arXiv subjects

Christian Corda

Publications and source records attributed to Christian Corda.

At least 19 recordsLinked to original sources

arXiv2026

From Quantum-Mechanical Acceleration Limits to Upper Bounds on Fluctuation Growth of Observables in Unitary Dynamics

Recently, the notion of a quantum acceleration limit has been proposed for any unitary time evolution of quantum systems governed by arbitrary nonstationary Hamiltonians. This limit articulates that the rate of change over time of the standard deviation of the Hamiltonian operator representing the acceleration of quantum evolution within projective Hilbert space is constrained by the standard deviation of the time-derivative of the Hamiltonian. In this paper, we extend our earlier findings to encompass any observable A within the framework of unitary quantum dynamics, leading to the inequality. This relationship signifies that the speed of the standard deviation of any observable is limited by the standard deviation of its associated velocity-like observable. Finally, for pedagogical purposes, we illustrate the relevance of our inequality by providing clear examples. We choose suitable observables related to the unitary dynamics of two-level quantum systems, as well as a harmonic oscillator within a finite-dimensional Fock space.

quant-ph↗

arXiv2025

Upper Bounds on Fluctuation Growths of Observables in Open Quantum Systems

The upper bounds for the rate of fluctuation growth of an observable in both open and closed quantum systems have been studied actively recently. In our recent work we showed that the rate of fluctuation growth for an observable in a closed quantum system is upper bounded by the fluctuation of its corresponding velocity-like observable. That bound also indicated a tradeoff between the time derivatives of the mean and the standard deviation. In this paper we will look at open quantum systems in two cases. For the first case we find the generator of evolution for an open system employing both the Taylor expansion and the standard time-ordered evolution via the Dyson series, while in the second case we consider no specific information about the evolution of the system. We then find the rate of fluctuation growth in each case. Comparing the upper bounds for each case and considering the upper bound found for a closed system suggest that including more details by separating the contributions of the system and state dynamics seems to result in looser bounds for the rate of fluctuation growth.

quant-ph↗

arXiv2025

Quantum corrections in general relativity explored through a GUP-inspired maximal acceleration analysis

A maximun acceleration analysis by Pati dating back to 1992 is here improved by replacing the traditional Heisenberg Uncertainty Principle (HUP) with the Generalized Uncertainty Principle (GUP), which predicts the existence of a minimum length in Nature. This new approach allows one to find a numerical value for the maximum acceleration existing in Nature for a physical particle that turns out to be a_{max}\simeq4\frac{c^{2}}{l_{P}}, that is, a function of two fundamental physical quantities such as the speed of light c and the Planck length l_{p}. An application of this result to black hole (BH) physics allows one to estimate a new quantum limit to general relativity. It is indeed shown that, for every real Schwarzschild BH, the maximum gravitational acceleration occurs, without becoming infinite, when the Schwarzschild radial coordinate reaches the gravitational radius. This means that quantum corrections to general relativity become necessary not at the Planck scale, as the majority of researchers in the field think, but at the Schwarzschild scale, in agreement with recent interesting results in the literature. In other words, the quantum nature of physics, which in this case manifests itself through the GUP, appears to prohibit the existence of real singularities, in this current case forbiddiing the gravitational acceleration of a Schwarzschild BH from becoming infinite.

gr-qc↗

arXiv2025

Connection stability of vector fields with astrophysical application to the Einstein-Vlasov system

In this paper we present a method for considering the stability of smooth vector fields on a smooth manifold which may not be compact. We show that these kind of stability which is called "connection stability" is equivalent to the structural stability in the case of compact manifolds. We prove if X is a connection stable vector field, then any multiplication of it by a nonzero scalar is also a connection stable vector field. We present an example of a connection stable vector field on a noncompact manifold, and we also show that harmonic oscillator is not a connection stable vector field. We present a technique to prove a class of vector fields are not connection stable. As a concrete physical example, we will apply the analysis to the Einstein- Vlasov system in an astrophysical context in which we propose an approach that could, in principle and partially, help to understand the problem of galaxy rotation curves.

gr-qc↗

arXiv2025

Resolving the S8 tension with the Lambda Prime ($Λ'$) model

The $S_8$ parameter, which quantifies the amplitude of matter fluctuations on scales of $8h^{-1}$ Mpc, has been a source of tension between weak lensing surveys (e.g. KiDS, DES, HSC) and the Planck Cosmic Microwave Background (CMB) measurements. This discrepancy challenges the standard $Λ$CDM model and has become one of the most significant tensions in modern cosmology. The ${Λ'}$ model offers a potential resolution by introducing modifications to the cosmic growth history through alterations to the gravitational sector. The alterations involve including a Ricci soliton into Einstein's field equations which introduce a time dependent factor yielding a time varying cosmological constant ${Λ'}=(1-{α(t)^2}{Λ_{DE}}\frac{ρ_g}{ρ_{DE}}$ and subsequently the evolution of the cosmos. The Ricci soliton is sourced from gravitational energy density. In this study we analyze results from six surveys and compare the results for $w_a$ and $w_0$ with the ${Λ'}$ model. We also find $σ_8={0.750}_{-0.020}^{+0.020}$ , $S_8={0.788}$. These values are closer to some low $S_8$ measurements from weak lensing surveys (e.g DES, KiDS), which report $S_8 \approx 0.76-0.78$, suggesting that the model may alleviate the $S_8$ tension. High values of ${α(t)}$ in the late universe are the cause of suppressed structure formation and low values of ${Λ'}$. The late universe in the ${Λ'}$ model is effectively or apparently 5-10% younger than in $Λ$CDM which translates to $H_0={72.734}_{-1.687}^{+1.687}$ km/s/Mpc, which is in agreement with late universe probes. ${Λ'}$ is classified under the dynamical dark energy models, however unlike alternatives, it does not invoke exotic particles nor phantom energy.

astro-ph.CO↗

arXiv2025

The information loss problem and Hawking radiation as tunneling

In this paper, we review some methods that tried to solve the information loss problem. In particular, we revisit the solution based on Hawking radiation as tunneling, and provide a detailed statistical interpretation on the black hole entropy in terms of the quantum tunneling probability of Hawking radiation from the black hole. In addition, we show that black hole evaporation is governed by a time-dependent Schrodinger equation that sends pure states into pure states rather than into mixed states (Hawking had originally established that the final result would be mixed states). This is further confirmation of the fact that black hole evaporation is unitary.

gr-qc↗

arXiv2024

From Uncertainty Relations to Quantum Acceleration Limits

The concept of quantum acceleration limit has been recently introduced for any unitary time evolution of quantum systems under arbitrary nonstationary Hamiltonians. While Alsing and Cafaro [Int. J. Geom. Methods Mod. Phys. 21, 2440009 (2024)] used the Robertson uncertainty relation in their derivation, Pati [arXiv:quant-ph/2312.00864 (2023)] employed the Robertson-Schrödinger uncertainty relation to find the upper bound on the temporal rate of change of the speed of quantum evolutions. In this paper, we provide a comparative analysis of these two alternative derivations for quantum systems specified by an arbitrary finite-dimensional projective Hilbert space. Furthermore, focusing on a geometric description of the quantum evolution of two-level quantum systems on a Bloch sphere under general time-dependent Hamiltonians, we find the most general conditions needed to attain the maximal upper bounds on the acceleration of the quantum evolution. In particular, these conditions are expressed explicitly in terms of two three-dimensional real vectors, the Bloch vector that corresponds to the evolving quantum state and the magnetic field vector that specifies the Hermitian Hamiltonian of the system. For pedagogical reasons, we illustrate our general findings for two-level quantum systems in explicit physical examples characterized by specific time-varying magnetic field configurations. Finally, we briefly comment on the extension of our considerations to higher-dimensional physical systems in both pure and mixed quantum states.

quant-ph↗

arXiv2024

Equivalence Principle and Machian origin of extended gravity

Chae's analyses on GAIA observations of wide binary stars have fortified the paradigm of extended gravity with particular attention to MOND-like theories. We recall that, starting from the origin of Einstein's general relativity, the request of Mach on the structure of the theory has been the core of the foundational debate. This issue is strictly connected with the nature of the mass-energy equivalence. This was exactly the key point that Einstein used to derive the same general relativity. On the other hand, the current requirements of particle physics and the open questions within extended gravity theories, which have recently been further strengthened by analyses of GAIA observations, request a better understanding of the Equivalence Principle. By considering a direct coupling between the Ricci curvature scalar and the matter Lagrangian a non geodesic ratio between the inertial and the gravitational mass can be fixed and MOND-like theories are retrieved at low energies.

gr-qc↗

arXiv2024

Universality of the thermodynamics of a quantum-mechanically radiating black hole departing from thermality

Mathur and Mehta won the third prize in the 2023 Gravity Research Foundation Essay Competition for proving the universality of black hole (BH) thermodynamics. Specifically, they demonstrated that any Extremely Compact Object (ECO) must have the same BH thermodynamic properties regardless of whether or not the ECO possesses an event horizon. The result is remarkable, but it was obtained under the approximation according to which the BH emission spectrum has an exactly thermal character. In fact, strong arguments based on energy conservation and BH back reaction imply that the spectrum of the Hawking radiation cannot be exactly thermal. In this work the result of Mathur and Mehta will be extended to the case where the radiation spectrum is not exactly thermal using the concept of BH dynamical state.

gr-qc↗

arXiv2024

Violation of Bell's Inequality in the Clauser-Horne-Shimony-Holt Form with Entangled Quantum States Revisited

Scientific imagination and experimental ingenuity are at the heart of physics. One of the most known instances where this interplay between theory (i.e., foundations) and experiments (i.e., technology) occurs is in the discussion of Bell's inequalities. In this paper, we present a revisitation of the violation of Bell's inequality in the Clauser-Horne-Shimony-Holt (CHSH) form with entangled quantum states. First, we begin with a discussion of the 1935 Einstein-Podolski-Rosen (EPR) paradox (i.e., incompleteness of quantum mechanics) that emerges from putting the emphasis on Einstein's locality and the absolute character of physical phenomena. Second, we discuss Bell's 1971 derivation of the 1969 CHSH form of the original 1964 Bell inequality in the context of a realistic local hidden-variable theory (RLHVT). Third, identifying the quantum-mechanical spin correlation coefficient with the RLHVT one, we follow Gisin's 1991 analysis to show that quantum mechanics violates Bell's inequality when systems are in entangled quantum states. For pedagogical purposes, we show how the extent of this violation depends both on the orientation of the polarizers and the degree of entanglement of the quantum states. Fourth, we discuss the basics of the experimental verification of Bell's inequality in an actual laboratory as presented in the original 1982 Aspect-Grangier-Roger (AGR) experiment. Finally, we provide an outline of some essential take home messages from this wonderful example of physics at its best.

quant-ph↗

arXiv2024

On the Generalized Lemaitre Tolman Bondi Metric: Classical Sensitivities and Quantum Einstein-Vaz Shells

In this paper, in the classical framework we evaluate the lower bounds for the sensitivities of the generalized Lemaitre Tolman Bondi metric. The calculated lower bounds via the linear dynamical systems L_{\frac{\partial}{\partialθ}}, L_{\frac{\partial}{\partial r}}, and L_{\frac{\partial}{\partialϕ}} are -\ln2+\ln|(\dot{R}B)^{2}-(R')^{2}|-2\ln|B|, 2\ln|\dot{B}|-\ln2 and -\ln2-2\ln|B|+\ln|(\dot{R}^{2}B^{2}-R'^{2})\sin^{2}θ-B^{2}\cos^{2}θ| respectively. We also show that the sensitivities and the lower sensitivities via L_{\frac{\partial}{\partial t}} are zero. In the quantum framework we analyse the properties of the Einstein-Vaz shells which are the final result of the quantum gravitational collapse arising from the Lemaitre Tolman Bondi discussed by Vaz in 2014. In fact, Vaz showed that continued collapse to a singularity can only be obtained if one combines two independent and entire solutions of the Wheeler-DeWitt equation. Forbidding such a combinatin leads naturally to matter condensing on the Schwarzschild surface during quantum collapse. In that way, an entirely new framework for black holes (BHs) has emerged. The approach of Vaz as also consistent with Einstein's idea in 1939 of the localization of the collapsing particles within a thin spherical shell. Here, following an approach of oned of us (CC), we derive the BH mass and energy spectra via a Schrodinger-like approach, by further supporting Vaz's conclusions that instead of a spacetime singularity covered by an event horizon, the final result of the gravitational collapse is an essentially quantum object, an extremely compact "dark star". This "gravitational atom" is held up not by any degeneracy pressure but by quantum gravity in the same way that ordinary atoms are sustained by quantum mechanics. Finally, we discuss the time evolution of the Einstein-Vaz shells

gr-qc↗

arXiv2024

On Mössbauer rotor effect, clock synchronization and third postulate of relativity

physics.gen-ph↗

arXiv2023

Schrodinger theory of black holes

The Schrodinger equation of the Schwarzschild black hole (SBH) is derived via Feynman's path integral approach by re-obtaining the same results found by the Author and collaborators in two recent research papers. In this two-particle system approach to BH quantum physics the traditional classical singularity in the core of the SBH is replaced by a nonsingular two-particle system where the two components, the "nucleus" and the "electron", strongly interact with each other through a quantum gravitational interaction. In other words, the SBH is the gravitational analog of the hydrogen atom and this could, in principle, drive to a space-time quantization based on a quantum mechanical particle approach. By following with caution the analogy between this SBH Schrodinger equation and the traditional Schrodinger equation of the s states (l=0) of the hydrogen atom, the SBH Schrodinger equation can be solved and discussed. The approach also permits us to find the quantum gravitational quantities which are the gravitational analogous of the fine structure constant and of the Rydberg constant. Remarkably, such quantities are not constants. Instead, they are dynamical quantities having well defined discrete spectra. In particular, the spectrum of the "gravitational fine structure constant" is exactly the set of non-zero natural numbers \mathbb{N}-\left\{ 0\right\} . Therefore, one argues the interesting consequence that the SBH results in a well defined quantum gravitational system, which obeys Schrodinger's theory: the "gravitational hydrogen atom".

gr-qc↗

arXiv2023

Schrödinger and Klein-Gordon theories of black holes from the quantization of the Oppenheimer and Snyder gravitational collapse

The Schrödinger equation of the Schwarzschild black hole (BH) shows that a BH is composed of a particle, the "electron", interacting with a central field, the "nucleus". Via de Broglie's hypothesis, one interprets the "electron" in terms of BH horizon's modes. Quantum gravity effects modify the BH semi-classical structure at the Schwarzschild scale rather than at the Planck scale. The analogy between this BH Schrödinger equation and the Schrödinger equation of the s states of the hydrogen atom permits us to solve the same equation. Therefore, BHs are well defined quantum gravitational systems obeying Schrödinger's theory: the "gravitational hydrogen atoms". By identifying the potential energy in the BH Schrödinger equation as being the gravitational energy of a spherically symmetric shell, a different nature of the quantum BH seems to surface. BHs are self-interacting, highly excited, spherically symmetric, massive quantum shells generated by matter condensing on the apparent horizon, concretely realizing the membrane paradigm. The quantum BH descripted as a "gravitational hydrogen atom" is a fictitious mathematical representation of the real, quantum BH, a quantum massive shell having as radius the oscillating gravitational radius. Nontrivial consequences emerge from this result: i) BHs have neither horizons nor singularities; ii) there is neither information loss in BH evaporation, nor BH complementarity, nor firewall paradox. These results are consistent with previous ones by Hawking, Vaz, Mitra and others. Finally, the special relativistic corrections to the BH Schrödinger equation give the BH Klein-Gordon equation and the corresponding eigenvalues.

gr-qc↗

arXiv2023

Black hole spectra from Vaz's quantum gravitational collapse

In 2014, in a famous paper Hawking strongly criticized the firewall paradox by claiming that it violates the equivalence principle and breaks the CPT invariance of quantum gravity. He proposed that the final result of the gravitational collapse should not be an event horizon, but an apparent horizon instead. On the other hand, Hawking did not give a mechanism for how this could work. In the same year, Vaz endorsed Hawking's proposal in a quantum gravitational model of dust collapse by winning the Second Prize in the 2014 Gravity Research Foundation Essay Competition. He indeed showed that continued collapse to a singularity can only be obtained if one combines two independent and entire solutions of the Wheeler-DeWitt equation. Vaz's interpretation of the paradox was in terms of simply forbidding such a combination. This leads naturally to matter condensing on the apparent horizon during quantum collapse. In that way, an entirely new framework for black holes (BHs) has emerged. The approach of Vaz was also consistent with Einstein's idea in 1939 of the localization of the collapsing particles within a thin spherical shell. In this work we derive the BH mass and energy spectra via a Schrodinger-like approach, by further supporting Vaz's conclusions that instead of a spacetime singularity covered by an event horizon, the final result of the gravitational collapse is an essentially quantum object, an extremely compact "dark star". This "gravitational atom" is held up not by any degeneracy pressure but by quantum gravity in the same way that ordinary atoms are sustained by quantum mechanics. Finally, by evoking the generalized uncertainty principle, the maximum value of the density of Vaz's shell will be estimated.

gr-qc↗

arXiv2022

On the equivalence between rotation and gravity: "Gravitational" and "cosmological" redshifts in the laboratory

The Mössbauer rotor effect recently gained a renewed interest due to the discovery and explanation of an additional effect of clock synchronization which has been missed for about 50 years, i.e. starting from a famous book of Pauli, till some recent experimental analyses. The theoretical explanation of such an additional effect is due to some recent papers in both the general relativistic and the special relativistic frameworks. In the first case (general relativistic framework) the key point of the approach is the Einstein's equivalence principle (EEP), which, in the words of the same Einstein, enables "the point of view to interpret the rotating system K' as at rest, and the centrifugal field as a gravitational field". In this paper, we analyse both the history of the Mössbauer rotor effect and its interpretation from the point of view of Einstein's general theory of relativity (GTR) by adding some new insight. In particular, it will be shown that, if on one hand the "traditional" effect of redshift has a strong analogy with the gravitational redshift, on the other hand the additional effect of clock synchronization has an intriguing analogy with the cosmological redshift. Finally, we show that a recent claim in the literature that the second effect of clock synchronization does not exist is not correct.

gr-qc↗

arXiv2021

Wormholes in Poincarè gauge theory of gravity

In the present work, we {study} static spherically symmetric solutions representing wormhole configurations in Poincarè gauge theory ({\sf PGT}). The gravitational sector of the Lagrangian is chosen as a subclass of {\sf PGT} Lagrangians for which, the spin-$0^+$ is the only propagating torsion mode. The spacetime torsion in {\sf PGT} has a dynamical nature even in the absence of intrinsic angular momentum (spin) of matter, hence, {torsion can play a principal role in the case of usual spin-less gravitating systems. We therefore} consider a spin-less matter distribution with an anisotropic energy momentum tensor ({\sf EMT}) as the supporting source for wormhole structure {to obtain a class of zero tidal force wormhole solutions.} It is seen that the matter distribution obeys the physical reasonability conditions, i.e., the weak ({\sf WEC}) and null ({\sf NEC}) energy conditions either at the throat and throughout the spacetime. We further consider varying equations of state in radial and tangential directions via definitions $w_r(r)=p_r(r)/ρ(r)$ and $w_t(r)=p_t(r)/ρ(r)$ and {investigate} the behavior of state parameters {at the throat of wormhole}. We observe that our solutions allow for wormhole configurations without the need of exotic matter. Observational features of the wormhole solutions are also discussed utilizing gravitational lensing effects. It is found that the light deflection angle diverges at the throat (which indeed, effectively acts as a photon sphere) and can get zero and negative values depending on the model parameters.

gr-qc↗

arXiv2021

Constraining the generalized uncertainty principle with neutron interferometry

The non-zero minimal length arises in various theories of gravity, leading to the so-called generalized uncertainty principle (GUP). In this short paper we analyze the GUP effects on neutron interferometry, showing that the obtained phase shifts depend on the mass and velocity of the particle. New upper bounds on the dimensionless GUP parameter have been found that are in agreement with the literature.

gr-qc↗