Searcharxiv⌕ Search

arXiv subjects

Nikodem Popławski

Publications and source records attributed to Nikodem Popławski.

At least 19 recordsLinked to original sources
arXiv2026

Universe in a black hole in Einstein$-$Cartan gravity

The conservation law for the angular momentum in curved spacetime, consistent with relativistic quantum mechanics, requires that the antisymmetric part of the affine connection (torsion tensor) is a variable in the principle of least action. The coupling between the spin of elementary particles and torsion in the Einstein$-$Cartan theory of gravity generates gravitational repulsion at extremely high densities in fermionic matter, approximated as a spin fluid, and thus avoids the formation of singularities in black holes. The collapsing matter in a black hole should therefore bounce at a finite density and then expand into a new region of space on the other side of the event horizon, which may be regarded as a nonsingular, closed universe. We show that quantum particle production caused by an extremely high curvature near a bounce can create enormous amounts of matter, produce entropy, and generate a finite period of exponential expansion (inflation) of this universe. This scenario can thus explain inflation without a scalar field and reheating. We show that, depending on the particle production rate, such a universe may undergo several nonsingular bounces until it has enough matter to reach a size at which the cosmological constant starts cosmic acceleration. The last bounce can be regarded as the big bang of this universe.

gr-qc↗
arXiv2026

Spinors with torsion and matter$-$antimatter asymmetry

The conservation law for the orbital plus spin angular momentum of a free Dirac particle in curved spacetime requires that the affine connection has the antisymmetric part: the torsion tensor, which extends general relativity to the Einstein$-$Cartan theory of gravity. In the presence of torsion, the Dirac equation becomes a nonlinear, cubic equation in the spinor wave function. We show that the energy eigenvalues of the corresponding Hamiltonian as functions of the momentum are different for the fermion and antifermion components of the spinor, violating charge conjugation symmetry, and also depend on the helicity. Consequently, particles of matter and antimatter have different dispersion relations and therefore different masses. This mass difference increases with density and becomes significant near the Cartan density, which existed in the early Universe. Because antimatter particles were more massive than matter particles, they were also slower during pair production in the early Universe and therefore had higher cross sections for gravitational capture by primordial black holes. This difference might have led to the matter$-$antimatter imbalance in the observable Universe: the missing antimatter fell into black holes.

gr-qc↗
arXiv2026

Gravitational collapse of a fluid with torsion into a universe in a black hole

We consider gravitational collapse of a spherically symmetric sphere of a fluid with spin and torsion into a black hole. We use the Tolman metric and the Einstein$-$Cartan field equations with a relativistic spin fluid as a source. We show that gravitational repulsion of torsion prevents a singularity and replaces it with a nonsingular bounce. Quantum particle production during contraction helps torsion to dominate over shear. Particle production during expansion can generate a finite period of inflation and produce enormous amounts of matter. The resulting closed universe on the other side of the event horizon may have several bounces. Such a universe is oscillatory, with each cycle larger in size than the previous cycle, until it reaches the cosmological size and expands indefinitely. Our universe might have therefore originated from a black hole.

gr-qc↗
arXiv2026

Black holes in the expanding Universe

The McVittie metric does not describe a physical black hole in an expanding Universe because the curvature scalar and pressure at its event horizon are infinite. We show that extending this metric to an inhomogeneous scale factor, which depends on both the time and radial coordinate, removes those infinities by imposing at the horizon the constancy of the Hubble parameter and a particular constraint on the gradient of the scale factor. We consider a special case of this metric, and show that the Hubble parameters at the event horizons of all centrally symmetric black holes are equal to the same constant $H_\textrm{hor}=(Λ/3)^{1/2}$. Because of this equality and the equivalence to the Kottler metric near the horizon, black holes do not grow with the Universe expansion.

gr-qc↗
arXiv2025

Gravitational collapse with torsion and universe in a black hole

We consider gravitational collapse of a fluid sphere with torsion generated by spin, which forms a black hole. We use the Tolman metric and the Einstein$-$Cartan field equations with a relativistic spin fluid as a source. We show that gravitational repulsion of torsion prevents a singularity, replacing it with a nonsingular bounce. Quantum particle creation during contraction prevents shear from overcoming torsion. Particle creation during expansion can generate a finite period of inflation and produce large amounts of matter. The resulting closed universe on the other side of the event horizon may have several bounces. Such a universe is oscillatory, with each cycle larger than the preceding cycle, until it reaches a size at which dark energy dominates and expands indefinitely. Our Universe might have therefore originated from a black hole existing in another universe.

gr-qc↗
arXiv2025

Torsional Regularization of Self-Energy and Bare Mass of Electron

In the presence of spacetime torsion, the momentum components do not commute; therefore, in quantum field theory, summation over the momentum eigenvalues will replace integration over the momentum. In the Einstein--Cartan theory of gravity, in which torsion is coupled to spin, the separation between the eigenvalues increases with the magnitude of the momentum. Consequently, this replacement regularizes divergent integrals in Feynman diagrams with loops by turning them into convergent sums. In this article, we apply torsional regularization to the self-energy of a charged lepton in quantum electrodynamics. We show that torsion eliminates the ultraviolet divergence of the standard self-energy. We also show that the infrared divergence is absent. In the end, we calculate the finite bare masses of the electron, muon, and tau lepton: $0.4329\,\mbox{MeV}$, $90.95\,\mbox{MeV}$, and $1543\,\mbox{MeV}$, respectively. These values constitute about $85\%$ of the observed, re-normalized masses.

hep-th↗
arXiv2025

Universe in a rotating black hole and preferred axis

If our universe was born as a baby universe on the other side of the event horizon of a black hole existing in a parent universe, then the corresponding white hole at rest provides the absolute frame of reference in the universe. In this frame, the cosmic microwave background radiation is isotropic on large scales. If the parent black hole is rotating, then its axis of rotation becomes a preferred axis in the universe. Accordingly, the absolute frame is non-inertial, although the non-inertial forces are small. To decrease their energies, galaxies tend to align their axes of rotation with the preferred axis, resulting in clockwise-counterclockwise asymmetry. The centrifugal force causes a large-scale bulk flow of galaxy clusters in directions perpendicular to the preferred axis. The astronomical data seem to support these motions. The angular velocity of the universe decreases as the universe expands, which is a consequence of the conservation of the angular momentum of the universe. The centrifugal force in a rotating universe, which also decreases, may be the origin of dark energy, in accordance with recent DES observations showing that dark energy becomes weaker with time.

physics.pop-ph↗
arXiv2025

Gravitational collapse in the expanding Universe

We use the Tolman metric to describe gravitational collapse of a sphere of a fluid without pressure in spacetime with the Hubble parameter $H$ related to the cosmological constant. We show that the largest radius of a galaxy formed from such a fluid with mass $M$ is given by $(GM/H^2)^{1/3}$.

gr-qc↗
arXiv2024

Gravitational deflection of light in interior Schwarzschild metric

We determine the angle of deflection of light by the gravitational field inside and outside a spherical body with a homogeneous mass density. We show that the largest deflections, which can be measured by weak gravitational lensing, are in a region displaced from the center of mass. This result can be extended to more general distributions of matter. This displacement, observed in galaxies and colliding galaxy clusters, may be therefore explained without dark matter, within general relativity.

gr-qc↗
arXiv2024

Classical Physics: Spacetime and Fields

We present a self-contained introduction to the classical theory of spacetime and fields. This exposition is based on the most general principles: the principle of general covariance (relativity) and the principle of least action. The order of the exposition is: 1. Spacetime (principle of general covariance and tensors, affine connection, curvature, metric, space and time, tetrad and spin connection, Lorentz group, spinors); 2. Fields (principle of least action, gravitational field, matter, symmetries and conservation laws, particle limit of field, gravitational field equations, spinor fields, electromagnetic field). In this order, a particle is a special case of a field existing in spacetime, and classical mechanics can be derived from field theory.

gr-qc↗
arXiv2023

Gravitational Collapse with Torsion and Universe in a Black Hole

We consider gravitational collapse of a sphere of a fluid with torsion generated by spin, which forms a black hole. We use the Tolman metric and the Einstein$-$Cartan field equations with a relativistic spin fluid as a source. We show that gravitational repulsion of torsion prevents a singularity, replacing it with a nonsingular bounce. Quantum particle creation during contraction prevents shear from overcoming torsion. Particle creation during expansion can generate a finite period of inflation and produce large amounts of matter. The resulting closed universe on the other side of the event horizon may have several bounces. Such a universe is oscillatory, with each cycle larger than the preceding cycle, until it reaches a size at which dark energy dominates and expands indefinitely. Our universe might have therefore originated from a black hole existing in another universe.

gr-qc↗
arXiv2021

The Origin of the Born Rule from Spacetime Averaging

The Born rule postulates that the probability of measurement in quantum mechanics is related to the squared modulus of the wave function $ψ$. We rearrange the equation for energy eigenfunctions to define the energy as the real part of $\hat{E}ψ/ψ$. For an eigenstate, this definition gives a constant energy eigenvalue. For a general wave function, the energy fluctuates in space and time. We consider a particle in a one-dimensional square well potential in a superposition of two states and average the energy over space and time. We show that, for most cases, such an energy expectation value differs by only a few percent from that calculated using the Born rule. This difference is consistent with experimental tests of the expectation value and suggests that the Born rule may be an approximation of spacetime averaging.

quant-ph↗
arXiv2021

Noncommutative momentum and torsional regularization

We show that in the presence of the torsion tensor $S^k_{\phantom{k}ij}$, the quantum commutation relation for the four-momentum, traced over spinor indices, is given by $[p_i,p_j]=2i\hbar S^k_{\phantom{k}ij}p_k$. In the Einstein--Cartan theory of gravity, in which torsion is coupled to spin of fermions, this relation in a coordinate frame reduces to a commutation relation of noncommutative momentum space, $[p_i,p_j]=iε_{ijk}Up^3 p_k$, where $U$ is a constant on the order of the squared inverse of the Planck mass. We propose that this relation replaces the integration in the momentum space in Feynman diagrams with the summation over the discrete momentum eigenvalues. We derive a prescription for this summation that agrees with convergent integrals: \[ \int\frac{d^4p}{(p^2+Δ)^s}\rightarrow 4πU^{s-2}\sum_{l=1}^\infty \int_0^{π/2} dϕ\frac{\sin^4ϕ\,n^{s-3}}{[\sinϕ+UΔn]^s}, \] where $n=\sqrt{l(l+1)}$ and $Δ$ does not depend on $p$. We show that this prescription regularizes ultraviolet-divergent integrals in loop diagrams. We extend this prescription to tensor integrals. We derive a finite, gauge-invariant vacuum polarization tensor and a finite running coupling. Including loops from all charged fermions, we find a finite value for the bare electric charge of an electron: $\approx -1.22\,e$. This torsional regularization may therefore provide a realistic, physical mechanism for eliminating infinities in quantum field theory and making renormalization finite.

gr-qc↗
arXiv2019

Big bounce and closed universe from spin and torsion

We analyze the dynamics of a homogeneous and isotropic universe in the Einstein$--$Cartan theory of gravity. The coupling between the spin and torsion prevents gravitational singularities and replaces the Big Bang with a nonsingular big bounce, at which the universe transitions from contraction to expansion. We show that a closed universe exists only when the product of the scale factor and temperature is higher than a particular threshold, contrary to a flat universe and an open universe, which are not restricted. During inflation, this product must increase to another threshold, so that the universe can reach dark-energy acceleration.

gr-qc↗
arXiv2019

The simplest origin of the big bounce and inflation

Torsion is a geometrical object, required by quantum mechanics in curved spacetime, which may naturally solve fundamental problems of general theory of relativity and cosmology. The black-hole cosmology, resulting from torsion, could be a scenario uniting the ideas of the big bounce and inflation, which were the subject of a recent debate of renowned cosmologists.

physics.pop-ph↗
arXiv2019

Primordial fluctuations of scale factor in closed Universe in Einstein$-$Cartan gravity

We consider a homogeneous and isotropic Universe, described by the minisuperspace Lagrangian with the scale factor as a generalized coordinate. We show that the energy of a closed Universe is zero. We apply the uncertainty principle to this Lagrangian and propose that the quantum uncertainty of the scale factor causes the primordial fluctuations of the matter density. We use the dynamics of the early Universe in the Einstein$-$Cartan theory of gravity with spin and torsion, which eliminates the big-bang singularity and replaces it with a nonsingular bounce. Quantum particle production in highly curved spacetime generates a finite period of cosmic inflation that is consistent with the Planck satellite data. From the inflated primordial fluctuations, we determine the magnitude of the temperature fluctuations in the cosmic microwave background, as a function of the numbers of the thermal degrees of freedom of elementary particles and the particle production coefficient, which is the only unknown parameter.

gr-qc↗
arXiv2019

Invariant temperature of a moving body

The temperature of a mechanical body has a kinetic interpretation: it describes the relative motion of particles within the body. Since the relative velocity of two particles is a Lorentz invariant, so is the temperature. In statistical physics, the temperature is defined as the inverse of the partial derivative of the entropy with respect to the internal energy (the energy in the rest frame of reference). Since the internal energy is a Lorentz invariant, so is the temperature. The Lorentz invariance of the temperature is a consequence of the symmetry between two bodies with equal proper temperatures, moving relative to one another with a constant relative speed, and in thermal contact. We give an equivalent, covariant definition of the temperature in terms of the energy and momentum of the body. We also note contradictions in the earlier articles that derived various transformation laws for the internal energy and temperature.

physics.class-ph↗