An atom falling freely into a Kerr black hole in a Boulware-like vacuum is shown to emit radiation with a Planck spectrum at the Hawking temperature. For a cloud of falling atoms with random initial times, the radiation is thermal. The existence of this radiation is due to the acceleration of the vacuum field modes with respect to the falling atom. Its properties can be traced to the dominant role of conformal quantum mechanics (CQM) in the neighborhood of the event horizon. We display this effect for a scalar field, though the acceleration radiation has a universal conformal behavior that is exhibited by all fields in the background of generic black holes.
We globally embed (3+1)-dimensional Schwarzschild and Schwarzschild-AdS black holes in massive gravity into (5+2)-dimensional flat spacetimes. Making use of embedding coordinates, we directly obtain the generalized Hawking, Unruh and freely falling temperatures in a Schwarzschild and Schwarzschild-AdS black hole due to massive graviton effects.
We find radiation in an infalling frame and present an explicit analytic evidence of the failure of no drama condition by showing that an infalling observer finds an infinite negative energy density at the event horizon. The negative and positive energy density regions are divided by the newly defined zero-energy curve. The evaporating black hole is surrounded by the negative energy which can also be observed in the infalling frame.
We show that the field equations of the Schwarzschild geometry are invariant under passive Lorentz transformations to a freely falling system. We decompose the field equations with respect to the accelerated system and find that the force of gravity is not transformed away but dynamically compensated.
We study the motion of free masses subject to the influence of standing gravitational waves in the polarized Gowdy cosmology with a three-torus topology. We show that antinodes attract freely falling particles and we trace the velocity memory effect.
We derive an expression for effective gravitational mass for any closed spacelike 2-surface. This effective gravitational energy is defined directly through the geometrical quantity of the freely falling 2-surface and thus is well adapted to intuitive expectation that the gravitational mass should be determined by the motion of test body moving freely in gravitational field. We find that this effective gravitational mass has reasonable positive value for a small sphere in the non-vacuum space-times and can be negative for vacuum case. Further, this effective gravitational energy is compared wi…
The structure of quantum vacuum in presence of gravity, and the corresponding vacuum energy density $ρ_{v}$, is expected to depend on the coupling between the UV scale $\ell_\mathrm{\textsf{UV}}$ and spacetime curvature. We determine this coupling in an arbitrary freely falling frame characterised by it's geodesic tangent $U^i(τ)$. We show that local vacuum modes within a small causal diamond based on $U^i(τ)$, whose size is set by wavelength of the modes, generically give a contribution $ρ_{0}$ to $ρ_v$ which, to leading order, scales as: $ρ_{0} = \left( π\hbar c/2 \right) {\mathrm{\textsf R}…
First sketch of black hole from M87 galaxy was obtained by Event Horizon Telescope, recently. As appearance of black hole shadow reflects space-time geometry of black holes, observations of black hole shadow may be a promising way to test general relativity in strong field regime. In this paper, we focus on angular radius of spherical black hole shadow with respect to freely falling observers. In the framework of general relativity, aberration formulation and angular radius-gravitational redshift relation are presented. For the sake of intuitive, we consider parametrized Schwarzschild black ho…
We carry out the first investigation of the entanglement and mutual information harvesting protocols for detectors freely falling into a black hole. Working in $(1+1)$-dimensional Schwarzschild black hole spacetime, we consider two pointlike Unruh-DeWitt (UDW) detectors in different combinations of free-falling and static trajectories. Employing a generalization of relative velocity suitable for curved spacetimes, we find that the amount of correlations extracted from the black hole vacuum, at least outside the near-horizon regime, is largely kinematic in origin (i.e. it is mostly due to the r…
Free fall in a uniform gravitational field is revisited in the case of quantum states with and without classical analogue. The interplay between kinematics and dynamics in the evolution of a falling quantum test particle is discussed allowing for a better understanding of the equivalence principle at the operational level.
We compute the black hole horizon entanglement entropy S_E for a massless scalar field, first with a hard cutoff and then with high frequency dispersion, both imposed in a frame that falls freely across the horizon. Using WKB methods, we find that S_E is finite for a hard cutoff or super-luminal dispersion, because the mode oscillations do not diverge at the horizon and the contribution of high transverse momenta is cut off by the angular momentum barrier. For sub-luminal dispersion the entropy depends on the behavior at arbitrarily high transverse momenta. In all cases it scales with the hori…
A good definition for the energy momentum tensor of gravity (EMTG) in General Relativity (GR) is a hard, if not impossible, task. On the other hand, in its teleparallel version, known as The Teleparallel Equivalent of General Relativity (TEGR), one can define the EMTG in a very satisfactory way. In this paper, it is proved that the EMTG of TEGR for linearized gravitational waves (GWs) is the same as the version of GR that is usually given in the literature. In addition, the exact version of the EMTG for a $pp-$wave with a $+$ polarization is obtained in a freely falling frame (FFF). Unlike the…
I briefly argue for logical necessity to incorporate, besides c, hbar, two fundamental length scales in the symmetries associated with the interface of gravitational and quantum realms. Next, in order to clear the proverbial bush, I discuss the CPT and indistinguishability issue related to recent non-linear deformations of special relativity and suggest why algebraically well-defined extensions of special relativity do not require non-linear deformations. That done, I suggest why the stable Snyder-Yang-Mendes Lie algebra should be considered as a serious candidate for the symmetries underlying…
We analyze Hawking radiation as perceived by a freely-falling observer and try to draw an inference about the region of origin of the Hawking quanta. To do so, first we calculate the energy density from the stress energy tensor, as perceived by a freely-falling observer. Then we compare this with the energy density computed from an effective temperature functional which depends on the state of the observer. The two ways of computing these quantities show a mismatch at the light ring outside the black hole horizon. To better understand this ambiguity, we show that even taking into account the (…
We evaluate the accuracy to be expected for the measurement of free fall acceleration of antihydrogen in the GBAR experiment, accounting for the recoil transferred in the photodetachment process. We show that the uncertainty on the measurement of gravity comes mainly from the initial velocity dispersion in the ion trap so that the photodetachment recoil is not the limiting factor to the precision as a naive analysis would suggest. This result will ease the constraints on the choice of the photodetachment laser parameters.
We study the Lamb shift of both freely-falling and static two-level atoms in interaction with quantized conformally coupled massless scalar fields in the de Sitter-invariant vacuum. We find that the Lamb shifts of both freely-falling and static atoms are in structural similarity to that of an inertial atom immersed in a thermal bath in a Minkowski spacetime. For the freely-falling atom, the Lamb shift gets a correction as if it was immersed in a thermal bath at the Gibbons-Hawking temperature, thus revealing clearly the intrinsic thermal nature of de Sitter spacetime. For the static atom, the …
The time evolution of a two-level atom which is simultaneously exposed to the field of a running laser wave and a homogeneous gravitational field is studied. The result of the coupled dynamics of internal transitions and center-of-mass motion is worked out exactly. Neglecting spontaneous emission and performing the rotating wave approximation we derive the complete time evolution operator in an algebraical way by using commutation relations. The result is discussed with respect to the physical implications. In particular the long time and short time behaviour is physically analyzed in detail. …
We consider the interpretation of tetrad fields as reference frames in spacetime. Reference frames may be characterized by an antisymmetric acceleration tensor, whose components are identified as the inertial accelerations of the frame (the translational acceleration and the frequency of rotation of the frame). This tensor is closely related to gravitoelectromagnetic field quantities. We construct the set of tetrad fields adapted to observers that are in free fall in the Schwarzschild spacetime, and show that the gravitational energy-momentum constructed out of this set of tetrad fields, in th…
It is well-known that the Riemann curvature tensor has no discontinuity at the black hole horizon. It is also well-known that a freely falling observer takes finite time to reach the horizon from an outside point. However, the usual assumption is that such an observer resides in a frame of reference (spaceship) of infinitesimal size. This assumption is justified as long as the coordinates are continuous enough to assume that the observer's frame is small compared to the variations of the metric from a local flat metric. Such an assumption may be invalid when the coordinate system has not only …
The analytical understanding of quasinormal mode ringing requires an accurate knowledge of the Green's function describing the response of the black hole to external perturbations. We carry out a comprehensive study of quasinormal mode excitation for Kerr black holes. Relying on the formalism developed by Mano, Suzuki and Takasugi, we improve and extend previous calculations of the quasinormal mode residues in the complex frequency plane ("excitation factors" B_q). Using these results we compute the "excitation coefficients" C_q (essentially the mode amplitudes) in the special case where the s…
The Karlhede invariant is formed from the contraction of the covariant derivative of the Riemann tensor. It is a coordinate invariant that vanishes at the Schwarzschild event horizon $r=2m$. The vanishing of the invariant allows an observer to construct a local measuring device and use it to detect an event horizon while falling into a black hole. Recent proposals postulate the existence of a "firewall" at the event horizon that may incinerate an infalling observer. These proposals face an apparent paradox if a freely falling observer detects nothing special in the vicinity of the horizon. The…
A recent calculation shows that the observed energy density in the Unruh state at the future event horizon as seen by a freely falling observer is finite if the observer is released from rest at any positive distance outside the horizon; however, it is getting larger and larger so that it is negatively divergent at the horizon in the limit that the observer starts falling from rest at the horizon, which corresponds to the infinite boost with respect to the freely falling observer at a finite distance from the horizon. In order to resolve some conflicts between the recent calculation and the co…
The principle of equivalence is used to examine covariant descriptions of quantum phenomena within the global exterior of geometries described using Painlevé- Gullstrand coordinates, which are everywhere non-singular away from their center. The differences between the descriptions of observers stationary within the curvilinear geometry and those in a locally-flat freely-falling system that is momentarily at rest are found to depend only on local proper accelerations, becoming vanishingly small for increasingly distant observers. Away from the horizon, the local detections of outgoing massless …
Freely falling point-like objects converge toward the center of the Earth. Hence the gravitational field of the Earth is inhomogeneous, and possesses a tidal component. The free fall of an extended quantum mechanical object such as a hydrogen atom prepared in a high principal-quantum-number state, i.e. a circular Rydberg atom, is predicted to fall more slowly than a classical point-like object, when both objects are dropped from the same height above the Earth's surface. This indicates that, apart from transitions between quantum states, the atom exhibits a kind of quantum mechanical incompres…
Dynamical evolution of black holes may be studied perturbatively in the membrane picture. We study the case of a body freely falling into a black hole, in the Rindler approximation. The motivation is to see if this process is accompanied by the induction of a non-zero supertranslation. Following previous studies, a notion of induction of supertranslation during a dynamical evolution is first introduced and then, the case of a freely falling body is investigated.
On the basis of the relativistic mass-energy concept we found that a proper mass of a test particle in a gravitational field depends on a potential energy, hence, a freely falling particle has a varying proper mass. Consequently, a multitude of freely falling reference frames cannot be regarded as a multitude of equivalent inertial reference frames. There is a class of experiments, in which an inner observer can distinguish between the state of free fall in a gravitational field and the state of free space by detecting the effect of a proper mass variation. If so, a demonstration of a violatio…
In the framework of open quantum systems, we study the geometric phase acquired by freely falling and static two-level atoms interacting with quantized conformally coupled massless scalar fields in de Sitter-invariant vacuum. We find that, for the freely falling atom, the geometric phase gets a correction resulting from a thermal bath with the Gibbons-Hawking temperature, thus it clearly reveals the intrinsic thermal nature of de Sitter spacetime from a different physical context. For the static atom, there is a correction to the geometric phase coming from both the intrinsic thermal nature of…
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 di…
We consider, in de Sitter spacetime, both freely falling and static two-level atoms in interaction with a conformally coupled massless scalar field in the de Sitter-invariant vacuum, and separately calculate the contributions of vacuum fluctuations and radiation reaction to the atom's spontaneous excitation rate. We find that spontaneous excitations occur even for the freely falling atom as if there is a thermal bath of radiation at the Gibbons-Hawking temperature and we thus recover, in a different physical context, the results of Gibbons and Hawking that reveals the thermal nature of de Sitt…
Scalar field theory on a lattice falling freely into a 1+1 dimensional black hole is studied using both WKB and numerical approaches. The outgoing modes are shown to arise from incoming modes by a process analogous to a Bloch oscillation, with an admixture of negative frequency modes corresponding to the Hawking radiation. Numerical calculations show that the Hawking effect is reproduced to within 0.5% on a lattice whose proper spacing where the wavepacket turns around at the horizon is $\sim0.08$ in units where the surface gravity is 1.
We present a quantum optics treatment of the near horizon behaviour of a quantum oscillator freely-falling into a pre-existing Schwarzschild black hole. We use Painleve-Gullstrand coordinates to define a global vacuum state. In contrast to an accelerated oscillator in the Minkowski vacuum, where there is no radiation beyond an initial transient, we find that the oscillator radiates positive energy to to infinity and negative energy into the black hole as it attempts to come into equilibrium with the ambient vacuum. We discuss the relationship of the model to Hawking radiation.
It is argued that it takes an infinite amount of external time for a freely falling test particle to reach the event horizon of a classical black hole (which happens in finite faller time), and that in this time the black hole would have evaporated due to Hawking radiation; so the freely falling test particle would itself evaporate at the event horizon, and so not pass through.
Analyzing test particles falling into a Kerr black hole, we study gravitational waves in Brans-Dicke theory of gravity. First we consider a test particle plunging with a constant azimuthal angle into a rotating black hole and calculate the waveform and emitted energy of both scalar and tensor modes of gravitational radiation. We find that the waveform as well as the energy of the scalar gravitational waves weakly depends on the rotation parameter of black hole $a$ and on the azimuthal angle. Secondly, using a model of a non-spherical dust shell of test particles falling into a Kerr black hole,…
The relation between Einstein equivalence principle and a continuous quantum measurement is analyzed in the context of the recently proposed flavor-oscillation clocks, an idea pioneered by Ahluwalia and Burgard (Gen. Rel Grav. Errata 29, 681 (1997)). We will calculate the measurement outputs if a flavor-oscillation clock, which is immersed in a gravitational field, is subject to a continuous quantum measurement. Afterwards, resorting to the weak equivalence principle, we obtain the corresponding quantities in a freely falling reference frame. Finally, comparing this last result with the measur…
Studying particle motion in the gravitational field of a black hole from the perspective of different observers is important for separating the coordinate artifacts from the physical phenomena. In this paper, we show that a freely falling test particle exhibits gravitational repulsion by a black hole as seen by an asymptotic observer, whereas nothing of the kind happens as recorded by a freely falling observer or by an observer located at a finite distance from the event horizon. This analysis is carried out for a general Reissner-Nordström, an extremal Reissner-Nordström, and a Schwarzschild …
We construct time-dependent multi-centre solutions to three-dimensional general relativity with zero or negative cosmological constant. These solutions correspond to dynamical systems of freely falling black holes and conical singularities, with a multiply connected spacetime topology. Stationary multi-black-hole solutions are possible only in the extreme black hole case.
Here we consider static, axially symmetric, rotating and charged Kerr-Sen Dilaton-Axion black hole metric in generalized Boyer-Lindquist coordinates as particle accelerators. We obtain the geodesic motions of particle. We find the effective potential and discuss the circular orbit of a particle. We investigate the center of mass energy of two colliding neutral particles with different rest masses falling from rest at infinity to near the non-extremal horizons (event horizon and Cauchy horizon) and extremal horizon of the Kerr-Sen black hole. Analogous to the Compton process, we discuss the col…
It is generally assumed that naked singularities must be physically excluded, as they could otherwise introduce unpredictable influences in their future null cones. Considering geodesics for a naked Reissner-Nordstrom singularity, it is found that the singularity is effectively clothed by its repulsive nature. Regarding electron as naked singularity, the size of the clothed singularity (electron) turns out to be classical electro-magnetic radius of the electron, to an observer falling freely from infinity, initially at rest. The size shrinks for an observer falling freely from infinity, with a…
We present a novel formulation of the Kerr spacetime solution, based on the Lemaître coordinates. Such an approach allows one to avoid the coordinate singularities of the Boyer-Lindquist metric, thus offering the possibility to explore in some detail the Kerr physics near and beyond the event horizon, adopting the point of view of a freely falling observer, whose adapted tetrad is moreover proven to be Fermi-Walker transported. We use the Lemaître form of the Kerr metric discussing the motion of radial photons close to the Cauchy horizon, also showing that their behaviour fairly agrees with ot…
In this paper, we investigate the center of mass energy of the collision for two neutral particles with different rest masses falling freely from rest at infinity in the background of a Kerr-Newman-Taub-NUT black hole. Further, we discuss the center of mass energy near the horizon(s) of an extremal and non-extremal Kerr-Newman-Taub-NUT black hole and show that an arbitrarily high center of mass energy is achievable under some restrictions. We will study the special case of the center of mass energy when the specific energy, specific angular momentum and Carter constant of both the particles ar…
We consider a freely falling holographic screen for the Schwarzschild and Reissner-Nordström black holes and evaluate the entropic force à la Verlinde. When the screen crosses the event horizon, the temperature of the screen agrees to the Hawking temperature and the entropic force gives rise to the surface gravity for both of the black holes.
We argue that the curvature generated by a gravitational field can be used to calculate the corresponding metric which determines the trajectories of freely falling test particles. To this end, we present a method to compute the metric from a given curvature tensor. We use Petrov's classification to handle the structure and properties of the curvature tensor, and Cartan's structure equations in an orthonormal tetrad to investigate the differential equations that relate the curvature with the metric. The second structure equation is integrated to obtain the explicit expression for the connectio…
We examine various methods of constructing conserved quantities in the Teleparallel Equivalent of General Relativity (TEGR). We demonstrate that in the covariant formulation the preferred method are the Noether charges that are true invariant quantities. The Noether charges depend on the vector field $ξ$ and we consider two different options where $ξ$ is chosen as either a Killing vector or a four-velocity of the observer. We discuss the physical meaning of each choice on the example of the Schwarzschild solution in different frames: static, freely falling Lemaitre frame, and a newly obtained …
Scattering of particles in the gravitational field of rotating black holes is considered. Expressions for scattering energy of particles in the centre of mass system are obtained. It is shown that scattering energy of particles in the centre of mass system can obtain very large values not only for extremal black holes but also for nonextremal ones. It is shown that for realizing of the collisions with infinite energy one needs the infinite interval not only of the coordinate time but also the infinite interval of the proper time of the free falling particle.
We obtain a (3+3)-dimensional global flat embedding of the generalized (2+1) charged Bañados-Teitelboim-Zanelli black holes in massive gravity. We also study the local free-fall temperatures for freely falling observers starting from rest and investigate the effect of the charge and graviton mass in free-fall temperatures.
Freely falling point-like objects converge towards the center of the Earth. Hence the gravitational field of the Earth is inhomogeneous, and possesses a tidal component. The free fall of an extended quantum object such as a hydrogen atom prepared in a high principal-quantum-number stretch state, i.e., a circular Rydberg atom, is predicted to fall more slowly that a classical point-like object, when both objects are dropped from the same height from above the Earth. This indicates that, apart from "quantum jumps," the atom exhibits a kind of "quantum incompressibility" during free fall in inhom…
In the context of the Teleparallel Equivalent of General Relativity (TEGR) we have investigated the role of local observers, associated with tetrad fields, in description of the gravitational interaction through the concepts of the gravitoelectric (GE) and gravitomagnetic (GM) fields. We start by analyzing the gravitoelectromagnetic (GEM) fields obtained from an observer freely falling in the Schwarzschild space-time. Then, we investigated whether it is possible to distinguish between this situation and to be at rest in the Minkowski space-time. We conclude that, although there are non-zero co…
The inspiral of a stellar mass compact object falling into a massive Kerr black hole can be broken into three different regimes: An adiabatic inspiral phase, where the inspiral timescale is much larger than the orbital period; a late-time radial infall, which can be approximated as a plunging geodesic; and a regime where the body transitions from the inspiral to plunge. In earlier work, Ori and Thorne have outlined a method to compute the trajectory during this transition for a compact object in a circular, equatorial orbit. We generalize this technique to include inclination and eccentricity.
