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Hristu Culetu

Publications and source records attributed to Hristu Culetu.

At least 19 recordsLinked to original sources
arXiv2025

Gravity and the Superposition Principle

The relation between gravity and quantum mechanics is investigated in this work. The link is given by the wave packet expansion process, rooted from the Uncertainty Principle. The basic idea is to express the de Broglie wavelength used by Schrodinger for a massive particle in terms of the associated Compton wavelength which is replaced by the Michell-Laplace radius $Gm/c^{2}$ of the spherical object of mass $m\geq m_{P}$, where $m_{P}$ is the Planck mass. The wave packet spreading is studying in spherical coordinates, having the width $σ(t)$, expressed in terms of $G$ and $c$ instead of $\hbar$. Therefore, for masses larger than the Planck mass, a faster dispersion rate of $σ(t)$ is obtained, compared to the standard case. The dispersion of the wave packet is observed only by a free falling observer and the process breaks down once the observer hits the surface of the object. Different freely falling observers notice different rates of expansion of the wave packet and the source of gravity is in a quantum superposition. We further confront the Mita formula for the mean energy of the wave packet with the de Broglie-Bohm quantum potential energy when the Schrodinger equation is expressed in the Madelung form.

physics.gen-ph↗
arXiv2025

On a star with expanding isotropic fluid

The generalized Gullstrand-Painleve geometry is investigated for expanding matter. Compared to other studies, we take into account an anisotropic stress tensor as the source of curvature with an equation of state resembling the MIT bag model form. The spacetime becomes de Sitter for $t>>1/\sqrtΛ, Λ$ being the equivalent cosmological constant. The energy density and pressures of the fluid are only time dependent but the scalar curvature is constant. The radial geodesics are computed.

gr-qc↗
arXiv2025

On a star with static conformally flat geometry inside

The properties of a star with constant positive energy density inside (as for the Schwarzschild interior geometry) and a negative pressure are investigated, using a static conformally flat spacetime. Because of the negative pressure, the gravitational field inside is repulsive. Ricci and Kretschmann curvature invariants are finite. The energy conditions for the stress tensor of the perfect fluid are satisfied, excepting the strong energy condition which is not obeyed for $r<R/\sqrt{2}$, where $R$ is the radius of the object. The Komar mass is calculated and discussed.

gr-qc↗
arXiv2024

On geodesics in spherical Rindler space

The geodesics in various spherical Rindler frames are investigated. A display of some kinematical quantities of the spacetime is given. The constant acceleration from the metric acts as the surface gravity of the horizon $r = 0$. The radial geodesics are computed both for the Balasubramanian et al. form of the spherical Rindler space and for the non-diagonal metric of Huang and Sun.

gr-qc↗
arXiv2024

Semiclassical corrections to a regularized Schwarzschild metric

A regular form of the Schwarzschild geometry is proposed. It is more suitable for application in microphysics because the source mass comes out both as a Schwarzschild radius and the Compton wavelength of the mass $m$. The Komar energy equals $mc^{2}$ in the classical situation ($\hbar = 0$).

gr-qc↗
arXiv2024

Geodesics in the conformally flat Eisenhart metric

The (4+1) dimensional conformally flat Eisenhart geometry is investigated in this work, stressing the contribution of the stress tensor generating its curvature. The energy-momentum tensor $T^{a}_{~b}$ is traceless and has only one nonzero component. It could be written as an anisotropic fluid with null transversal pressures and nonzero energy fluxes. The null and timelike geodesics are computed in the pure cosmological case when the Eisenhart potential energy is $V(r) = -mω^{2}r^{2}/2$, where $ω$ is related to the cosmological constant $Λ$. Although the metric is curved, the radial null geodesics $R(T)$ and $Y(T)$ are straight lines, with finite $R_{max}$ and $Y_{max}$, $Y$ being the 5th coordinate. In contrast, for a radial timelike geodesic, $Y_{max} \rightarrow \infty$ if $T \rightarrow T_{max} = 1/ω$.

physics.gen-ph↗
arXiv2023

A regular version of the extremal RN spacetime

A modified extremal Reissner-Nordstrom geometry, void of singularities, is proposed in this work, by means of an exponential factor depending on a positive constant $k$. All the metric coefficients are positive and finite and the spacetime has no any horizon. The curvature invariants are regular at the origin of coordinates and at infinity. The energy conditions for the stress tensor associate to the imperfect fluid are investigated. The gravitational field presents repulsive properties near the gravitational radius associated to the mass $m$. With the choice $k = 1/m$, the Komar energy $W_{K}$ of the mass $m$ changes its sign at $r = λ$ ($λ$ is the Compton wavelength of $m$), when the classical energy $mc^{2}$ equals the energy $\hbar c/r$.

gr-qc↗
arXiv2022

A Vaidya-type spacetime with no singularities

A regular Vaidya-type line-element is proposed in this work. The mass function depends both on the temporal and the spatial coordinates. The curvature invariants and the source stress tensor $T^{a}_{~b}$ are finite in the whole space. The energy conditions for $T^{a}_{~b}$ are satisfied if $k^{2}<2vr$, where $k$ is a positive constant and $v,r$ are coordinates. It is found that the radial pressure has a maximum very close to $r = 2m~ (r>2m), v = 2m$. The energy crossing a sphere of constant radius is akin to Lundgren-Schmekel-York quasilocal energy. The Newtonian acceleration of the timelike geodesics has an extra term (compared to the result of Piesnack and Kassner) which leads to rejecting effects.

gr-qc↗
arXiv2022

On a modified Rindler geometry

Following a previous idea, a curved geometry is proposed as being valid in accelerated systems, in Minkowski space. The curvature turns out to be generated by the source of the accelerated motion. An exponential factor depending on $ρ$ (the coordinate along the acceleration) and a constant length is introduced in the metric. The source stress tensor appears to represent an imperfect fluid with zero energy density but nonzero tangential pressures which do not depend on Newton's constant even for $ρ>>l_{p}$, where $l_{p}$ is the Planck length. The Komar mass is proportional to the constant acceleration $g$ and it does not depend on the choice of the value of the constant $k$ from the exponential factor. Null and timelike geodesics along the $ρ$ direction are investigated. A slight change in the metric leads to nonzero energy density and pressure along the acceleration direction, with all the energy conditions being satisfied far from the Planck world.

physics.gen-ph↗
arXiv2021

On a conformal Schwarzschild-de Sitter spacetime

On the basis of the C-metric, we investigate the conformal Schwarzschild - deSitter spacetime and compute the source stress tensor and study its properties, including the energy conditions. Then we study its extremal version ($b^{2} = 27m^{2}$, where $b$ is the deS radius and $m$ is the source mass), when the metric is nonstatic. The weak-field version is analyzed in several frames, and the metric becomes flat with the special choice $b = 1/a$, $a$ being the constant acceleration of the Schwarzschild-like mass or black hole. This form is Rindler's geometry in disguise and is also conformal to a de Sitter metric where the acceleration plays the role of the Hubble constant. In its time dependent version, one finds that the proper acceleration of a static observer is constant everywhere, in contrast with the standard Rindler case. The timelike geodesics along the z-direction are calculated and proves to be hyperbolae.

gr-qc↗
arXiv2021

Regular Schwarzschild-like spacetime embedded in a five dimensional bulk

We take advantage of the Shiromizu et al. covariant formalism to find out the brane properties originating from the five dimensional bulk spacetime. Making a different choice for the conformal factor $e^{-2b(z)}$ compared to Estrada [24], we reach a new solution with a lot of interesting properties, where $b(z) = ln(1/\sqrt{cosh2μz})$. The non-local tensor $E_{ab}$ rooted from the 5-dimensional Riemann tensor gives an anisotropic stress energy tensor on the brane with positive energy density and negative radial pressure. The BH on the brane looks like a black string in the 5-dimensional space, with no singularities of the curvature invariants.

gr-qc↗
arXiv2020

Pattern for a star filled with imperfect fluid

A static, spherically symmetric spacetime with negative pressures is conjectured inside a star. The gravitational field is repulsive and so a central singularity is avoided. The positive energy density and the pressures of the imperfect fluid are finite everywhere. The Tolman-Komar energy of the space is negative, as for a de Sitter geometry. From the Darmois-Israel junction conditions on the star surface one finds the constant length $b$ from the metric and the expression of the surface tension $σ$ of the thin shell separating the interior from the Schwarzschild exterior. Some properties of the timelike and null geodesics in the Painleve-Gullstrand coordinates are investigated.

gr-qc↗
arXiv2020

Accelerating imperfect fluid

An inhomogeneous fluid in accelerated motion is investigated. When the velocity field $v(x)$ is not constant, the geometry viewed by a static observer is curved, as if the observer were immersed in a gravitational field. A velocity-dependent semiclassical gravitational potential is introduced, which obeys an Yukawa-type equation, written in Cartesian coordinates. The timelike and null geodesic equations are investigated. One finds that the fluid has zero energy density corresponding to the perfect fluid part but nonzero anisotropic energy density. The pressures will no longer depend on $\hbar$ for time intervals $t>>1/m$, where $m$ is the field mass.

gr-qc↗
arXiv2019

Quantum potential and wave packet spreading

The effects of the de Broglie-Bohm quantum potential on a test particle of mass $m$ are investigated in a conformally-flat geometry. A real, nonlinear, scalar field $Ψ$ is introduced and related directly to the conformal factor and to the effective mass $M(r,t)$ of the particle. The radial acceleration of a static observer in the conformally-flat metric is negative (the field is repulsive), and the corresponding proper acceleration resembles that one of the "peak radius" where the radial probability density has a global maximum during the wave packet spreading phenomenon. The timelike radial geodesics are computed in the conformally-flat spacetime in double-null coordinates and proves to be hyperbolae in the region $r>t$.

physics.gen-ph↗
arXiv2019

Hyperbolic vacuum decay

The properties of an hyperbolically-expanding wormhole are studied. Using a particular equation of state for the fluid on the wormhole throat, we reached an equation of motion for the throat that leads to a constant surface energy density $σ$. The Lagrangean leading to the above equation of motion contains the "rest mass" of the expanding particle as a potential energy. The associated Hamiltonian corresponds to a relativistic free particle of a total Planck energy $E_{P}$. When the wormhole is embedded in de Sitter space, we found that the cosmological constant is of Planck order of magnitude but hidden at very tiny scales, in accordance with Carlip's recipe.

gr-qc↗
arXiv2019

On a regular modified C-metric

A particular form of the C-metric is investigated, giving it a non-standard interpretation and removing any singularity at $r = 0$. In the weak field limit of the accelerating black hole, the proper acceleration $A$ of a static observer is constant and the geometry becomes conformally-flat (anti de Sitter). The stress tensor is of $Λ$-type ($Λ= -3a^{2}/8πG$) and its energy density is negative. We propose that $Λ$ is responsible of inertial forces that appear in uniformly accelerated systems (far from the accelerating source $m$ and for $r << 1/a$ the dominant term in the expression of $a^{r}$ is $-a cosθ$). The components of the stress tensor and all invariants of the conformally-flat Schwarzschild spacetime are regulated by means of the exponential factor $exp(-k/r), k > 0$.

gr-qc↗
arXiv2018

On a nonstatic Painleve-Gullstrand spacetime

A time dependent geometry outside a spherically symmetric mass is proposed. The source has zero energy density but nonzero radial and tangential pressures. The time variable is interpreted as the duration of measurement performed upon the physical system. For very short time intervals, the effect of the mass source is much reduced, going to zero when $t \rightarrow 0$. All physical quantities are finite when $t \rightarrow 0$ and $r \rightarrow 0$ and also at infinity. The total energy flux measured on a hypersurface of constant $r$ is vanishing.

physics.gen-ph↗