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In this work we investigate the entropic information measure in the context of braneworlds with nonconstant curvature. The braneworld entropic information is studied for gravity modified by the square of the Ricci scalar, besides the usual Einstein-Hilbert term. We showed that the minimum value of the brane configurational entropy provides a stricter bound on the parameter that is responsible for the F(R) model differing from the Einstein-Hilbert standard one. Our results are moreover consistent to a negative bulk cosmological constant. [ABSTRACT FROM AUTHOR]

In this paper, we consider third-order Lovelock gravity with a cosmological constant term in an n-dimensional spacetime M4 x /Cn-4, where A/n-4 is a constant curvature space. We decompose the equations of motion to four and higher dimensional ones and find wormhole solutions by considering a vacuum /Cn-4 space. Applying the latter constraint, we determine the second- and third-order Lovelock coefficients and the cosmological constant in terms of specific parameters of the model, such as the size of the extra dimensions. Using the obtained Lovelock coefficients and Λ, we obtain the four-dimensional matter distribution threading the wormhole. Furthermore, by considering the zero tidal force case and a specific equation of state, given by p = (γp - τ)/ω{ 1 + γ)], we find the exact solution for the shape function which represents both asymptotically flat and nonflat wormhole solutions. We show explicitly that these wormhole solutions in addition to traversibility satisfy the energy conditions for suitable choices of parameters and that the existence of a limited spherically symmetric traversable wormhole with normal matter in a four-dimensional spacetime implies a negative effective cosmological constant. [ABSTRACT FROM AUTHOR]

We carry out numerical experiments in the critical collapse of a spherically symmetric massless scalar field in 2 + 1 spacetime dimensions in the presence of a negative cosmological constant and compare them against a new theoretical model. We approximate the true critical solution as the n = 4 Garfinkle solution, matched at the light cone to a Vaidya-like solution, and corrected to leading order for the effect of Λ < 0. This approximation is only C³ at the light cone and has three growing modes. We conjecture that pointwise it is a good approximation to a yet unknown true critical solution that is analytic with only one growing mode (itself approximated by the top mode of our amended Garfinkle solution). With this conjecture, we predict a Ricci-scaling exponent of γ = 8/7 and a mass-scaling exponent of δ = 16/23, compatible with our numerical experiments. [ABSTRACT FROM AUTHOR]

Using the latest observational data we obtain a lower bound on the initial value of the quintessence field in thawing quintessence models of dark energy. For potentials of the form V((Ф) ~ (Ф±2 we find that the initial value |Фi| > 7 x 1018 GeV. We then relate Фi to the duration of inflation by assuming that the initial value of the quintessence field is determined by quantum fluctuations of the quintessence field during inflation. From the lower bound on Фi- we obtain a lower bound on the number of e-foldings of inflation, namely, N > 2 x 1011. We obtain similar bounds for other power law potentials for which too we obtain |Фi| > 0(MP). [ABSTRACT FROM AUTHOR]

Stationary, axially symmetric Brans-Dicke-Maxwell solutions are reexamined in the framework of the Brans-Dicke (BD) theory. We see that, employing a particular parametrization of the standard axially symmetric metric simplifies the procedure of obtaining the Ernst equations for axially symmetric electrovacuum spacetimes for this theory. This analysis also permits us to construct a two parameter extension in both Jordan and Einstein frames of an old solution generating technique frequently used to construct axially symmetric solutions for BD theory from a seed solution of general relativity. As applications of this technique, several known and new solutions are constructed including a general axially symmetric BD-Maxwell solution of Plebanski-Demianski with vanishing cosmological constant, i.e., the Kinnersley solution and general magnetized Kerr-Newman-type solutions. Some physical properties and the circular motion of test particles for a particular subclass of Kinnersley solution, i.e., a Kerr-Newman-NUT-type solution for BD theory, are also investigated in some detail. [ABSTRACT FROM AUTHOR]

Almost a century ago, Einstein used a weak field approximation around Minkowski spacetime to calculate the energy earned away by gravitational waves emitted by a time changing mass-quadrupole. However, by now there is strong observational evidence for a positive cosmological constant, Λ. To incorporate this fact, Einstein's celebrated derivation is generalized by replacing Minkowski spacetime with de Sitter spacetime. The investigation is motivated by the fact that, because of the significant differences between the asymptotic structures of Minkowski and de Sitter spacetimes, many of the standard techniques, including the usual 1/r expansions, cannot be used for Λ > 0. Furthermore, since, e.g., the energy carried by gravitational waves is always positive in Minkowski spacetime but can be arbitrarily negative in de Sitter spacetime irrespective of how small Λ is, the limit Λ → 0 can fail to be continuous. Therefore, a priori it is not clear that a small Λ would introduce only negligible corrections to Einstein's formula. We show that, while even a tiny cosmological constant does introduce qualitatively new features, in the end, corrections to Einstein's formula are negligible for astrophysical sources currently under consideration by gravitational wave observatories. [ABSTRACT FROM AUTHOR]

Using superconformal methods we derive an explicit de Sitter supergravity action invariant under spontaneously broken local N = 1 supersymmetry. The supergravity multiplet interacts with a nilpotent Goldstino multiplet. We present a complete locally supersymmetric action including the graviton and the fermionic fields, gravitino and Goldstino, no scalars. In the global limit when the supergravity multiplet decouples, our action reproduces the Volkov-Akulov theory. In the unitary gauge where the Goldstino vanishes we recover pure supergravity with the positive cosmological constant. The classical equations of motion, with all fermions vanishing, have a maximally symmetric solution: de Sitter space. [ABSTRACT FROM AUTHOR]

In the framework of the Einstein-Maxwell-aether theory, we present two new classes of exact charged black hole solutions, which are asymptotically flat and possess the universal as well as Killing horizons. We also construct the Smarr formulas and calculate the temperatures of the horizons, using the Smarr mass-area relation. We find that, in contrast to the neutral case, a temperature obtained this way is not proportional to its surface gravity at either of the two types of horizons. Einstein-Maxwell-aether black holes with the cosmological constant and their topological cousins are also presented. [ABSTRACT FROM AUTHOR]

Many different cosmological models have been proposed to address the cosmological constant problem and the coincidence problem. We compare here four different models that can be used to describe an effective (time-dependent) cosmological constant Λ(z). A numerical analysis of the Λ(z) evolution obtained for each model shows that it can be used for distinguishing between all four models. We calculate next the ω(Λ) frequencies for quasinormal modes of gravitational perturbations of Schwarzschild-de Sitter black holes at different redshifts. Considering that the variation of Λ happens on cosmological time scales, the combined ω(Λ(z)) could be used in principle to track the evolution of the cosmological constant. We quantify the resulting minute frequency shift in the quasinormal mode frequencies and show that the relative frequency shift grows as M². However, even in a most optimistic scenario with an extremely high mass supermassive black hole there is no prospect for the detection of this effect. [ABSTRACT FROM AUTHOR]

We critically examine the gauge and field-parametrization dependence of renormalization group flows in the vicinity of non-Gaußian fixed points in quantum gravity. While physical observables are independent of such calculational specifications, the construction of quantum gravity field theories typically relies on offshell quantities such as β functions and generating functionals and thus face potential stability issues with regard to such generalized parametrizations. We analyze a two-parameter class of covariant gauge conditions, the role of momentum-dependent field rescalings and a class of field parametrizations. Using the product of Newton and cosmological constant as an indicator, the principle of minimum sensitivity identifies stationary points in this parametrization space which show a remarkable insensitivity to the parametrization. In the most insensitive cases, the quantized gravity system exhibits a non-Gaußian UV stable fixed point, lending further support to asymptotically safe quantum gravity. One of the stationary points facilitates an analytical determination of the quantum gravity phase diagram and features ultraviolet and infrared complete RG trajectories with a classical regime. [ABSTRACT FROM AUTHOR]

The global structure of the family of Kerr-de Sitter spacetimes is reexamined. Taking advantage of the natural length scale set by the cosmological constant Λ > 0, conditions on the parameters (Λ, M, a) have been found, so that a Kerr-de Sitter spacetime either describes a black hole with well-separated horizons, or describes degenerate configurations where two or more horizons coincide. As long as the rotation parameter a² is subject to the constraint a²Λ ≪ 1, and the mass parameter M is subject to a² [1 + O(a²Λ)²)] < M² < 1/9Λ [1 + 2a²Λ + O(a²Λ)²)], then a Kerr-de Sitter spacetime with parameters in these ranges describes a black hole possessing an inner horizon separated from an outer horizon and the hole is embedded within a pair of cosmological horizons. Still for a²Λ ≪ 1, but assuming that either M² > 1/9Λ[1 + 2a²Λ + O(a²Λ)²)] or M² < a² [1 + O(a²Λ)²)], the Kerr-de Sitter spacetime describes a ringlike singularity enclosed by two cosmological horizons. A Kerr-de Sitter spacetime may also describe configurations where the inner, the outer and one of the cosmological horizons coincide. However, we found that this coalescence occurs provided M²Λ ~ 1 and due to the observed smallness of Λ, these configurations are probably irrelevant in astrophysical settings. Extreme black holes, i.e. black holes where the inner horizon coincides with the outer black hole horizon, are also admitted. We have found that in the limit M²Λ ≪ 1 and a²Λ ≪ 1, extreme black holes occur, provided a² = Ma² (1 + O(ΛM²)). Finally a coalescence between the outer and the cosmological horizon, although in principle possible, is likely to be unimportant at the astrophysical level, since this requires M²Λ ~ 1. Our analysis shows that as far as the structure of the horizons is concerned, the family of Kerr-de Sitter spacetimes exhibits similar structure to the Reissner-Nordstrom-de Sitter family of spacetimes. [ABSTRACT FROM AUTHOR]

We investigate the influence of a cosmological constant A on gravitational lensing effects. By the method of an elliptic integral, we give the solution to the null geodesic equation in Schwarzschild-de Sitter spacetime. The deflection angle of light is obtained by studying the intrinsic geometry of the spatial equatorial plane in Schwarzschild-de Sitter spacetime. By applying the expansion of elliptic integrals, we find the deflection angle in the weak field limit and in the strong field limit, respectively. We verify that the deflection angle, angular position, and magnification of images are all monotonically decreasing functions of A. [ABSTRACT FROM AUTHOR]

The time evolution of cosmological parameters in the early Universe at the deconfinement transition is studied by an equation of state (EoS) which takes into account the finite baryon density and the background magnetic field. The nonperturbative dynamics is described by the field correlator method which gives, with a small number of free parameters, a good fit of lattice data. The entire system has two components, i.e., the quark-gluon plasma and the electroweak sector, and the solutions of the Friedmann equation show that the scale factors a(t) and H(t) = (1/a)da/dt are weakly dependent on the EoS, but the deceleration parameter q(t) and the jerk j(t) are strongly modified above the critical temperature Tc, corresponding to a critical time tc ≃ 20-25 μs. The time evolution of the cosmological parameters suggests that above and around Tc, there is a transient state of acceleration typical of a matter-dominated universe; this is entailed by the QCD strong interaction. The effect of the hadronic matter below Tc does not qualitatively change the previous behavior and one can consistently follow the cosmological evolution up to 100 μs. [ABSTRACT FROM AUTHOR]

Ekpyrotic bouncing cosmologies have been proposed as alternatives to inflation. In these scenarios, the Universe is smoothed and flattened during a period of slow contraction preceding the bounce while quantum fluctuations generate nearly scale-invariant superhorizon perturbations that seed structure in the post-bounce Universe. An analysis by Tolley and Wesley (2007) showed that, for a wide range of ekpyrotic models, generating a scale-invariant spectrum of adiabatic or entropic fluctuations is only possible if the cosmological background is unstable, in which case the scenario is highly sensitive to initial conditions. In this paper, we analyze an important counterexample: a simple action that generates a Gaussian, scaleinvariant spectrum of entropic perturbations during ekpyrotic contraction without requiring fine-tuned initial conditions. Based on this example, we discuss some generalizations. [ABSTRACT FROM AUTHOR]

It has been argued that the small perturbations to the homogeneous and isotropic configurations of a canonical scalar field in an expanding universe do not grow. We show that this is not true in general, and clarify the root of the misunderstanding. We revisit a simple model in which the zero mode of a free scalar field oscillates with high frequency around the minimum of the potential. Under this assumption the linear perturbations grow like those in the standard cold dark matter scenario, but with a Jeans length at the scale of the Compton wavelength of the scalar particle. Contrary to previous analyses in the literature our results do not rely on time averages and/or fluid identifications, and instead we solve both analytically (in terms of a well-defined series expansion) and numerically the linearized Einstein-Klein-Gordon system. Also, we use gauge-invariant fields, which makes the physical analysis more transparent and simplifies the comparison with previous works carried out in different gauges. As a byproduct of this study we identify a time-dependent modulation of the different physical quantities associated to the background as well as the perturbations with potential observational consequences in dark matter models. [ABSTRACT FROM AUTHOR]

In the standard cosmological framework of the Oth-order Friedmann-Lemaitre-Robertson-Walker (FLRW) metric and the use of perfect fluids in the stress-energy tensor, dark energy with an equationof- state parameter w < - 1 (known as phantom dark energy) implies negative kinetic energy and vacuum instability when modeled as a scalar field. However, the accepted values for present-day w from Planck and WMAP9 include a significant range of values less than -1 . We find that it is not as obvious as one might think that phantom dark energy has negative kinetic energy categorically. Analogously, we find that field models of quintessence dark energy (wϕ, > -1 ) do not necessarily have positive kinetic energy categorically. Staying within the confines of observational constraints and general relativity, for which there is good experimental validation, we consider a few reasonable departures from the standard Oth-order framework in an attempt to see if negative kinetic energy can be avoided in these settings despite an apparent w < - 1. We consider a more accurate description of the universe through the perturbing of the isotropic and homogeneous FLRW metric and the components of the stress-energy tensor, and we consider dynamic w and primordial isocurvature and adiabatic perturbations. We find that phantom dark energy does not necessarily have negative kinetic energy for all relevant length scales at all times, and we also find that, by the same token, quintessence dark energy does not necessarily have positive kinetic energy for all relevant length scales at all times. [ABSTRACT FROM AUTHOR]

It is well known that the problem of the cosmological constant appears in a new light in unimodular gravity. In particular, the zero-momentum piece of the potential does not automatically produce a corresponding cosmological constant. Here we show that quantum corrections do not renonnalize the classical value of this observable. [ABSTRACT FROM AUTHOR]

We investigate the Higgs potential beyond the Planck scale in the superstring theory, under the assumption that the supersymmetry is broken at the string scale. We identify the Higgs field as a massless state of the string, which is indicated by the fact that the bare Higgs mass can be zero around the string scale. We find that, in the large field region, the Higgs potential is connected to a runaway vacuum with vanishing energy, which corresponds to opening up an extra dimension. We verify that such universal behavior indeed follows from the toroidal compactification of the nonsupersymmetric 50(16) x 50(16) heterotic string theory. We show that this behavior fits in the picture that the Higgs field is the source of the eternal inflation. The observed small value of the cosmological constant of our universe may be understood as the degeneracy with this runaway vacuum, which has vanishing energy, as is suggested by the multiple point criticality principle. [ABSTRACT FROM AUTHOR]

The general stationary cylindrically symmetric solution of Einstein-massless scalar field system with a nonpositive cosmological constant is presented. It is shown that the general solution is characterized by four integration constants. Two of these essential parameters have a local meaning and characterize the gravitational field strength. The other two have a topological origin, as they define an improper coordinate transformation that provides the stationary solution from the static one. The Petrov scheme is considered to explore the effects of the scalar field on the algebraic classification of the solutions. In general, these spacetimes are of type I. However, the presence of the scalar field allows us to find a nonvacuum type O solution and a wider family of type D spacetimes, in comparison with the vacuum case. The mass and angular momentum of the solution are computed using the Regge-Teitelboim method in the case of a negative cosmological constant. In absence of a cosmological constant, the curvature singularities in the vacuum solutions can be removed by including a phantom scalar field, yielding nontrivial locally homogeneous spacetimes. These spacetimes are of particular interest, as they have all their curvature invariants constant. [ABSTRACT FROM AUTHOR]

We present a space-time model of the collision of two homogeneous, plane impulsive gravitational waves (each having a delta function profile) propagating in a vacuum before collision and for which the postcollision space-time has constant curvature. The profiles of the incoming waves are kδ{u) and lδ(v) where k, l are real constants and u = 0. v = 0 are intersecting null hypersurfaces. The cosmological constant A in the postcollision region of the space-time is given by Λ = - 6 kl. [ABSTRACT FROM AUTHOR]

We consider metric-affine scenarios where a modified gravitational action is sourced by electrovacuum fields in a three dimensional space-time. We first study the case of f(R) theories, finding deviations near the center as compared to the solutions of general relativity. We then consider Born-Infeld gravity, which has raised a lot of interest in the last few years regarding its applications in astrophysics and cosmology, and show that new features always arise at a finite distance from the center. Several properties of the resulting space-times, in particular in presence of a cosmological constant term, are discussed. [ABSTRACT FROM AUTHOR]

We examine the concept of black hole thermodynamic volume and its consistency with thermodynamic mass in spacetimes that are not asymptotically flat but instead have anisotropic Lifshitz scaling symmetry. We find that the generalized Smarr relation in anti-de Sitter space-extended to include a pressure-volume term-holds here as well, and that there exists a definition of thermodynamic mass and thermodynamic volume that satisfy both this relation and the first law of thermodynamics. We compare the thermodynamic mass with other known quantities such as Amowitt-Deser-Misner, Brown-York, and Hollands-Ishibashi- Marolf masses. We also conjecture methods for obtaining a thermodynamic mass where there is ambiguity due to the cosmological constant length scale depending on the horizon radius length scale. [ABSTRACT FROM AUTHOR]

Linearized gravitational waves in de Sitter spacetime are analyzed in detail to obtain guidance for constructing the theory of gravitational radiation in presence of a positive cosmological constant in full, nonlinear general relativity. Specifically, (i) In the exact theory, the intrinsic geometry of I is often assumed to be conformally flat in order to reduce the asymptotic symmetry group from Diff(X) to the de Sitter group. Our results show explicitly that this condition is physically unreasonable, (ii) We obtain expressions of energy-momentum and angular momentum fluxes carried by gravitational waves in terms of fields defined at I+. (iii) We argue that, although energy of linearized gravitational waves can be arbitrarily negative in general, gravitational waves emitted by physically reasonable sources carry positive energy. Finally, (iv) we demonstrate that the flux formulas reduce to the familiar ones in Minkowski spacetime in spite of the fact that the limit Λ ≤ 0 is discontinuous (since, in particular, I changes its spacelike character to null in the limit). [ABSTRACT FROM AUTHOR]

We consider inflation in a universe with a positive cosmological constant and a nonminimally coupled scalar field, in which the field couples both quadratically and quartically to the Ricci scalar. When considered in the Einstein frame and when the nonminimal couplings are negative, the field starts in slow roll and inflation ends with an asymptotic value of the principal slow-roll parameter, ϵE = 4/ 3. Graceful exit can be achieved by suitably (tightly) coupling the scalar field to matter, such that at late time the total energy density reaches the scaling of matter, ϵE = ϵm. Quite generically the model produces a red spectrum of scalar cosmological perturbations and a small amount of gravitational radiation. With a suitable choice of the nonminimal couplings, the spectral slope can be as large as ns ≃ 0.955, which is about one standard deviation away from the central value measured by the Planck satellite. The model can be ruled out by future measurements if any of the following is observed: (a) the spectral index of scalar perturbations is ns > 0.960; (b) the amplitude of tensor perturbations is above about r ~ 10-2; (c) the running of the spectral index of scalar perturbations is positive. [ABSTRACT FROM AUTHOR]

Breather-type (time-periodic and spatially localized) solutions with spherical symmetry are investigated in a massless scalar field theory coupled to Einstein's gravity with cosmological constant in d spatial dimensions imposing anti-de Sitter (AdS) asymptotics on space-time. Using a code constructed with the Kadath library that enables the use of spectral methods, the phase space of breather solutions is explored in detail for d = 3 and d = 4. It is found that there are discrete families of solutions indexed by an integer and by their frequency. Using a time evolution code these AdS breathers are found to be stable for up to a critical central density, in analogy to boson stars. Using an analytical perturbative expansion small amplitude breathers are worked out for arbitrary dimensions d. [ABSTRACT FROM AUTHOR]

Black holes supported by self-interacting conformal scalar fields can be considered as renormalizably dressed since the conformal potential is nothing but the top power-counting renormalizable self-interaction in the relevant dimension. On the other hand, potentials defined by powers which are lower than the conformal one are also phenomenologically relevant since they are in fact super-renormalizable. In this work we provide a new map that allows one to build black holes dressed with all the (super-)renormalizable contributions starting from known conformal seeds. We explicitly construct several new examples of these solutions in dimensions D=3 and D=4, including not only stationary configurations but also time-dependent ones. [ABSTRACT FROM AUTHOR]

A class of Siklos waves, representing exact vacuum solutions of general relativity with a cosmological constant, is extended to a new class of Siklos waves with torsion, defined in the framework of the Poincaré gauge theory. Three particular exact vacuum solutions of this type, the generalized Kaigorodov, the homogeneous solution and the exponential solution, are explicitly constructed. [ABSTRACT FROM AUTHOR]

It has been established in Schwarzschild spacetime (and more generally in Kerr spacetime) that pairs of geometrically different timelike geodesies with the same radial and azimuthal frequencies exist in the strong-field regime. The occurrence of this so-called isofrequency pairing is of relevance in view of gravitational-wave observations. In this paper we generalize the results on isofrequency pairing in two directions. Firstly, we allow for a (positive) cosmological constant, i.e., we replace the Schwarzschild spacetime with the Schwarzschild-de Sitter spacetime. Secondly, we consider not only spinless test particles (i.e., timelike geodesies) but also test particles with spin. In the latter case we restrict to the case that the motion is in the equatorial plane with the spin perpendicular to this plane. We find that the cosmological constant as well as the spin have distinct impacts on the description of bound motion in the frequency domain. [ABSTRACT FROM AUTHOR]

In this work we study different classes of effective composite metrics proposed in the context of one-loop quantum corrections in bimetric gravity. For this purpose we consider contributions of the matter loops in the form of cosmological constants and potential terms yielding two types of effective composite metrics. This guarantees a nice behavior at the quantum level. However, the theoretical consistency at the classical level needs to be ensured additionally. It turns out that among all these possible couplings, only one unique effective metric survives these criteria at the classical level. [ABSTRACT FROM AUTHOR]

We present a nonlinear post-Friedmann framework for structure formation, generalizing to cosmology the weak-field (post-Minkowskian) approximation, unifying the treatment of small and large scales. We consider a universe filled with a pressureless fluid and a cosmological constant A, the theory of gravity is Einstein's general relativity and the background is the standard flat ACDM cosmological model. We expand the metric and the energy-momentum tensor in powers of 1/c, keeping the matter density and peculiar velocity as exact fundamental variables. We assume the Poisson gauge, including scalar and tensor modes up to 1/c4 order and vector modes up to 1/c5 terms. Through a redefinition of the scalar potentials as a resummation of the metric contributions at different orders, we obtain a complete set of nonlinear equations, providing a unified framework to study structure formation from small to superhorizon scales, from the nonlinear Newtonian to the linear relativistic regime. We explicitly show the validity of our scheme in the two limits: at leading order we recover the fully nonlinear equations of Newtonian cosmology; when linearized, our equations become those for scalar and vector modes of first-order relativistic perturbation theory in the Poisson gauge. Tensor modes are nondynamical at the 1/c4 order we consider (gravitational waves only appear at higher order): they are purely nonlinear and describe a distortion of the spatial slices determined at this order by a constraint, quadratic in the scalar and vector variables. The main results of our analysis are as follows: (a) at leading order a purely Newtonian nonlinear energy current sources a framedragging gravitomagnetic vector potential, and (b) in the leading-order Newtonian regime and in the linear relativistic regime, the two scalar metric potentials are the same, while the nonlinearity of general relativity makes them different. Possible applications of our formalism include the calculations of the vector potential [1,2] and the difference between the two scalar potentials from Newtonian N-body simulations, and the extension of Newtonian approximations used in structure formation studies, to include relativistic effects. [ABSTRACT FROM AUTHOR]

We study the P-V criticality and phase transition in the extended phase space of charged anti-de Sitter black holes in canonical ensemble of ghost-free massive gravity, where the cosmological constant is viewed as a dynamical pressure of the black hole system. We give the generalized thermodynamic first law and the Smarr relation with massive gravity correction. We find that not only when the horizon topology is spherical but also in the Ricci flat or hyperbolic case, there appear the P-V criticality and phase transition up to the combination k + C0²c2m² in the four-dimensional case, where k characterizes the horizon curvature and c2m² is the coefficient of the second term of massive potential associated with the graviton mass. The positivity of such combination indicate the van der Waals-like phase transition. When the spacetime dimension is larger then four, the Maxwell charge there seems unnecessary for the appearance of critical behavior, but a infinite repulsion effect needed, which can also be realized through negative valued C3m² or c4m², which is third or fourth term of massive potential. When c3m² is positive, a Hawking-Pagelike black hole to vacuum phase transition is shown in the five-dimensional chargeless case. For the van der Waals-like phase transition in four and five spacetime dimensions, we calculate the critical exponents near the critical point and find they are the same as those in the van der Waals liquid-gas system. [ABSTRACT FROM AUTHOR]