On Spherically Symmetric Minimally Coupled Brane Worlds

For a static, spherically symmetric brane in the framework of the RS2 concept, we study the conditions under which the 4D tensor E _v, arising from the 5D Weyl tensor, vanishes on the brane. Gravity on the brane is then decoupled from the bulk geometry, it is the so-called minimally coupled brane world (MCBW). Assuming E _v =0 in the whole bulk, we try to solve the 5D Einstein equations G _AB + _5gAB =0 and obtain an overdetermined set of equations for functions of the radial coordinate. Some special solutions are found, among which are the well-known black string solution with the Schwarzschild metric on the brane and its generalizations with Schwarzschild–(A)dS on-brane metrics. It is concluded that a MCBW can be embedded, in general, in a bulk where E_v is not identically zero but only vanishes on the brane. We also present some previous results on the general properties of scalar fields on the brane and give an example of a wormhole supported by a scalar field in a MCBW.     

Spherically Symmetric Vacuum Brane and Wormhole Solutions

In this letter, we have obtained static, spherically symmetric solutions of the effective vacuum Einstein field equations on a brane embedded in a five dimensional space time. The effective stress tensor is induced by the interaction with the bulk gravitational field and is given by the electric part of the five dimensional Weyl tensor. Due to traceless nature of this non-local effect of the bulk, any solution of  ⁽⁴⁾ R=0 is a possible solution of the vacuum brane. We have derived a class of solutions, which corresponds to wormhole solution. Physical properties and characteristics of the wormhole are studied.     

Entropy of N-Dimensional Spherically Symmetric Charged Black Hole

By using the method of quantum statistics, we derive directly the partition functions of bosonic andfermionic fields in the N-dimensional spherically symmetric charged black hole space-time. The statistical entropy ofblack hole is obtained by an improved brick-wall method. When we choose proper parameters in our results, we canobtain that the entropy of black hole is proportional to the area of horizon. In our result, there do not exist neglectedterm and divergent logarithmic term given in the original brick-wall method. We avoid the difficulty in solving the waveequation of scalar and Dirac fields. We offer a simple and direct way of studying entropy of the higher-dimensional black hole.     

Entropy of Four-Dimensional Spherically Symmetric Black Holes with Planck Length

Considering corrections to all orders in Planck length on the quantum state density from a generalized uncertainty principle （GUP）, we calculate the statistical entropy of the Bose field and Fermi field on the background of the four-dimensional spherically symmetric black holes without any cutoff. It is obtained that the statistical entropy is directly proportional to the area of horizon.     

Quasinormal Modes of Spherically Symmetric Curve Spacetime with Dark Matter Term

We study quasinormal modes of scalar field perturbation and electromagnetic field perturbation in a black hole space-time with dark matter by using WKB approximation method. The result shows clearly that the real part of black hole quasinormal modes is mainly determined by angular quantum number while its imaginary part mainly determined by model number. We also found out that the dark matter will restrain the perturbation frequency and slow down the speed of damping in spacetime. In addition; dark matter has a greater influence upon quasinormal modes in the electromagnetic field than that in the scalar field.     

Entropy of Four-Dimensional Spherically Symmetric Black Holes with Planck Length

Considering corrections to all orders in Planck length on the quantum state density from a generalized uncertainty principle (GUP), we calculate the statistical entropy of the Bose field and Fermi field on the background of the four-dimensional spherically symmetric black holes without any cutoff. It is obtained that the statistical entropy is directly proportional to the area of horizon.     

Negative Energies on the Brane

It has recently been proposed that our universe is a three-brane embedded in a higher dimensional spacetime. Here I show that black holes on the brane, black strings intersecting the brane, and gravitational waves propagating in the bulk induce an effective energy-momentum tensor on the brane that contains negative energy densities.     

Tunneling Radiation from a Static Spherically Symmetric Black Hole Surrounded by Quintessence

By extending the Parikh-Wilczek tunneling framework, we investigate the tunneling radiation of uncharged massless particles from a static spherically symmetric black hole surrounded by quintessence. The results are consistent with an underlying unitary theory.     

Tunneling Radiation from a Static Spherically Symmetric Black Hole Surroundedby Quintessence

By extending the Parikh-Wilczek tunneling framework, we investigate the tunneling radiation of uncharged massless particles from a static spherically symmetric black hole surrounded by quintessence. The results are consistent with an underlying unitary theory.     

The Entropy of Spherically Symmetric Black Holes Due to Arbitrary Spin Fields

Using the membrane model which is based on brick-wall model, we calculated the free energy and entropy of spherically symmetric black holes due to arbitrary spin. The result shows that the entropy of a scalar field and the entropy of a Fermionic field have similar formulas. There is only a coefficient between them.     

The T-Domain and Extreme Matter Phases Inside Spherically Symmetric Black Holes

Black hole interiors (the T-domain) are studied here in great detail. Both the general and particular T-domain solutions are presented including non-singular ones. Infinitely many local T-domain solutions may be modeled with this scheme. The duality between the T and R domains is presented. It is demonstrated how generally well behaved R-domain solutions will give rise to exotic phases of matter when collapsed inside the event horizon. However, as seen by an external observer, the field is simply that of the Schwarzschild vacuum with well behaved mass term and no evidence of this behaviour may be observed. A singularity theorem is also presented which is independent of energy conditions.     

Spherically Symmetric Static Solutions of the Einstein Equations with Elastic Matter Source

The Einstein equations for a spherically symmetric static distribution of elastic matter are examined. The existence of regular solutions near the center is proven under a fairly mild hypothesis on the constitutive equation. These solutions are uniquely determined by the choice of central pressure and constitutive equation. It is also shown for a Hookean elastic material that these solutions can be integrated outward till the radial pressure vanishes, thus one can join an exterior Schwarzschild metric to obtain a maximal solution of the Einstein equations.     

Schwarzschild Solution on the Brane

In this paper it is shown that Schwarzschild solution is possible in brane world for some specific choices of brane matter and the non-local effects from the bulk. A conformally flat bulk space time with fine-tuned vacuum energy (brane tension) shows that Schwarzschild solution may also be the vacuum solution for brane world scenario.     

Hawking Radiation from a Spherically Symmetric Static Black Hole

The massive particles’ Hawking radiation from a spherically symmetric static black hole is investigated with Parikh-Wilczek method, Hamilton–Jacobi method and Damour–Ruffini’s method. When energy conservation is considered, the same result can be concluded that the radiation spectrum is not precisely thermal. The corrected spectrum is consistent to the underlying unitary quantum theory, which can be used to explain the information loss paradox possibly.      

Brane tilings and their applications

We review recent developments in the theory of brane tilings and four‐dimensional 𝒩 = 1 supersymmetric quiver gauge theories. This review consists of two parts. In part I, we describe foundations of brane tilings, emphasizing the physical interpretation of brane tilings as fivebrane systems. In part II, we discuss application of brane tilings to AdS/CFT correspondence and homological mirror symmetry. More topics, such as orientifold of brane tilings, phenomenological model building, similarities with BPS solitons in supersymmetric gauge theories, are also briefly discussed. This paper is a revised version of the author's master's thesis submitted to Department of Physics, Faculty of Science, the University of Tokyo on January 2008, and is based on his several papers and some works in progress [1–7].     

Phantom Divide Crossing on Brane World

We study the RSII brane world corrected by the four-dimensional scalar curvature and five-dimensional Gauss-Bonnet curvature. The energy transfer between brane and bulk is also taken into account. Parameterizing the energy transfer, the resulting Friedmann equation on brane is solved at low energy. It is shown that phantom divide crossing may be achieved in the braneworld model with wide possibilities, embodying the combined effect of brane-bulk energy transfer, curvature corrections, and the fine-turning mechanics.     

Inconsistence of Non-Singular Spherically Symmetric Solution and a Satisfactory Energy-Momentum Complex

Two spherically symmetric non-singular black hole solutions in Moiler tetrad theory of gravitation have been obtained. Although the two solutions have the same form of metric （spherically symmetric nonsingular black hole）, their energy contents are different. We use another method given by Gibbons and Hawking to calculate the energy content of these solutions. We also obtained different value of energy. Study the requirements of a satisfactory energymomentum complex given by Moiler we find that the second solution, which behaves as 1/√r, is not transformed as a four-vector under Lorentz transformation.     

Constraints via the Event Horizon Telescope for Black Hole Solutions with Dark Matter under the Generalized Uncertainty Principle Minimal Length Scale Effect

Four spherically symmetric but non-asymptotically flat black hole solutions surrounded with spherical dark matter distribution perceived under the minimal length scale effect is derived via the generalized uncertainty principle. Here, the effect of this quantum correction, described by the parameter $\gamma$, is considered on a toy model galaxy with dark matter and the three well-known dark matter distributions: the cold dark matter, scalar field dark matter, and the universal rotation curve. The aim is to find constraints to $\gamma$ by applying these solutions to the known supermassive black holes: Sagittarius A (Sgr. A*) and Messier 87* (M87*), in conjunction with the available Event Horizon telescope. The effect of $\gamma$ is then examined on the event horizon, photonsphere, and shadow radii, where unique deviations from the Schwarzschild case are observed. As for the shadow radii, bounds are obtained for the values of $\gamma$ on each black hole solution at $3\sigma$ confidence level. The results revealed that under minimal length scale effect, black holes can give positive (larger shadow) and negative values (smaller shadow) of $\gamma$, which are supported indirectly by laboratory experiments and astrophysical or cosmological observations, respectively.     

Abundance of Asymmetric Dark Matter in Brane World Cosmology

Relic abundance of asymmetric Dark Matter particles in brane world cosmological scenario is investigated in this article. Hubble expansion rate is enhanced in brane world cosmology and it affects the relic abundance of asymmetric Dark Matter particles. We analyze how the relic abundance of asymmetric Dark Matter is changed in this model. We show that in such kind of nonstandard cosmological scenario, indirect detection of asymmetric Dark Matter is possible if the cross section is small enough which let the anti-particle abundance kept in the same amount with the particle. We show the indirect detection signal constraints can be used to such model only when the cross section and the 5-dimensional Planck mass scale are in appropriate values.     

Brane singularities with mixtures in the bulk

By extending previous analysis of the authors, a systematic study of the singularity structure and possible asymptotic behaviors of five‐dimensional braneworld solutions is performed in the case where the bulk is a mixture of an analog of perfect fluid (with a density and pressure depending on the extra coordinate) and a massless scalar field. The two bulk components interact by exchanging energy so that the total energy is conserved. In a particular range of the interaction parameters, we find flat brane general solutions avoiding the singularity at finite distance from the brane, in the same region of the equation of state constant parameter γ = P/ρ that we found previously in the absence of the bulk scalar field (‐1 < γ < ‐1/2).