Narrow Results

In general, elementary particles as well as extensive bodies have internal degrees of freedom that naturally turn their trajectories into accelerated curves. Hence, we propose to describe the kinematical properties of nongeodesic congruences and study how tidal forces are modified. Once the general scenario is well established, we analyze in details tidal effects due to electromagnetic fields, i.e. the relative acceleration between test charged particles. An algebraic analysis of these fields is developed together with a geometrical interpretation in terms of local field lines. In this framework, we compare general relativity and electrodynamics in terms of operationally equivalent objects.

We study the properties of the congruence of null geodesics propagating near the so-called truly naked horizons (TNHs) — objects having a finite Kretschmann scalar but with diverging tidal acceleration for freely falling observers. The expansion of outgoing rays near the future horizon always tends to vanish for the nonextremal case but may be nonzero for the distorted (ultra)extremal one. It tends to diverge for the ingoing rays if the the null energy condition (NEC) is satisfied in the vicinity of the horizon outside. However, it also tends to zero for NEC-violating cases except for the remote horizons. We also discuss the validity of test particle approximation for TNHs and find the sufficient condition for the backreaction to remain small.

Tidal forces produced by black holes are an important result of General Relativity related to the spacetime curvature tensor. Among the astrophysical implications of tidal forces, the tidal disruption events stand out. We analyze the tidal forces in the spacetime of an electrically charged Hayward regular black hole, obtaining the components of the tidal tensor and the geodesic deviation equation. We find that the radial and angular tidal forces may vanish and change sign unlike in the Schwarzschild spacetime. We note that tidal forces are finite at the origin of the radial coordinate in this regular black hole spacetime. We obtain the geodesic deviation vector for a body constituted of dust infalling towards the black hole with two different initial conditions.

In this paper, we take a closer and new look at the effects of tidal forces on the free fall of a quantum particle inside a spherically symmetric gravitational field. We derive the corresponding Schrödinger equation for the particle by starting from the fully relativistic Klein–Gordon equation in order (i) to briefly discuss the issue of the equivalence principle and (ii) to be able to compare the relativistic terms in the equation to the tidal-force terms. To the second order of the nonrelativistic approximation, the resulting Schrödinger equation is that of a simple harmonic oscillator in the horizontal direction and that of an inverted harmonic oscillator in the vertical direction. Two methods are used for solving the equation in the vertical direction. The first method is based on a fixed boundary condition, and yields a discrete-energy spectrum with a wavefunction that is asymptotic to that of a particle in a linear gravitational field. The second method is based on time-varying boundary conditions and yields a quantized-energy spectrum that is decaying in time. Moving on to a freely-falling reference frame, we derive the corresponding time-dependent energy spectrum. The effects of tidal forces yield an expectation value for the Hamiltonian and a relative change in time of a wavepacket’s width that are mass-independent. The equivalence principle, which we understand here as the empirical equivalence between gravitation and inertia, is discussed based on these various results. For completeness, we briefly discuss the consequences expected to be obtained for a Bose–Einstein condensate or a superfluid in free fall using the nonlinear Gross–Pitaevskii equation.

Vacuum models of charged or spinning black holes possess two horizons, the inner of which has the oft-overlooked property that gravitational tidal forces initially spaghettifying a freely falling observer will eventually change signs and flatten the observer like a pancake. Inner horizons also may induce a classical blueshift instability known as mass inflation, and a number of recent studies have found that inner horizons exhibit even stronger quantum singular behavior. In this essay, we explore the quantum effect of Hawking radiation, which in the presence of compressive tidal forces seems to predict negative temperatures. By analyzing the interaction of quantum fields with black hole geometries, we can come to a closer semiclassical understanding of what really happens near a black hole’s inner horizon.

In the paper the work of the tidal forces that arise when the relative deviation of the protons on distance of the order of the Compton wavelength near the horizon of Kerr black hole is considered. For ease of calculation the assumption is made that the proton has only a radial component of the velocity. It is shown that the work of the tidal forces at speeds close to the speed of light sharply increases with Lorentz factor and it can obtain very high energy of the Grand Unification order.

In the paper the dependence of the tidal forces for the two protons at a distance of the order of the Compton wavelength from the polar angle in the Kerr spacetime is considered. It is shown that in approach to the equatorial plane the tidal forces are increase.