Valeri P. Frolov’s research while affiliated with University of Alberta and other places

Recently it was demonstrated that by adding to the Einstein-Hilbert action a series in powers of the curvature invariants with specially chosen coefficients one can obtain a theory of gravity which has spherically symmetric solutions describing regular black holes. Its reduced action depends on a function of one of the basic curvature invariants of the corresponding metric. In this paper we study a generalization of this model to the case when this function depends on all the basic curvature invariants. We show that the metrics which are solutions of such a model possess a universal scaling property. We demonstrate that there exists a special class of such models for which the "master" equation basic curvature invariant is a linear second order ordinary differential equation. We specify a domain in the space of parameters of the model for which the corresponding solutions describe regular static spherically symmetric black holes and study their properties.

In this paper, we consider a rotating black hole with electric and magnetic monopole charges that moves in a static homogeneous electromagnetic field. We assume that both the charges and the fields are weak, so that they have no effect on the spacetime geometry, which is described by the Kerr metric. We present exact solutions to Maxwell’s equations describing the field of a charged rotating black hole moving in an external field background. We use these solutions to calculate the energy, momentum, and angular momentum fluxes of the electromagnetic field into the black hole. Using these results, we obtain expressions for the torque and force acting on the moving charged rotating black hole arising as a result of its interaction with the external electromagnetic field. We calculate these quantities both in the frame comoving with the black hole and in the frame of the external background field. We use this result to derive the equations that govern the change in the black hole’s mass and spin as well as the motion of the black hole. We provide exact solutions for specific cases which illustrate the role of charge and spin on the motion of the black hole.

In this paper we consider a rotating black hole with electric and magnetic monopole charges that moves in a static homogeneous electromagnetic field. We assume that both the charges and the fields are weak, so that they have no effect on the spacetime geometry, which is described by the Kerr metric. We present exact solutions to Maxwell's equations describing the field of a charged rotating black hole moving in an external field background. We use these solutions to calculate the energy, momentum, and angular momentum fluxes of the electromagnetic field into the black hole. Using these results, we obtain expressions for the torque and force acting on the moving charged rotating black hole arising as a result of its interaction with the external electromagnetic field. We calculate these quantities both in the frame comoving with the black hole and in the frame of the external background field. We use this result to derive the equations that govern the change in the black hole's mass and spin, as well as the motion of the black hole. We provide exact solutions for specific cases which illustrate the role of charge and spin on the motion of the black hole.

In this paper we consider the motion of a rotating black hole through a static, homogeneous, massless scalar field. In the general case, a constant vector of the field gradient can be timelike, spacelike, or null. We consider and compare all of these cases. We demonstrate that as a result of the interaction of the black hole with the scalar field, its mass, spin, and relative velocity with respect to the field can change. We obtain the equations describing the evolution of these parameters and present solutions of the obtained equations for some simple cases.

In the present paper, we consider a rotating black hole moving in a static homogeneous electromagnetic field. We assume that the field is weak and neglect its backreaction on the geometry, so that the metric at far distance from the black hole is practically flat. We present an exact solution for a stationary electromagnetic field in the presence of the black hole for this problem and use it to calculate fluxes of the energy, momentum and angular momentum into the black hole. Using these results we derive the equations of motion of the rotating black hole in the electromagnetic field and discuss some of the interesting solutions of these equations. In particular, we demonstrate how the interaction of the spin of the black hole with the external magnetic field changes its trajectory.

In the present paper, we consider a rotating black hole moving in a homogeneous massless scalar field. We assume that the field is weak and neglect its backreaction so that the metric at far distance from the black hole is practically flat. In this domain, one can introduce two reference frames, K and K˜. The frame K˜ is associated with the homogeneous scalar field, in which its constant gradient has only time component. The other frame, K, is the frame in which the black hole is at rest. To describe the Kerr metric of the black hole, we use its Kerr-Schild form gμν=ημν+Φlμlμ, where ημν is the (asymptotic) flat metric in K frame. We find an explicit solution of the scalar field equation, which is regular at the horizon, and properly reproduce the asymptotic form of the scalar field at the infinity. Using this solution, we calculate the fluxes of the energy, momentum and the angular momentum of the scalar field into the black hole. This allows us to derive the equation of motion of the rotating black hole. We discuss main general properties of solutions of these equations and obtain explicit solutions for special type of the motion of the black hole.

In the present paper, we discuss a nonlocal modification of the Kerr metric. Our starting point is the Kerr–Schild form of the Kerr metric gμν=ημν+Φlμlμ. Using Newman’s approach, we identify a shear free null congruence l with the generators of the null cone with apex at a point p in the complex space. The Kerr metric is obtained if the potential Φ is chosen to be a solution of the flat Laplace equation for a point source at the apex p. To construct the nonlocal modification of the Kerr metric, we modify the Laplace operator ▵ by its nonlocal version exp(−ℓ2▵)▵. We found the potential Φ in such an infinite derivative (nonlocal) model and used it to construct the sought-for nonlocal modification of the Kerr metric. The properties of the rotating black holes in this model are discussed. In particular, we derived and numerically solved the equation for a shift of the position of the event horizon due to nonlocality. AlbertaThy 5–23.

In the present paper, we discuss a nonlocal modification of the Kerr metric. Our starting point is the Kerr-Schild form of the Kerr metric $g_{\mu\nu}=\eta_{\mu\nu}+\Phi l_{\mu}l_{\mu}$. Using Newman's approach we identify a shear free null congruence $\boldsymbol{l}$ with the generators of the null cone with apex at a point p in the complex space. The Kerr metric is obtained if the potential $\Phi$ is chosen to be a solution of the flat Laplace equation for a point source at the apex p. To construct the nonlocal modification of the Kerr metric we modify the Laplace operator $\triangle$ by its nonlocal version $\exp(-\ell^2\triangle)\triangle$. We found the potential $\Phi$ in such an infinite derivative (nonlocal) model and used it to construct the sought-for nonlocal modification of the Kerr metric. The properties of the rotating black holes in this model are discussed. In particular, we derived and numerically solved the equation for a shift of the position of the event horizon due to nonlocality.

In this paper, the orbits of a charged particle near the event horizon of a magnetized black hole are investigated. For a static black hole of mass M immersed in a homogeneous magnetic field B, the dimensionless parameter b=eBGM/(mc4) controls the radius of the circular orbits and determines the position of the innermost stable circular orbit (ISCO), where m and e are the mass and charge of the particle. For large values of the parameter b, the ISCO radius can be very close to the gravitational radius. We demonstrate that the properties of such orbits can be effectively and easily found by using a properly constructed “near-horizon approximation.” In particular, we show that the effective potential (which determines the position of the orbit) can be written in a form which is invariant under rescaling of the magnetic field and as a result is universal in this sense. We also demonstrate that in the near-horizon approximation, the particle orbits are stationary worldlines in Minkowski spacetime. We use this property to solve the equation describing slow changes in the distance of the particle orbit from the horizon, which arise as a result of the electromagnetic field radiated by the particle itself. This allows us to evaluate the lifetime of the particle before it reaches the ISCO and ultimately falls into the black hole.

In the present paper we discuss properties of a model of a ring wormhole, recently proposed by Gibbons and Volkov [Phys. Rev. D 96, 024053 (2017); J. Cosmol. Astropart. Phys. 05 (2017) 039; Phys. Lett. B 760, 324 (2016)]. Such a wormhole connects two flat spacetimes which are glued through disks of the radius a bounded by the string with negative angle deficit −2π. The presence of the string’s matter violating the null-energy condition makes the wormhole static and traversable. We study gravitational field of static sources in such a spacetime in the weak-field approximation. In particular, we discuss how a field of an oblate thin massive shell surrounding one of the wormhole’s mouths is modified by its presence. We also obtain a solution of a similar problem when both mouths of the wormhole are located in the same space. This approximate solution is found for the case when the distance L between these mouths is much larger than the radius a of the ring. We demonstrate that the corresponding locally static gravitational field in such a multiply connected space is nonpotential. As a result of this, the proper time gap for the clock’s synchronization linearly grows with time and closed timelike curves are formed. This process inevitably transforms such a traversable ring wormhole into a time machine. We estimate the timescale of this process.