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F. R. Klinkhamer

Publications and source records attributed to F. R. Klinkhamer.

At least 19 recordsLinked to original sources
arXiv2025

Big Bang as spacetime defect

We review the suggestion that it is possible to eliminate the Big Bang curvature singularity of the Friedmann cosmological solution by considering a particular type of degenerate spacetime metric. Specifically, we take the 4-dimensional spacetime metric to have a spacelike 3-dimensional defect with a vanishing determinant of the metric. This new solution suggests the existence of another "side" of the Big Bang (perhaps a more appropriate description than "pre-Big-Bang" phase used in our original paper). The corresponding new solution for defect wormholes is also briefly discussed.

gr-qc↗
arXiv2023

Higher-dimensional extension of a vacuum-defect wormhole

We present a 5D metric which interpolates between the standard 4D Schwarzschild metric with mass parameter $M$ and a new 4D $M$-deformed vacuum-defect-wormhole metric. The 5D spacetime can, in principle, have an infinite mass density that gives rise to the $M$ parameter of the 4D $M$-deformed vacuum-defect wormhole. For completeness, we also give 4D interpolating metrics between the original vacuum-defect wormhole at the wormhole throat and the $M$-deformed vacuum-defect wormhole at spatial infinity.

gr-qc↗
arXiv2023

Vacuum-defect wormholes and a mirror world

We have recently discovered a smooth vacuum-wormhole solution of the first-order equations of general relativity. Here, we obtain the corresponding multiple-vacuum-wormhole solution. Assuming that our world is essentially Minkowski spacetime with a large number of these vacuum-defect wormholes inserted, there is then another flat spacetime with opposite spatial orientation, which may be called a "mirror" world. We briefly discuss some phenomenological aspects and point out that there will be no significant vacuum-Cherenkov radiation in our world, so that ultrahigh-energy cosmic rays do not constrain the typical size and separation of the wormhole mouths (different from the constraints obtained for a single Minkowski spacetime with similar defects). Other signatures from a "gas" of vacuum-defect wormholes are mentioned, including a possible time machine.

gr-qc↗
arXiv2023

Defect wormhole: A traversable wormhole without exotic matter

We present a traversable-wormhole solution of the gravitational field equation of General Relativity without need of exotic matter (exotic matter can, for example, have negative energy density and vanishing isotropic pressure). Instead of exotic matter, the solution relies on a 3-dimensional "spacetime defect" characterized by a locally vanishing metric determinant.

gr-qc↗
arXiv2023

Emergent gravity from the IIB matrix model and cancellation of a cosmological constant

We review a cosmological model where the metric determinant plays a dynamical role and present new numerical results on the cancellation of the vacuum energy density including the contribution of a cosmological constant. The action of this model is only invariant under restricted coordinate transformations with unit Jacobian (the same restriction appears in the well-known unimodular-gravity approach to the cosmological constant problem). As to the possible origin of the nonstandard terms in the matter action of the model, we show that these terms can, in principle, arise from the emergent gravity in the IIB matrix model, a nonperturbative formulation of superstring theory.

hep-th↗
arXiv2022

Extension of unimodular gravity and the cosmological constant

A new way is proposed to cancel the cosmological constant. The proposal involves the metric determinant acting as a type of self-adjusting $q$-field without need of a fine-tuned chemical potential. Since the determinant of the metric now plays a role in the physics, the allowed coordinate transformations are restricted to those with unit Jacobian. This approach to the cosmological constant problem is, therefore, similar to the unimodular-gravity approach of the previous literature. The resulting cosmology has been studied and the obtained results show the natural cancellation of an initial cosmological constant if quantum-dissipative effects are included.

hep-th↗
arXiv2022

IIB matrix model, bosonic master field, and emergent spacetime

The IIB matrix model has been suggested as a particular formulation of nonperturbative superstring theory (M-theory). It has now been realized that an emerging classical spacetime may reside in its large-$N$ master field. This bosonic master field can, in principle, give rise to Minkowski and Robertson-Walker spacetimes. The outstanding task is to solve the bosonic master-field equation, which is essentially an algebraic equation. In this article, we present new results for the $(D,\,N)=(10,\,4)$ bosonic master-field equation of the IIB matrix model, where $D$ is the number of bosonic matrices and $N$ the matrix size. We also give, in a self-contained appendix, explicit results for critical points of the effective bosonic action. The main physics application of the (dimensionless) IIB matrix model may be in providing a (conformal) phase that replaces the Friedmann big bang singularity.

hep-th↗
arXiv2022

Big bang as a topological quantum phase transition

It has been argued that a particular type of quantum-vacuum variable $q$ can provide a solution to the main cosmological constant problem and possibly also give a cold-dark-matter component. We now show that the same $q$-field may suggest a new interpretation of the big bang, namely as a quantum phase transition between topologically inequivalent vacua. These two vacua are characterized by the equilibrium values $q=\pm \, q_{0}$ and there is a kink-type solution $q(t)$ interpolating between $q=- q_{0}$ for $t\to -\infty$ and $q= +q_{0}$ for $t\to \infty$, with conformal symmetry for $q=0$ at $t=0$.

hep-th↗
arXiv2022

Towards a numerical solution of the bosonic master-field equation of the IIB matrix model

A direct algebraic solution has been obtained from the full bosonic master-field equation of the IIB matrix model for low dimensionality $D=3$ and small matrix size $N=3$. A different method is needed for larger values of $D$ and $N$. Here, we explore an indirect numerical approach and obtain an approximate numerical solution for the nontrivial case $(D,\,N)=(10,\,4)$ with a complex Pfaffian. We also present a suggestion for numerical calculations at larger values of $N$.

hep-th↗
arXiv2021

A first look at the bosonic master-field equation of the IIB matrix model

The bosonic large-$N$ master field of the IIB matrix model can, in principle, give rise to an emergent classical spacetime. The task is then to calculate this master field as a solution of the bosonic master-field equation. We consider a simplified version of the algebraic bosonic master-field equation and take dimensionality $D=2$ and matrix size $N=6$. For an explicit realization of the pseudorandom constants entering this simplified algebraic equation, we establish the existence of a solution and find, after diagonalization of one of the two obtained matrices, a band-diagonal structure of the other matrix.

hep-th↗
arXiv2021

Solutions of the bosonic master-field equation from a supersymmetric matrix model

It has been argued that the bosonic large-$N$ master field of the IIB matrix model can give rise to an emergent classical spacetime. In a recent paper, we have obtained solutions of a simplified bosonic master-field equation from a related matrix model. In this simplified equation, the effects of dynamic fermions were removed. We now consider the full bosonic master-field equation from a related supersymmetric matrix model for dimensionality $D=3$ and matrix size $N=3$. In this last equation, the effects of dynamic fermions are included. With an explicit realization of the random constants entering this algebraic equation, we establish the existence of nontrivial solutions. The small matrix size, however, does not allow us to make a definitive statement as to the appearance of a diagonal/band-diagonal structure in the obtained matrices.

hep-th↗
arXiv2021

M-theory and the birth of the Universe

In this review article, we first discuss a possible regularization of the big bang curvature singularity of the standard Friedmann cosmology, where the curvature singularity is replaced by a spacetime defect. We then consider the hypothesis that a new physics phase gave rise to this particular spacetime defect. Specifically, we set out on an explorative calculation using the IIB matrix model, which has been proposed as a particular formulation of nonperturbative superstring theory (M-theory).

hep-th↗
arXiv2021

IIB matrix model and regularized big bang

The large-$N$ master field of the Lorentzian IIB matrix model can, in principle, give rise to a particular degenerate metric relevant to a regularized big bang. The length parameter of this degenerate metric is then calculated in terms of the IIB-matrix-model length scale.

hep-th↗
arXiv2021

Quantum scattering process and information transfer out of a black hole

We calculate the probability amplitude for tree-level elastic electron-muon scattering in Minkowski spacetime with carefully prepared initial and final wave packets. The obtained nonzero amplitude implies a nonvanishing probability for detecting a recoil electron outside the light-cone of the initial muon. Transposing this Minkowski-spacetime scattering result to a near-horizon spacetime region of a massive Schwarzschild black hole and referring to a previously proposed Gedankenexperiment, we conclude that, in principle, it is possible to have information transfer from inside the black-hole horizon to outside.

gr-qc↗
arXiv2021

IIB matrix model: Extracting the spacetime metric

The large-$N$ master field of the Lorentzian IIB matrix model is of course not known, but we can assume that we already have it and investigate how the emerging spacetime metric could be extracted. We show that, in principle, it is possible to obtain both the Minkowski metric and the spatially flat Robertson-Walker metric.

hep-th↗
arXiv2021

IIB matrix model: Extracting the spacetime points

Assuming that the large-$N$ master field of the Lorentzian IIB matrix model has been obtained, we go through the procedure of how the coordinates of emerging spacetime points can be extracted. Explicit calculations with test master fields suggest that the genuine IIB-matrix-model master field may have a fine-structure that is essential for producing the spacetime points of an expanding universe.

hep-th↗