and expanding solutions to the Einstein-Maxwell equations of algebraic type D, for which the two double principal null directions (PNDs) of the Weyl tensor are not aligned with the null eigendirections of the Faraday tensor. In addition to systematically deriving this new class, we present its various metric forms and convenient parameterizations. We show that in Boyer-Lindquist-type coordinates these solutions depend on 7 parameters, namely the Kerr and NUT (Newman-Unti-Tamburino) twist parameters a and l, mass parameter m, acceleration \alpha, strength of the Maxwell field |c|, and angular parameters \beta and \gamma that represent two duality rotations of the Faraday tensor, which include the rotation between the electric and magnetic charges generating the aligned part of the Maxwell field. This coordinate parameterization, analogous to the Griffiths-Podolský form of the Plebański-Demiański solutions, allows us to perform various limits, explicitly identify the subcases, and determine the physical interpretation of the new class. Interestingly, by considering the limit with no acceleration (\alpha->0), one obtains either the famous Kerr-Newman-NUT black holes (if the parameter |c| remains constant) or the novel Kerr-Bertotti-Robinson black holes, announced recently in our work arXiv:2507.05199 (if |c|\to \infty while \alpha|c|=const.). We may thus conclude that this new class of spacetimes represents twisting charged accelerating black holes, immersed in an external magnetic (or electric) field. In the non-twisting subcase, we obtain the previously known solution of Van den Bergh-Carminati.
We review the existing classifications of degenerate higher-order modified (metric) gravity theories with a focus on those which admit at most third order field equations, from Lovelock theories, Horndeski's scalar-tensor and generalised electrodynamics to the more recent higher-order Maxwell-Einstein (HOME) theories, involving a metric and a U(1) gauge field. We present the most general quadratic HOME whose field equations involve at most second and third derivative of the metric and U(1) gauge field, respectively. We comment on degeneracy conditions, ghost-freeness and non-integrable fields such as Proca and 2-form field theories.
Oldřich Semerák