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Of the various energy conditions which can be assumed when studying mathematical general relativity, intuitively the simplest is the weak energy condition $\mu\geq 0$ which simply states that the observed mass-energy density must be…

Quantized space described by time reversal invariant and rotationally invariant noncommutative algebra of canonical type is studied. A particle in uniform field is considered. We find exactly the energy of a particle in uniform field in the…

We study potentially observable consequences of spatiotemporal discreteness for the motion of massive and massless particles. First we describe some simple intrinsic models for the motion of a massive point particle in a fixed causal set…

When Hawking radiation from a rotating or non-rotating black hole becomes sufficiently intense, its own stress energy can no longer be treated as a perturbation on a fixed background. In this regime the outgoing flux may generate an…

We suggest a new relativity principle, which asserts the impossibility to distinguish the state of rest and the state of motion at the constant velocity of a system, if no work is done to the system in question during its motion. We suggest…

We consider a run-and-tumble particle whose speed and tumbling rate are space-dependent on an infinite line. Unlike most of the previous work on such models, here we make the physical assumption that at large distances, these rates saturate…

We present a new upper limit on the energy that may be extracted from a Kerr black hole by means of particle collisions in the ergosphere (i.e., the "collisional Penrose process"). Earlier work on this subject has focused largely on…

The monopole singularity string, infinite direct line in the rest reference frame, is considered as a rigid physical line, and behavior of its geometrical form under the Lorentz transformations is studied. The method to test the form of any…

We study the question of conditions for the existence of negative-energy states of particles in the absence of external fields in inertial and noninertial frames of reference. We show that in the nonrelativistic case in noninertial…

In this paper, we revisit the interpretation of the circular Unruh effect. To this aim, we rely on the principle of general covariance applied to the decay properties of non-inertial particles. Specifically, we show how the tree-level decay…

Non-time-orthogonal frame analysis is applied to determine the frequency and wavelength of light as observed i) in a relativistically rotating frame when emission is from a source fixed in the non-rotating frame, ii) in a non-rotating frame…

The equation of the Doppler shift of two bodies in inertial motion in a reference frame at rest (i.e., stationary reference frame) is derived. In this derivation, the wave-particle duality of photons in the theory of special relativity is…

We show that recent observation made in Grib and Pavlov, Europhys. Lett. 101 (2013) 20004 for the Kerr black hole is valid in the general case of rotating axially symmetric metric. Namely, collision of two particles in the ergosphere leads…

This paper investigates the repetitive Penrose process in accelerating Kerr black holes and explores the influence of the acceleration factor on the repetitive Penrose process. After a brief review of accelerating Kerr black holes, we study…

Results from general relativistic theoretical Monte Carlo computer simulations of Compton scattering and e-e+ pair production processes in the ergosphere of a supermassive (10^8 solar mass) rotating black hole are presented. Particles from…

We consider the Penrose process with the charged particles in the Reissner-Nordstr\"{o}m (RN) background. Let parent particle 0 decay to particles 1 and 2. With the assumption that all three particles move in the equatorial plane, the exact…

The detection of quantum gravity effects is highly limited in both macroscopic and microscopic scenarios: The small quantum parameter makes most large-scale observations practically indistinguishable from general relativity. While at the…

We consider a particle moving towards a rotating black hole. We are interested in the number of its revolution $n$ around a black hole. In our previous work (Pavlov and Zaslavskii in Gen Relativ Gravit 50: 14, 2018. arXiv:1707.02860) we…

A monochromatic linear source of light is rotated with certain angular frequency and when such light is analysed after reflection then a change of frequency or wavelength may be observed depending on the location of the observer. This…

We consider the quasi-black hole limit of a stationary body when its boundary approaches its own gravitational radius, i.e., its quasi-horizon. It is shown that there exists a perfect correspondence between the different mass contributions…