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We utilize the gravitational decoupling via the extended geometric deformation to extend the Schwarzschild vacuum solution to new black holes in Rastall theory. By employing linear transformations that deform both the temporal and radial…
We consider the Brans-Dicke theory in non-metricity gravity, which belongs to the family of symmetric teleparallel scalar-tensor theories. Our focus lies in exploring the implications of the conformal transformation, as we derive the…
Applying a non-diagonal spherically symmetric tetrad field having arbitrary function, $S(r)$, that is corresponding to local Lorentz transformation, to the field equations of f(T) gravity theories. An analytic vacuum solutions with…
We study exact static spherically symmetric vacuum solutions in generic six-derivative gravity (i.e., without assuming specific relations between the coupling constants). Using modified Schwarzschild coordinates, we systematically classify…
Conformal Carrollian groups are known to be isomorphic to Bondi-Metzner-Sachs (BMS) groups that arise as the asymptotic symmetries at the null boundary of Minkowski spacetime. The Carrollian algebra is obtained from the Poincare algebra by…
We investigate to construct a conformal scattering theory of the spin-$1/2$ massless Dirac equation on the Kerr spacetime by using the conformal geometric method and under an assumption on the pointwise decay of the Dirac field. In…
As a preparation for a mathematically consistent study of the physics of symmetric spacetimes in a noncommutative setting, we study symmetry reductions in deformed gravity. We focus on deformations that are given by a twist of a Lie algebra…
Spherically symmetric static empty space solutions are studied in f(R) theories of gravity. We reduce the set of modified Einstein's equations to a single equation and show how one can construct exact solutions in different f(R) models. In…
Linear perturbations on Minkowski space are used to probe numerically the remote region of an asymptotically flat space-time close to spatial infinity. The study is undertaken within the framework of Friedrich's conformal field equations…
In this talk I show how to canonically quantize a massless scalar field in the background of a Schwarzschild black hole in Lema\^itre coordinates and then present a simplified derivation of Hawking radiation based upon this procedure. The…
We study the dynamics near the central singularity in spherically symmetric collapse of a massless scalar field toward Schwarzschild black hole formation. The equations of motion take different simplified forms in the early and late stages…
The field equations of a special class of tetrad theory of gravitation have been applied to tetrad space having three unknown functions of radial coordinate. The spherically symmetric vacuum stress-energy momentum tensor with one assumption…
We study the negative mass Schwarzschild spacetime, which has a naked singularity, and show that it is perturbatively unstable. This is achieved by first introducing a modification of the well known Regge - Wheeler - Zerilli approach to…
We demonstrate the uniqueness of the spacetimes recently found by us in [H. Ovcharenko and J. Podolsky, Phys. Rev. D 112 (2025) 064076]. First, we prove that the conformal-to-Carter metric ansatz we used therein is the only possible for…
Conformal Carter-Penrose diagrams are used for the visualization of hyperboloidal slices, which are smooth spacelike slices reaching null infinity. The focus is on the Schwarzschild black hole geometry in spherical symmetry, whose Penrose…
Certain exact solutions of the Einstein field equations over nonsimply-connected manifolds are reviewed. These solutions are spherically symmetric and have no curvature singularity. They provide a regularization of the standard…
We show that there exist some intimate connections between three unconventional Schr\"odinger equations based on the use of deformed canonical commutation relations, of a position-dependent effective mass or of a curved space, respectively.…
An origin and necessity of so called conformal (or,Penrose-Chernikov-Tagirov) coupling of scalar field to the metric of n-dimensional Riemannian space-time is discussed in brief. The corresponding general-relativistic field equation implies…
In the class of vacuum Petrov type D spacetimes with cosmological constant, which includes the Kerr-(A)dS black hole as a particular case, we find a set of four-dimensional operators that, when composed {\em off shell} with the Dirac,…
This article outlines the search for an exact general relativistic description of the exterior (vacuum) gravitational field of a rotating spheroidal black hole surrounded by a realistic axially symmetric disc of matter. The problem of…