In the first part of my talk I will discuss the variational principle for general relativity and some associated subtle facts. In particular, I will try to arrive at the correct action principle for general relativity in presence of null boundaries. Possible generalization to Lovelock theories will also be presented. In the second part of my talk, I will discuss the thermodynamics of null surfaces. In particular, I will show that three different projections of gravitational momentum related to an arbitrary null surface in the space time leads to three different equations, all of which have thermodynamic interpretations.
I will review my recent work concerning three different topics: exact solutions due to a magnetic field balanced by the cosmological constant, an infinite periodic configuration of black holes, and a toy model mimicking the fall of an oscillating spring into a Schwarzschild black hole.
A notable class of torsionful but curvatureless gravitational theories of gravity, known as teleparallel theories of gravity (or teleparallel gravity in brief), arise from assuming that both the non-metricity and the curvature of the affine connection are zero. Teleparallel theories of gravity have a long history of analysis, including Einstein himself who believed that the space of distant parallelism, (also called ``absolute parallelism'' or ``tele-parallelism'' by others) was the most promising candidate to unify gravitation and electromagnetism. Intriguingly, there exists a subclass of teleparallel theories of gravity that are dynamically equivalent to general relativity.
In teleparallel gravity and its generalizations, a frame basis replaces the metric as the central object of study, although the metric can still be constructed from the frame basis. Consequently, the concept of an isometry as a symmetry of the metric may no longer act as a symmetry of a solution to a given teleparallel gravity theory. However, for any teleparallel gravity solution, the set of symmetries are related to the set of invariants and studying the set of invariants will provide information about the symmetries. In this talk, I will discuss the equivalence algorithm for teleparallel gravity, which provides a set of invariants that uniquely characterizes (locally) a teleparallel gravity solution, and use this set of invariants to determine the group of symmetries for the space.
I will discuss the problem which arises by the existence of zero cover measures in the classical limit of the consistent histories approach of quantum theory. I will analyze the time-of-arrival of a (semi-) classical free particle in an infinite square well and I will show how we end up with contrary inferences.
The global hyperbolicity assumption present in gravitational collapse singularity theorems is in tension with the quantum mechanical phenomenon of black hole evaporation. In this work I show that the causality conditions in Penrose’s theorem can be almost completely removed. As a result, it is possible to infer the formation of spacetime singularities even in absence of predictability and hence compatibly with quantum field theory and black hole evaporation.
The effective action was originally proposed by J. Schwinger who used his differential technique based on the proper time. Later B.S. DeWitt included gravity and non-Abelian gauge fields that made the theory geometrical. G.A. Vilkovisky proposed the covariant perturbation theory which delivers the covariant nonlocal effective action, intially designed to be applied to the Hawking radiation problem. The effective action, derived from the kernel of the evolution equation with the Laplace type operator, is a phenomenological functional expressed in the field strength tensors of physical fields. It is finite in all orders of the tensors (curvatures) and nonlocal starting from the second order. For the Dirac operartor, its two lowest local orders correspond to the cosmological constant term and the gravity action. This explains the Sakharov-DeWitt conjecture in a purely geometrical language. The effective action generates the covariant nonlocal energy-momentum tensor that can solve evolution problems with gravitational and electromagnetic fields, with backreaction. The action's higher order, nonlocal terms generalize the classical actions of gravity and gauge fields.
The ESA-led mission LISA (Laser interferometer space antenna) is a space-based gravitational-wave detector planned to be launched in the 2030s. It promises to probe binaries within our galaxy, and to catch a few events involving supermassive black holes. Apart from that, it could also spot more speculative phenomena from intermediate-mass black holes to decays of cosmic strings. But what should we do next? Should we explore other gravitational-wave bands, or dig deeper in the LISA frequency range? Or should we instead increase our angular resolution so that telescopes in the electromagnetic band can take a look as well? In the Voyage 2050 call issued by ESA the members of the LISA consortium built a case for each of those options, and in this talk I report on the discussion.
The Teukolsky master equation — fundamental equation for test fields of any spin, or perturbations, in type D spacetimes — is usually treated in its separated form in analytical calculations. Then the solutions representing even the simplest sources — point particles — are expressed in terms of series. The only known exception is a static particle (charge or mass) in the vicinity of Schwarzschild black hole. We present a generalization of this result to a static point particle of arbitrary spin at the axis of Kerr black hole. A simple algebraic formula for the Debye potential from which all the NP components of the field under consideration can be generated is written down. Later, we focus on the electromagnetic field and employ the old Appell's trick to get so called electromagnetic magic field on the Kerr background. We also show that a static electric point charge above the Kerr black hole induces, except an expected electric monopole, also a magnetic monopole charge on the black hole itself. This contribution has to be compensated. On a general level we show that any solution of Teukolsky equation can serve as a Debye potential for field of the same spin and vice versa. We also discuss the Teukolsky–Starobinsky identities.