86,565 research outputs found
On the quantization of the extremal Reissner-Nordström black hole
No full textFollowing Rosen's quantization rules, two of the authors (C. Corda and F. Feleppa) recently described the Schwarzschild black hole (BH) formed after the gravitational collapse of a pressureless “star of dust” in terms of a “gravitational hydrogen atom”. Here we generalize this approach to the gravitational collapse of a charged object, namely, to the geometry of a Reissner-Nordström BH (RNBH) and calculate the gravitational potential, the Schrödinger equation and the exact solutions of the energy levels of the gravitational collapse. By using the concept of BH effective state, previously introduced by one of us (CC), we describe the quantum gravitational potential, the mass spectrum and the energy spectrum for the extremal RNBH. The area spectrum derived from the mass spectrum finds agreement with a previous result by Bekenstein. The stability of these solutions, described with the Majorana approach to the Archaic Universe scenario, shows the existence of oscillatory regimes or exponential damping for the evolution of a small perturbation from a stable state
Underlining some mathematical and physical aspects about the concept of motion in general relativity
No full textThe Einstein initial foundations of general relativity have to do with his great intuition and they are not clear as it is for special relativity. As has been widely emphasized, for example, in the book of Ohanian and Ruffini, the very name of the theory indicates a misconception. Despite this, the high school textbooks (at least the Italian ones) and books of scientific divulgation introduce the Einstein gravitational theory still following the initial approach leading, in our opinion, to misinterpretations. A careful student, for example, immediately asks: it is not true that the Earth rotates because I can consider it at rest thanks to general relativity theory. The relativity of motion is trivial in mathematics while it has deep meaning in physics and it is not sufficiently analyzed. Similarly, the arbitrary choice of the origin and the perfect equivalence between all coordinate systems are mathematical properties satisfied by general relativity and students can confuse it with physical equivalence between reference systems that have a deeper meaning and the Einstein theory does not verify it. Gravitational force does not exist and this is the real core of Einsteinian revolution. As happens in Newtonian physics and Special Relativity, also in general relativity the relative motions are the geodesic motions with the difference that spacetime can be curved and geodesics may not be a straight line. Similarly, in general relativity forces cause non-geodesic motion. Geodesic and non-geodesic are tensorial properties and for this reason they are absolute
Constraining the Generalized Uncertainty Principle with the light twisted by rotating black holes and M87*
No full textWe test the validity of the Generalized Heisenberg's Uncertainty principle in the presence of strong gravitational fields nearby rotating black holes; Heisenberg's principle is supposed to require additional correction terms when gravity is taken into account, leading to a more general formulation also known as the Generalized Uncertainty Principle. Using as probes electromagnetic waves acquiring orbital angular momentum when lensed by a rotating black hole, we find from numerical simulations a relationship between the spectrum of the orbital angular momentum of light and the corrections needed to formulate the Generalized Uncertainty Principle, here characterized by the rescaled parameter β0, a function of the Planck's mass and the bare mass of the black hole. Then, from the analysis of the observed twisted light due to the gravitational field of the compact object observed in M87, we find new limits for the parameter β0. With this method, complementary to black hole shadow circularity analyses, we obtain more precise limits from the experimental data of M87*, confirming the validity of scenarios compatible with General Relativity, within the uncertainties due to the experimental errors present in EHT data and those due to the numerical simulations and analysis
Twisted light, a new tool for general relativity and beyond — Revealing the properties of rotating black holes with the vorticity of light —
No full textWe describe and present the first observational evidence that light propagating near a rotating black hole is twisted in phase and carries orbital angular momentum. The novel use of this physical observable as an additional tool for the previously known techniques of gravitational lensing allows us to directly measure, for the first time, the spin parameter of a black hole. With the additional information encoded in the orbital angular momentum, not only can we reveal the actual rotation of the compact object, but we can also use rotating black holes as probes to test general relativity
Hartle-Hawking boundary conditions as Nucleation by de Sitter Vacuum
No full textIt is shown that, for a de Sitter Universe, the Hartle–Hawking (HH) wave function can be obtained in a simple way starting from the Friedmann–Lemaitre–Robertson–Walker (FLRW) line element of cosmological equations. An oscillator having imaginary time is indeed derived starting from the Hamiltonian obtaining the HH condition. This proposes again some crucial matter on the meaning of complex time in cosmology. In order to overcome such difficulties, we propose an interpretation of the HH framework based on de Sitter Projective Holography
Quantum coupling between gravity and mass in bouncing ball dynamics
No full textWe review the dynamics of a bouncing ball, both from the classical and the quantum points of view, studying the role of its inertial and gravitational masses. We analyze the behavior of quantum particles of different masses, embedded in a uniform gravitational field. We show that the bouncing ball is a useful didactic example to show that the coupling between rest mass and gravity cannot be avoided at the quantum level and that the equivalence principle must be reformulated in quantum mechanics. Galileo's experiment of falling bodies can be still satisfied if one considers only the average quantum values of observables
On the distinction between coordinate and physical speed of light in General Relativity
No full textThe present paper has a pedagogical aim. On this basis, we will discuss the concept of velocity in General Relativity and try to explain it using some well-known metrics in the scientific literature. While none of the examples in this work is new except for the last one, such a systematic treatment could be a useful contribution to the teaching of General Relativity at an introductory level. In particular, in the last section, we will focus on rotating coordinates and give our interpretation within this framework
Strong deflection limit analysis of black hole lensing in inhomogeneous plasma
No full textThis paper investigates gravitational lensing effects in the presence of plasma in the strong deflection limit, which corresponds to light rays circling around a compact object and forming higher-order images. While previous studies of this case have predominantly focused on the deflection of light in a vacuum or in the presence of a homogeneous plasma, this work introduces an analytical treatment for the influence of a nonuniform plasma. After recalling the exact expression for the deflection angle of photons in a static, asymptotically flat and spherically symmetric spacetime filled with cold nonmagnetized plasma, a strong deflection limit analysis is presented. Particular attention is then given to the case of a Schwarzschild spacetime, where the deflection angle of photons for different density profiles of plasma is obtained. Moreover, perturbative results for an arbitrary power-law radial density profile are also presented. These formulas are then applied to the calculation of the positions and magnifications of higher-order images, concluding that the presence of a nonuniform plasma reduces both their angular size and their magnifications, at least within the range of the power-law indices considered. These findings contribute to the understanding of gravitational lensing in the presence of plasma, offering a versatile framework applicable to various asymptotically flat and spherically symmetric spacetimes
Is Dark Energy due to an excited quantum state of the Universe?
No full textOne of the mysteries of modern cosmology is the origin of dark energy. The current cosmological model, that is in agreement with the experimental data, predicts that the expansion of the galaxies is accelerated. In order to take this acceleration into account, an additional term is introduced in the Einstein equations invoking the existence of a cosmological constant. The origin of this additional term is still unknown. The aim of this paper is to explain dark energy as the energy of the quantum state of the universe that, instead of being in a fundamental state with zero energy, is in an excited state with a non-vanishing value of energy. The experimental value found for the cosmological constant is shown to be compatible with the model, taking, in our equations, the only free parameter of the order of Planck length
Quantum oscillations in the black hole horizon
No full textBy applying Rosen's quantization approach to the historical Oppenheimer and
Snyder gravitational collapse and by setting the constraints for the formation
of the Schwarzschild black hole (SBH), in a previous paper [1] two of the
Authors (CC and FF) found the gravitational potential, the Schrodinger
equation, the solution for the energy levels, the area quantum and the quantum
representation of the ground state at the Planck scale of the SBH. Such results
are consistent with previous ones in the literature. It was also shown that the
traditional classical singularity in the core of the SBH is replaced by a
quantum oscillator describing a non-singular two-particle system where the two
components, named the "nucleus" and the "electron", strongly interact with each
other through a quantum gravitational interaction. In agreement with the de
Broglie hypothesis, the "electron" is interpreted in terms of the quantum
oscillations of the BH horizon. In other words, the SBH should be the
gravitational analogous of the hydrogen atom. In this paper, it is shown that
these results allow us to compute the SBH entropy as a function of the BH
principal quantum number in terms of Bekenstein-Hawking entropy and three
sub-leading corrections. In addition, the coefficient of the formula of
Bekenstein-Hawking entropy is reduced to a quarter of the traditional value.
Then, it is shown that, by performing a correct rescaling of the energy levels,
the semi-classical Bohr-like approach to BH quantum physics, previously
developed by one of the Authors (CC), is consistent with the obtained results
for large values of the BH principal quantum number. After this, Hawking
radiation will be analysed by discussing its connection with the BH quantum
structure. Finally, it is shown that the time evolution of the above mentioned
system solves the BH information paradox.Comment: 29 pages.Comments are welcome. arXiv admin note: text overlap with
arXiv:1912.0647
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