Cardy-Verlinde Formula and Thermodynamics of Black Hole in Higher Dimensional Space-Time

In this paper we discuss thermodynamics parameters of black hole horizon and cosmological horizon in general high-dimensional space-time. We obtain that the entropy of a cosmological horizon can be described by the Cardy-Verlinde formula. However, the entropy of black hole horizon will be expressed in a form of the Cardy-Verlinde formula, if one adopts the methods given by Abbott and Deser to compute the mass of a black hole in general high-dimensional space-time. Through discussion, relation among various thermodynamics parameters of the black hole in general high-dimensional space-time is given. That is, differential formula of the first law of thermodynamics is obtained. Because we discuss the general high-dimensional space-time, our result has universality. PACS: 04.20.Dw, 97.60.Lf     

Vaidya Space-Time in Black-Hole Evaporation

We take a boundary-value approach to quantum amplitudes arising in gravitational collapse to a black hole. Pose boundary data on initial and final space-like hypersurfaces Σ _F,I , separated at spatial infinity by a Lorentzian proper-time interval T. Quantum amplitudes are calculated following Feynman's approach; rotate: T→|T|exp (−iθ) into the complex, where 0< θ≤π/2, and solve the corresponding well-posed complex classical boundary-value problem. We compute the classical Lorentzian action S _class and corresponding semi-classical quantum amplitude, proportional to exp (iS _class). To recover the Lorentzian amplitude, take the limit θ→ 0₊ of the semi-classical amplitude. For the classical boundary-value problem with given perturbative boundary data, we compute an effective spherically-symmetric energy-momentum tensor 〉 T ^μν〈 _EFF , averaged over several wavelengths of the radiation, describing the averaged extra energy-momentum contribution in the Einstein field equations, due to the perturbations. This takes the form of a null fluid, describing the radiation (of quantum origin) streaming radially outwards. The classical space-time metric, in this region of the space time, is of Vaidya form, justifying the adiabatic radial mode equations, for spins s = 0 and s = 2.     

Gravitational Collapse in Higher Dimensional Space-Time

Spherically symmetric inhomogeneous dust collapse has been studied in higher dimensional space-time and the appearance of a naked singularity has been analyzed both for the non-marginal and the marginally bound cases. It has been shown that a naked singularity is possible for any arbitrary dimension in the non-marginally bound case. For the marginally bound case we have examined the radial null geodesics from the singularity and found that a naked singularity is possible up to five dimensions.     

String Cosmology with Brans–Dicke Theory in Higher Dimensional Space-Time

We develop string cosmology in the presence ofa Brans–Dicke (BD) scalar field coupled toEinstein gravity for higher dimensional space-time.Solutions are obtained for the equation of state for thep-string, and physical situations arediscussed.     

Letter: Gravitational Thermodynamics of a Vaidya Black Hole

The path integral approach is applied to the statistical thermodynamics of a radiating Vaidya black hole. The entropy still satisfies the Bekenstein-Hawking formula, except for a negligible term. The entropy production, as a measurement of the irreversibility, is also obtained.     

Thermodynamics of a Higher Dimensional Noncommutative Inspired Anti-de Sitter-Einstein-Born-Infeld Black Hole

We analyze noncommutative deformations of a higher dimensional anti-de Sitter-Einstein-Born-Infeld black hole. Two models based on noncommutative inspired distributions of mass and charge are discussed and their thermodynamical properties such as the equation of state are explicitly calculated. In the (3 + 1)-dimensional case the Gibbs energy function of each model is used to discuss the presence of phase transitions.     

FRW Bulk Viscous Cosmology in Multi Dimensional Space-Time

The exact solutions of the field equations are obtained by using the gamma law equation of state p=(γ−1)ρ in which the parameter γ depends on scale factor R. The fundamental form of γ(R) is used to analyze a wide range of phases in cosmic history: inflationary phase and radiation-dominated phase. The corresponding physical interpretations of cosmological solutions are also discussed in the framework of (n+2) dimensional space time.     

Higher dimensional Vaidya metric in Einstein and de Sitter background

Spherically symmetric non-static higher dimensional metrics are considered in connection with Einstein’s field equations. Two exact solutions are derived. One of them corresponds to a mixture of perfect fluid and pure radiation field and represents higher dimensional Vaidya metric in the cosmological background of Einstein static universe. The other corresponds to a pure radiation field and represents higher dimensional Vaidya metric in the background de Sitter universe. For both of these solutions, the cosmological constant is taken to be non-zero. Many known solutions are derived as particular cases.     

Generalized Vaidya metrics

We investigate criteria under which one may construct the energy tensor of a null radiation field from an algebraically special vacuum metric. The field bears the same relationship to the original metric as does Vaidya's to Schwarzschild's. As an example we generate a class of null radiation fields from a class of vacuum metrics without symmetry discovered by Robinson and Robinson.Supported in part by the National Science Foundation (GP-8868, GP-20033, and GU-1598), Air Force Office of Scientific Research under Grant AF-AFOSR-903-67 and by the National Aeronautics and Space Administration under NASA Grant No. NGL 44-004-001.     

Vaidya spacetime in the diagonal coordinates

We have analyzed the transformation from initial coordinates (v, r) of the Vaidya metric with light coordinate v to the most physical diagonal coordinates (t, r). An exact solution has been obtained for the corresponding metric tensor in the case of a linear dependence of the mass function of the Vaidya metric on light coordinate v. In the diagonal coordinates, a narrow region (with a width proportional to the mass growth rate of a black hole) has been detected near the visibility horizon of the Vaidya accreting black hole, in which the metric differs qualitatively from the Schwarzschild metric and cannot be represented as a small perturbation. It has been shown that, in this case, a single set of diagonal coordinates (t, r) is insufficient to cover the entire range of initial coordinates (v, r) outside the visibility horizon; at least three sets of diagonal coordinates are required, the domains of which are separated by singular surfaces on which the metric components have singularities (either g ₀₀ = 0 or g ₀₀ = ∞). The energy–momentum tensor diverges on these surfaces; however, the tidal forces turn out to be finite, which follows from an analysis of the deviation equations for geodesics. Therefore, these singular surfaces are exclusively coordinate singularities that can be referred to as false fire-walls because there are no physical singularities on them. We have also considered the transformation from the initial coordinates to other diagonal coordinates (η, y), in which the solution is obtained in explicit form, and there is no energy–momentum tensor divergence.     

The Vaidya solution in higher dimensions

The Vaidya metric representing the gravitational field of a radiating star is generalized to spacetimes of dimensions greater than four.     

Evaporating black hole in Vaidya metric

The energy momentum tensor for an evaporating black hole modelled with Vaidya metric is computed. The result indicates that the evaporation does not create a naked singularity.     

On Hexagonal Structures in Higher Dimensional Theories

We analyze the geometrical background under which many Lie groups relevant to particle physics are endowed with a (possibly multiple) hexagonal structure. There are several groups appearing, either as special holonomy groups on the compactification process from higher dimensions, or as dynamical string gauge groups; this includes groups like SU(2), SU(3), G ₂, Spin(7), O(8) as well as E ₈ and O(32). We emphasize also the relation of these hexagonal structures with the octonion division algebra, as we expect as well eventually some role for octonions in the interpretation of symmetries in High Energy Physics.     

Thermodynamics and Stability of Five Dimensional AdS Reissner-Nordstrom Black Hole

In this paper we consider five dimensional AdS Reissner-Nordstrom black hole and calculate thermodynamical variables such as entropy, specific heat and free energy. In that case we can obtain stability conditions of the black hole and fix black hole charge and mass for phase transition.     

LETTER: Generalized Vaidya Solutions

A large family of solutions, representing, ingeneral, spherically symmetric Type II fluid, ispresented, which includes most of the known solutions tothe Einstein field equations, such as, the monopole-de Sitter-charged Vaidya ones.     

Higher Dimensional Spherically Symmetric Gravitational Collapse

In this paper, the gravitational collapse of type I matter has been investigated in the context of higher dimensional spherically symmetric spacetime. The equation of state $P_{R}=\frac{1}{b}\rho$ with b>0 is assumed. The effects of more than four dimensions on the nature of the singularity are being discussed.     

A Higher Dimensional Inflationary Universe in General Relativity

A five dimensional Kaluza-Klein inflationary universe is investigated in the presence of massless scalar field with a flat potential. To get an inflationary universe a flat region in which potential V is constant is considered. Some physical and kinematical properties of the universe are also discussed.     

Energy and momentum in Vaidya spacetime

The components of the energy-momentum pseudotensors of Einstein, Tolman, Landau and Lifshitz, and Møller are evaluated for the Vaidya radiating spacetime. These pseudotensors are found to be traceless for this spacetime. The pseudotensors of Einstein and Tolman give exactly same result for all their components. Unlike in the case of the Kerr-Newman field, the pseudotensor of Møller gives the same energy as given by that of the Einstein, Tolman or Landau and Lifshitz.