arXiv subjects

Ren Tsuda

Publications and source records attributed to Ren Tsuda.

6 recordsLinked to original sources

arXiv2026

Fan-Wang type regular black holes in Quasi-Topological Gravity

We construct a class of regular black hole solutions of the Fan-Wang type within quasi-topological gravity (QTG) in arbitrary spacetime dimensions greater than four. In contrast to the original Fan-Wang solution, which was obtained in four-dimensional general relativity coupled to nonlinear electrodynamics, our higher-dimensional generalization does not require any matter fields. Instead, regularity is achieved purely through an infinite tower of higher-curvature corrections. We demonstrate that the Fan-Wang-type metric is a solution to the QTG field equations by explicitly determining the corresponding coupling constants for each curvature order. Within an appropriate parameter regime, the solution describes an asymptotically flat black hole spacetime with a regular center. Remarkably, even in the case of negative mass, the geometry can remain completely regular, in sharp contrast to Einstein gravity.

gr-qc↗

arXiv2023

Existence conditions of nonsingular dyonic black holes in nonlinear electrodynamics

General relativity coupled to nonlinear electrodynamics is known to have nonsingular black hole solutions. We investigate the existence conditions for such solutions in two-parameter Lagrangian ${\cal L} \left( {\cal F} , {\cal G} \right)$. In particular, we obtain a criterion on the Lagrangian for the existence of nonsingular black hole with a dyonic charge. In addition, we present a simple example of two-parameter Lagrangian satisfying the criterion, in which the existence of the dyonic solution is actually confirmed. Moreover, apart from the actual existence of dyonic solutions, we consider some examples for the Lagrangian satisfying such a criterion.

gr-qc↗

arXiv2023

Acoustic black and white holes of potential flow in a tube

We propose a new simple model of acoustic black hole in a thin tube, where the difference in the gravitational potential is used to create a transonic flow. The main merit of our transonic flow model is that the Euler equations can be solved analytically. In fact, we can obtain an exact solution to the equation in terms of a height function in the monatomic case $\gamma=5/3$. For arbitrary $\gamma$, we find that it takes a simple form by the near-sonic approximation. Moreover, we obtain two analytic solutions describing a backward wave and a forward wave, from which we can confirm the existence of sonic horizons.

gr-qc↗

arXiv2021

Expanding Polyhedral Universe in Regge Calculus

The closed Friedmann--Lemaître--Robertson--Walker (FLRW) universe of Einstein gravity with positive cosmological constant in three dimensions is investigated by using the Collins--Williams formalism in Regge calculus. A spherical Cauchy surface is replaced with regular polyhedrons. The Regge equations are reduced to differential equations in the continuum time limit. Numerical solutions to the Regge equations approximate well the continuum FLRW universe during the era of small edge length. The deviation from the continuum solution becomes larger and larger with time. Unlike the continuum universe, the polyhedral universe expands to infinite within finite time. To remedy the shortcoming of the model universe we introduce geodesic domes and pseudo-regular polyhedrons. It is shown that the pseudo-regular polyhedron model can approximate well the results of the Regge calculus for the geodesic domes. The pseudo-regular polyhedron model approaches the continuum solution in the infinite frequency limit.

gr-qc↗

arXiv2021

Oscillating 4-Polytopal Universe in Regge Calculus

The discretized closed Friedmann-Lemaître-Robertson-Walker (FLRW) universe with positive cosmological constant is investigated by Regge calculus. According to the Collins-Williams formalism, a hyperspherical Cauchy surface is replaced with regular 4-polytopes. Numerical solutions to the Regge equations approximate well to the continuum solution during the era of small edge length. Unlike the expanding polyhedral universe in three dimensions, the 4-polytopal universes repeat expansions and contractions. To go beyond the approximation using regular 4-polytopes we introduce pseudo-regular 4-polytopes by averaging the dihedral angles of the tessellated regular 600-cell. The degree of precision of the tessellation is called the frequency. Regge equations for the pseudo-regular 4-polytope have simple and unique expressions for any frequency. In the infinite frequency limit, the pseudo-regular 4-polytope model approaches the continuum FLRW universe.

gr-qc↗

arXiv2021

Higher Dimensional Polytopal Universe in Regge Calculus

Higher dimensional closed Friedmann-Lemaître-Robertson-Walker (FLRW) universe with positive cosmological constant is investigated by Regge calculus. A Cauchy surface of discretized FLRW universe is replaced by a regular polytope in accordance with the Collins-Williams (CW) formalism. Polytopes in an arbitrary dimensions can be systematically dealt with by a set of five integers integrating the Schläfli symbol of the polytope. Regge action in continuum time limit is given. It possesses reparameterization invariance of the time variable. Variational principle for edge lengths and struts yields Hamiltonian constraint and evolution equation. They describe oscillating universe in dimensions larger than three. To go beyond the approximation by regular polytopes, we propose pseudo-regular polytopes with fractional Schläfli symbols as a substitute for geodesic domes in higher dimensions. We examine the pseudo-regular polytope model as an effective theory of Regge calculus for the geodesic domes. In the infinite frequency limit, the pseudo-regular polytope model reduces to the continuum FLRW universe.

gr-qc↗